Rate of reaction.
“The rate (speed or velocity) of reaction is the rate of change in concentration of reactants or products in unit
time.”
A → Product Conc. of product
a0
When, t = 0 (a–x) x Where a is the initial concentration and (a-x) is Conc. (mole/lit.)
After, t = t concentration of reactant after time t and x will
be the concentration of product after time t.
Rate of reaction = Total change in concentration of reactants or products Conc. of reactant
Change in time (in sec.)
Time (Sec)
If dx is the change in concentration in time interval dt then,
Change of concentration
dx dx with increase in time
dt dt
The reaction rate for reactants = − ; The reaction rate for products = +
• The negative sign indicates that the concentration of reactant decreases with time.
• The positive sign indicates that the concentration of products increases with time.
• The concentration change may be positive or negative but the rate of reaction is always positive.
• The rate of chemical reaction decreases as the reaction proceeds.
• The concept of mechanical speed or velocity can not be used in measuring rate of reaction. Rate of reaction
depends on molar concentration.
(1) Types of rate of reactions : There are two types of rate of reactions.
(i) Average rate of reaction : The average rate is defined as the change in the concentration (active mass)
of reactants or products over a long time interval.
Consider the general chemical reaction, aA + bB + ........ → c C + dD + ……….
Average rate = Amount of reactant consumed (or product formed)/time interval.
Average rate = − ∆[ A] = − ∆[B] .......... . = + ∆[C] = + ∆[D] = + ........
a∆t b∆t c∆t d∆t
The average rate over the time interval ∆t approaches the instantaneous rate
as ∆t approaches zero.
(ii) Instantaneous rate of reaction : The instantaneous rate of reaction Conc. (x)
gives the tendency of the reaction at a particular instant. The term ∆t becomes dx
smaller and eventually approaches zero, then the rate of reaction at a particular
dt
moment called the instantaneous rate (Rt ) is given by, Time θ
Instantaneous rate = (Average rate) ∆t→0
Rt = − ∆[ A] = ∆[B] or Rt d[ A] = d[B]
∆t ∆t→0 ∆t = − dt dt
∆t →0
Where, d[A], d[B] and dt being infinitesimally small changes in the concentration of A and B , that of time
respectively. Instantaneous rate of reaction at any instant of time is obtained by finding the slope of the tangent to
the curve (which is obtained by plotting concentration of any suitable reactant or product versus time) at the point
corresponding to that instant of time. Rate of reaction = tanθ = dx
dt
(2) Unit of rate of reaction : Unit of rate of reaction = Unit of concentration = mole litre –1 time –1
Unit of time
(i) If reactants and products are in gaseous state then the pressure may be taken in place of concentration
thus rate will have unit of atm sec–1 or atm min–1
(ii) The unit of time can be second, minute, hours, days and years so the unit of rate of reaction may be expressed as
follows: mol/litre sec ( mol l −1s −1 ) or mol/litre min ( mol l −1 min −1 ) or mol/litre hour (mol l −1h−1 ) or mol/litre day
(mol l −1d −1 ) or mol/litre year (mol l −1 y −1 )
Example : 1 For the reaction N2 + 3H2 ⇌ 2NH 3 , if ∆[NH 3 ] = 2 × 10 −4 mol l −1 s −1 , the value of −∆[H 2 ] would be
∆t ∆t
[MP PMT 2000]
(a) 1 × 10 −4 mol l −1s −1 (b) 3 × 10 −4 mol l −1s −1 (c) 4 × 10 −4 mol l −1s −1 (d) 6 × 10 −4 mol l −1s −1
Solution: (b) N 2 + 3H 2 ⇌ 2NH 3
−∆[N 2 ] = − 1 ∆[H 2 ] = 1 ∆[NH 3 ] ; ∴ ∆[H 2 ] = 3 × ∆[NH 3 ] = 3 × 2 × 10 −4 = 3 × 10 −4 mol l −1s −1 .
∆t 3 ∆t 2 ∆t ∆t 2 ∆t 2
Example : 2 A gaseous hypothetical chemical equation 2A ⇌ 4B + C is carried out in a closed vessel. The concentration of
B is found to increase by 5 × 10 −3 mol l −1 in 10 second. The rate of appearance of B is [AFMC 2001]
(a) 5 × 10 −4 mol l −1 sec −1 (b) 5 × 10 −5 mol l −1 sec −1
(c) 6 × 10 −5 mol l −1 sec −1 (d) 4 × 10 −4 mol l −1 sec −1
Solution: (a) Increase in concentration of B = 5 × 10−3 mol l −1 , Time = 10 sec.
Rate of appearance of B = Increase of concentration of B = 5 × 10−3 mol l −1 = 5 × 10−4 mol l −1 sec −1 .
Time taken 10 sec
Example : 3 If 3A → 2B then the rate of reaction of + d(B) is equal to [CBSE 2002]
dt
(a) + 2 d(A) (b) − 1 d(A) (c) − 2 d(A) (d) − 3 d(A)
dt 3 dt 3 dt 2 dt
Solution: (c) 3A → 2B ; Rate = − 1 d [A] = 1 d [B] ; ∴ + d [B] = − 2 d [ A]
3 dt 2 dt dt 3 dt
Example: 4 A gaseous reaction, A2 (g) → B(g) + 1 C(g) ; Shows increase in pressure from 100 mm to 120 mm in 5
2
minutes. The rate of disappearance of A2 is
(a) 4 mm min −1 (b) 8 mm min −1 (c) 16 mm min −1 (d) 2 mm min −1
Solution: (b) A2 (g) → B(g) + 1 C(g)
2
100 0 0
100 − p p 1 p
2
100 − p + p+ 1 p = 120 or p = 40mm
2
∴ − dp A2 = 40 = 8 mm min −1
dt 5
Experimental methods of Rate studies.
Many physical and chemical methods are available for studying the reaction rate :
(1) Volume or Pressure measurement : The reaction rate can be followed by measuring the volume or
pressure change provided one or more of the components are gases.
(2) Titrimetry : The reaction course can be followed using acid-base or oxidation-reduction titration if at least
one of the components in the reaction is an acid or a base or an oxidising agent or a reducing agent.
(3) Conductometry or Potentiometry : It is a suitable method based on conductivity or potentiometric
measurements if one or more of the ions are present or produced in the reaction.
(4) Spectrophotometry : When a component of the reaction has a strong absorption band at a particular
wavelength region, spectrophotometers could be used for measuring the reaction rate.
(5) Polarimetry : The reaction rate can be studied from the measurements of optical rotation when at least
one of the component of a reaction is optically active.
Factors affecting Reaction rate.
The rate of a chemical reaction depends on the rate of encounter between the molecules of the reactants
which in turn depends on the following things.
(1) Effect of temperature on reaction rate : The rate of chemical reaction generally increases on
increasing the temperature.
(2) Nature of reactants : (i) Reactions involving polar and ionic substances including the proton transfer
reactions are usually very fast. On the other hand, the reaction in which bonds is rearranged, or electrons
transferred are slow.
(ii) Oxidation-reduction reactions, which involve transfer of electrons, are also slow as compared to the ionic
substance.
(iii) Substitution reactions are relatively much slower.
(3) pH of the medium : The rate of a reaction taking place in aqueous solution often depends upon the
H + ion concentration. Some reactions become fast on increasing the H+ ion concentration while some become
slow. Potential Energy Reaction path
Without catalyst
(4) Concentration of reactants : The rate of a chemical reaction is Ea
directly proportional to the concentration of the reactants means rate of Ea Reaction
reaction decreases with decrease in concentration. path with
catalyst
(5) Surface area of reactant : Larger the surface area of reactant, Reactants
the probability of collisions on the surface of the reactant particles by the Energy of Reaction
surrounding molecules increases and thus rate of reaction increases.
Products
(6) Presence of catalyst : The function of a catalyst is to lower
A catalyst changes the reaction path
down the activation energy. The greater the decrease in the activation energy caused by the catalyst, higher will be
the reaction rate. In the presence of a catalyst, the reaction follows a path of lower activation energy. Under this
condition, a large number of reacting molecules are able to cross over the energy barrier and thus the rate of
reaction increases. Fig. shows how the activation energy is lowered in presence of a catalyst.
(7) Effect of sunlight : There are many chemical reactions whose rate are influenced by radiations
particularly by ultraviolet and visible light. Such reactions are called photochemical reactions. For example,
Photosynthesis, Photography, Blue printing, Photochemical synthesis of compounds etc.
H2 + Cl2 sunlight (hν ) → 2HCl : The radiant energy initiates the chemical reaction by supplying the necessary
activation energy required for the reaction.
Rate law, Law of mass action and Rate constant.
(1) Rate law : The actual relationship between the concentration of reacting species and the reaction rate is
determined experimentally and is given by the expression called rate law.
For any hypothetical reaction, aA + bB → cC + dD
Rate law expression may be, rate = k[A]a[B]b
Where a and b are constant numbers or the powers of the concentrations of the reactants A and B
respectively on which the rate of reaction depends.
(i) Rate of chemical reaction is directly proportional to the concentration of the reactants.
(ii) The rate law represents the experimentally observed rate of reaction, which depends upon the slowest step
of the reaction.
(iii) Rate law cannot be deduced from the relationship for a given equation. It can be found by experiment only.
(iv) It may not depend upon the concentration of species which do not appear in the equation for the over all
reaction.
(2) Law of mass action : (Guldberg and Wage 1864) This law relates rate of reaction with active mass or
molar concentration of reactants. According to this law, “At a given temperature, the rate of a reaction at a particular
instant is proportional to the product of the reactants at that instant raised to powers which are numerically equal to
the numbers of their respective molecules in the stoichiometric equation describing the reactions.”
Active mass = Molar concentration of the substance = Number of gram moles of the substance = W /m = n
Volume in litres V V
Where W = mass of the substance, m is the molecular mass in grams, ‘n’ is the number of g moles and V is
volume in litre.
Consider the following general reaction, m1 A1 + m2 A2 + m3 A3 → Products
Rate of reaction ∝ [A1 ]m1 [A2 ]m2 [A3 ]m3
(3) Rate constant : Consider a simple reaction, A → B . If CA is the molar concentration of active mass of A
at a particular instant, then, dx ∝ CA or dx = kCA ; Where k is a proportionality constant, called velocity
dt dt
constant or rate constant or specific reaction rate constant.
At a fixed temperature, if CA = 1 , then Rate = dx =k
dt
“Rate of a reaction at unit concentration of reactants is called rate constant.”
(i) The value of rate constant depends on, Nature of reactant, Temperature and Catalyst
(It is independent of concentration of the reactants)
(ii) Unit of rate constant : Unit of rate constant = litre n−1 × sec −1 or = mol 1−n × sec −1
mol litre
Where n = order of reaction
Difference between Rate law and Law of mass action
Rate law Law of mass action
It is an experimentally observed law. It is a theoretical law.
It depends on the concentration terms on which the It is based upon the stoichiometry of the equation
rate of reaction actually depends
Example for the reaction, aA + bB → Products Example for the reaction, aA + bB → Products
Rate = k[A]a [B]b
Rate = k [A]m[B]n
Difference between Rate of reaction and Rate constant
Rate of reaction Rate constant
It is the speed with which reactants are converted into It is proportionality constant.
products.
It is measured as the rate of decrease of the It is equal to rate of reaction when the
concentration of reactants or the rate of increase of concentration of each of the reactants is unity.
concentration of products with time.
It depends upon the initial concentration of the It is independent of the initial concentration of
reactants. the reactants. It has a constant value at fixed
temperature.
Order of Reaction.
“The order of reaction is defined as the number of atoms or molecules whose concentration change during the
chemical reaction.”
Or
“The total number of molecules or atoms whose concentration determine the rate of reaction is known as
order of reaction.”
Order of reaction = Sum of exponents of the concentration terms in rate law
xA + yB → Products
By the rate law, Rate = [A]x [B[y , then the overall order of reaction. n = x + y , where x and y are the orders
with respect to individual reactants.
If reaction is in the form of reaction mechanism then the order is determined by the slowest step of mechanism.
2A + 3B → A2B3
A + B → AB(fast)
AB + B2 → AB3 (slow) (Rate determining step)
AB3 + A → A2 B3 (fast)
(Here, the overall order of reaction is equal to two.)
An order of a reaction may be zero, negative, positive or in fraction and greater than three. Infinite and
imaginary values are not possible.
(1) First order reaction : When the rate of reaction depends only on the one concentration term of reactant.
Examples : • A → product
• H 2O2 → H2O + 1 O2
2
• All radioactive reactions are first order reaction.
• Rate of growth of population if there is no change in the birth rate or death rate.
• Rate of growth of bacterial culture until the nutrients are exhausted.
Exception : H 2O, H + , OH − and excess quantities are not considered in the determining process of order.
Examples : • CH 3 COOC2 H 5 + H 2O → CH 3 COOH + C2 H 5 OH ; Order = 1; R = k [CH 3COOC2 H5 ]
• 2A(excess) + B → product ; Order = 1; R = k [B]
• 2N 2O5 → 4 NO2 + O2 ; Order = 1; R = k [N 2O5 ]
• 2Cl2O7 → 2Cl2 + 7O2 ; Order = 1; R = k [Cl2O7 ]
• (CH 3 )3 − C − Cl + OH − → (CH 3 )3 C − OH + Cl − ; Order = 1; R = k [(CH 3 )3 C − Cl]
(i) Velocity constant for first order reaction : Let us take the reaction
Initially t = 0 A → Product
a0
After time t = t (a − x) x
Here, ' a' be the concentration of A at the starting and (a − x) is the concentration of A after time t i.e., x
part has been changed in to products. So, the rate of reaction after time t is equal to
dx ∝ (a − x) or dx = k(a − x) or dx = k.dt …..(i)
dt dt (a − x)
integrated rate constant is,
k = 2.303 log 10 a x) …..(ii)
t (a −
t = 2.303 log 10 (a a x) …..(iii)
k −
(ii) Half life period of the first order reaction : when t = t1 / 2; x = a , then eq. (ii) becomes
2
t1/ 2 = 2.303 log 10 a a a ; t1/ 2 = 2.303 log 10 a
k − 2 k a/2
t1/ 2 = 2.303 log 10 2 ( log 2 = 0.3010 ); ∴ t1/ 2 = 2.303 × 0.3010
k k
t1/ 2 = 0.693
k
Half life period for first order reaction is independent from the concentration of reactant.
Time for completion of nth fraction, t1/ n = 2.303 log 1 1 1
K − n
(iii) Unit of rate constant of first order reaction : k = (sec)−1
(2) Second order reaction : Reaction whose rate is determined by change of two concentration terms is said
to be a second order reaction. For example,
• CH 3 COOH + C2 H 5 OH → CH 3 COOC2 H 5 + H 2O A + B → product
• S2O82− + 2I − → 2SO42− + I 2
(i) Calculation of rate constant : 2A → product or
When concentration of A and B are same.
A + B → Product
aa 0
Initially t = 0
After time t = t (a − x) (a − x) x
dx = k[A] [B] = k [a − x] [a − x]
dt
dx = k [a − x]2 ; Integrated equation is k = 1 . x x) ; t = 1 . x x)
dt t a(a − k a(a −
When concentration of A and B are taken different
A + B → Product
a b0
Initially t = 0 (a – x) (b – x) x
After time t = t
dx = k [a − x].[b − x] , Integrated equation is,
dt
k = 2.303 log b(a − x) ; t = 2.303 log b(a − x)
t(a − b) a(b − x) k(a − b) a(b − x)
(ii) Half life period of the second order reaction : When t = t1/ 2 ; x= a ; t1/ 2 1 a 1
2 2 ka
= a2) =
k
a × (a −
Half life of second order reaction depends upon the concentration of the reactants. t1/ 2 ∝ 1
a
(iii) Unit of rate constant : k = mol1−∆n litΔ n−1 sec −1 ; ∆n = 2 , k = mol −1 lit.sec −1 (Where ∆n = order of
reaction)
(3) Third order reaction : A reaction is said to be of third order if its rate is determined by the variation of
three concentration terms. When the concentration of all the three reactants is same or three molecules of the same
reactant are involved, the rate expression is given as
3A → products or A + B + C → products
(i) Calculation of rate constant : dx = k(a − x)3 , Integrated equation is k = 1 . x(2a − x)
dt t 2a 2 (a − x)2
(ii) Half life period of the third order reaction : Half life period = 3 ; t1/ 2 ∝ 1 ; Thus, half life is
2a 2k a2
inversely proportional to the square of initial concentration.
mol −2
litre
(iii) Unit of rate constant : k = time −1 or k = litre 2mol −2time −1
(4) Zero order reaction : Reaction whose rate is not affected by concentration or in which the concentration
of reactant do not change with time are said to be of zero order reaction. For example,
• H2 + Cl2 Sunlight → 2HCl
• Dissociation of HI on gold surface.
• Reaction between acetone and bromine.
• The formation of gas at the surface of tungsten due to adsorption.
(i) Calculation of Rate Constant : Let us take the reaction
A → Product
Initially t = 0 a 0
dx = k[A]0 , dx = k ; dx = k. dt
dt dt
Integrated rate equation, k= x ; The rate of reaction is independent of the concentration of the reacting
t
substance.
(ii) Half life period of zero order reaction : When t = t1 / 2 ; x= a ; t1/ 2 = a or t1/ 2 ∝ a ; The half life
2 2k
period is directly proportional to the initial concentration of the reactants.
(iii) Unit of Rate constant : k = mole ; Unit of rate of reaction = Unit of rate constant.
lit.sec .
Note : In general, the units of rate constant for the reaction of nth order are:
Rate = k[A]n
mol L−1 = k(mol L−1 )n or k = (mol L−1 )1−n s −1
s
Units of rate constants for gaseous reactions: In case of gaseous reactions, the concentrations are
expressed in terms of pressure in the units of atmosphere. Therefore, the rate has the units of atm per second. Thus,
the unit of different rate constants would be:
(i) Zero order reaction : atm s −1 (ii) First order reaction : s −1
(iii) Second order reaction: atm−1s −1 (iv) Third order reaction: atm−2s −1
In general, for the gaseous reaction of nth order, the units of rate constant are (atm)1–ns–1
Modified expressions for rate constants of some common reactions of first order
Reaction Expression for rate constant
N 2O5 → 2NO2 + 1 O2 k = 2.303 log V∞
2 t V∞ − Vt
Here Vt = volume of O2 after time t and V∞ = volume of O2
after infinite time.
NH 4 NO2 (aq) → 2H 2O + N 2 Same as above, here Vt and V∞ are volumes of N2 at time t
and at infinite time respectively.
H 2O2 → H 2O + 1 O2 k = 2.303 log V0
2 t Vt
Here V0 and Vt are the volumes of KMnO4 solution used for
titration of same volume of reaction mixture at zero time
(initially) and after time t .
CH3COOC2H5 + H2O H+ → CH3COOH + C2H5OH k = 2.303 log V∞ − V0
t V∞ − Vt
Here V0 , Vt and V∞ are the volumes of NaOH solution used for
titration of same volume of reaction mixture after time, 0 , t
and infinite time respectively.
C12H22O11 + H2O H+ → C6H12O6 + C6H12O6 k = 2.303 log r0 − r∞
d −Sucrose d −Glucose l −Fructose t rt − r∞
(After the reaction is complete the equimolar Here, r0 , rt and r∞ are the polarimetric readings after time 0, t
mixture of glucose and fructose obtained is and infinity respectively.
laevorotatory)
Examples of reactions having different orders
Examples Rate Law Order
First order reaction r = k [H2O2] 1
r = k [C2H5Cl] 1
2H2O2 → 2H2O + O2 r = k [N2O5] 1
r = k [SO2Cl2] 1
C2H5Cl → C2H4 + HCl r = k [ester][H2O]0 1
r = k [sugar][H2O]0 1
2N2O5 → 4 NO2 + O2 r = k [radioactive species] 1
SO2Cl2 → SO2 + Cl2
CH3COOC2H5 + H2O → CH3COOH + C2H5OH
C12H22O11 + H2O → C6H12O6 + C6H12O6
All radioactive decay
Second order reactions r = k [NO] [O3] 2
NO + O3 → NO2 + O2 r = k [NO2]2 2
2NO2 → 2NO + O2 r = k[H2][I2] 2
H2 + I2 → 2HI 2
CH3COOC2H5 + OH − → CH3COO− + C2H5OH r = k [CH3CO2C2H5][OH −] 2
2
C2H4 + H2 → C2H6 r = k [C2H4 ][H2] 2
2N2O → 2N2 + O2 r = k [N 2O]2
2CH3CHO → 2CH4 + 2CO 3
Third order reactions r = k [CH3CHO]2 3
2NO + O2 → 2NO2 3
2NO + Br2 → 2NOBr r = k [NO]2[O2] 3
r = k [NO]2[Br2]
2NO + Cl2 → 2NOCl r = k [NO]2[Cl2]
Fe 2+ + 2I − → FeI 2 r = k [Fe2+][I −]2
Zero order reactions
H 2 + Cl2 → 2HCl (over water) r = k [H2]0[Cl2]0 0
2NH3 Pt → N2 + 3H2 r = k [NH3]0 0
Fractional order reactions
Para H 2 → ortho H 2 r = k [para H2]1.5 1.5
CO + Cl 2 → COCl 2 r = k [CO]2[Cl2]1 / 2 2.5
COCl 2 → CO + Cl 2 r = k [COCl2 ]3 / 2 1.5
r = k [CH3CHO]3 / 2 1.5
CH 3CHO → CH 4 + CO
Negative order reaction r = k[O3]2[O2]−1 –1 with respect to O2 .
2O3 → 3O2 Overall order = 1
Methods for Determination of Order of a reaction.
(1) Substitution method in integrated rate equation (Hit and Trial method)
(i) The method can be used with various sets of a, x and t with integrated rate equations.
(ii) The value of k is determined and checked for all sets of a, x and t .
(iii) If the value of k is constant, the used equation gives the order of reaction.
(iv) If all the reactants are at the same molar concentration, the kinetic equations are :
k = 2.303 log 10 (a a x) (For first order reactions)
t −
k = 1 1 − a 1 x (For second order reactions)
t a −
k = 1 1 − 1 (For third order reactions)
2t (a − x)2 a 2
(2) Half life method : This method is employed only when the rate law involved only one concentration term.
t1 / 2 ∝ a1−n ; t1 / 2 = ka1−n ; log t1 / 2 = log k + (1 − n) log a , a plotted graph of log t1 / 2 vs log a gives a straight line
with slope (1 − n), determining the slope we can find the order n . If half life at different concentration is given then.
(t1 / 2 )1 ∝ 1 ; (t1 / 2 )2 ∝ 1 ; (t1 / 2 )1 = a2 n−1
a1n−1 a n−1 (t1 / 2 )2 a1
2
log 10 (t1 / 2 )1 − log 10 (t1 / 2 )2 = (n − 1) [log 10 a2 − log 10 a1 ]
n =1+ log 10 (t1 / 2 )1 − log10 (t1 / 2 )2 ; This relation can be used to determine order of reaction ‘n’
(log10 a2 − log10 a1 )
Plots of half-lives Vs concentrations (t1/2 ∝ a1–n)
Zero order 1st order 2nd order 3rd order
t1/2 →
t1/2 →
t1/2 →
t1/2 →
Conc. Conc. 1/a 1/a2
(3) Graphical method : A graphical method based on the respective rate laws, can also be used.
(i) If the plot of log(a − x) Vs t is a straight line, the reaction follows first order.
(ii) If the plot of 1 Vs t is a straight line, the reaction follows second order.
(a − x)
(iii) If the plot of (a 1 Vs t is a straight line, the reaction follows third order.
− x)2
(iv) In general, for a reaction of nth order, a graph of 1 Vs t must be a straight line.
(a − x)n−1
Graphical determination of order of the reaction
Order Equation Straight line plot Slope Intercept on
Y-axis
Zero x = k0t Y- axis X-axis k0
First t −k 0
x log 10 a
Second 2.303
log10(a − x) = −k1t + log10 a log10 (a − x) t k2 a −1
n th 2.303 (n − 1)kn a 1−n
(a − x)−1 = k2t + a −1 (a − x)−1 t
(a − x)1−n t
(a − x)1−n = (n − 1)knt + a1−n
Plots from integrated rate equations
Conc. [A] → Zero order log. [A] → 1st order 2nd order 3rd order
t
1 1
Zero order [ A] [ A]2
t tt
Plots of rate Vs concentrations [Rate = k(conc.)n ]
Rate → Rate → 1st order Rate → 2nd order Rate → 3rd order
Conc. Conc. (Conc.)2 (Conc.)3
(4) Van't Haff differential Method : The rate of reaction varies as the nth power of the concentration Where
' n' is the order of the reaction. Thus for two different initial concentrations C1 and C2 equation, can be written in
the form, − dC1 = kC1n and − dC2 = kC n
dt dt 2
Taking logarithms, log 10 − dC1 = log 10 k + n log 10 C1 …..(i)
dt
and log 10 − dC2 = log 10 k + n log 10 C2 …..(ii)
dt
Subtracting equation (ii) from (i),
log 10 − dC1 − log − dC2
dt dt
10
n = log 10 C1 − log 10 C2 …..(iii)
− dC1 and − dC2 are determined from concentration Vs time graphs and the value of ' n' can be
dt dt
determined.
(5) Ostwald's isolation method (Initial rate method) : This method can be used irrespective of the number
of reactants involved e.g., consider the reaction, n1 A + n2 B + n3C → Products .
This method consists in finding the initial rate of the reaction taking known concentrations of the different
reactants (A, B, C). Now the concentration of one of the reactants is changed (say that of A) taking the
concentrations of other reactants (B and C) same as before. The initial rate of the reaction is determined again. This
gives the rate expression with respect to A and hence the order with respect to A. The experiment is repeated by
changing the concentrations of B and taking the same concentrations of A and C and finally changing the
concentration of C and taking the same concentration of A and B. These will give rate expressions with respect to B
and C and hence the orders with respect to B and C respectively. Combining the different rate expressions, the
overall rate expression and hence the overall order can be obtained.
Suppose it is observed as follows:
(i) Keeping the concentrations of B and C constant, if concentration of A is doubled, the rate of reaction
becomes four times. This means that, Rate ∝ [A]2 i.e., order with respect to A is 2
(ii) Keeping the concentrations of A and C constant, if concentration of B is doubled, the rate of reaction is
also doubled. This means that, Rate ∝ [B] i.e., order with respect to B is 1
(iii) Keeping the concentrations of A and B constant, if concentration of C is doubled, the rate of reaction
remains unaffected. This means that rate is independent of the concentration of C i.e., order with respect to C is
zero. Hence the overall rate law expression will be, Rate = k[A]2 [B] [C]0
∴ Overall order of reaction = 2 + 1 + 0 = 3.
Example : 5 For a reaction, activation energy (Ea ) = 0 and rate constant (k) = 3.2 × 106 s −1 at 300K. What is the value of
Solution : (b) the rate constant at 310K. [KCET (Med.) 1999)
Example : 6
Solution : (a) (a) 3.2 × 10 −12 s −1 (b) 3.2 × 10 6 s −1 (c) 6.4 × 1012 s −1 (d) 6.4 × 10 6 s −1
Example : 7 When Ea = 0, the rate constant is independent of temperature so that rate constant (k) = 3.2 × 106 sec −1 .
87.5% of a radioactive substance disintegrates in 40 minutes. What is the half life of the substance
(a) 13.58 min (b) 135.8 min (c) 1358 min (d) None of these
Determination of k by substituting the respective values.
k = 2.303 log a x = 2.303 log a = 2.303 log a = 2.303 log 8 = 0.051 min−1
t a− 40 a − 0.875a 40 0.125a 40
∴ t1 / 2 = 0.693 = 0.693 = 13.58 min
k 0.051
The half-life period of a first order reaction is 100 sec. The rate constant of the reaction is
[MP PMT 1997; MP PET 2001]
(a) 6.93 × 10−3 sec−1 (b) 6.93 × 10−4 sec−1 (c) 0.693 sec−1 (d) 69.3 sec−1
Solution : (a) k = 0.693 = 0.693 = 6.93 × 10−3 sec−1
Example : 8 t1 / 2 100 sec
The rate constant of a first order reaction is 3 × 10−6 per second. If the initial concentration is 0.10mol, the
initial rate of reaction is [AFMC 1999; Pb. PMT 1999, 2000; BHU 1999; AIIMS 1999; Karnataka CET 2000]
(a) 3 × 10−5 mol s−1 (b) 3 × 10−6 mol s−1 (c) 3 × 10−8 mol s−1 (d) 3 × 10−7 mol s−1
Solution : (d) Given that, rate constant for first order reaction (k) = 3 × 10−6 per sec and initial concentration (a) = 0.10 mol
we know that initial rate of reaction = k(a) = 3 × 10−6 × 0.10 = 3 × 10−7mol sec−1
Example : 9 In a first order reaction the concentration of reactant decreases from 800mol / dm3 to 50mol / dm3 in
Solution : (c)
2 × 102 sec . The rate constant of reaction in sec−1 is [IIT Screening 2003]
(a) 2 ×104 (b) 3.45 × 10−5 (c) 1.386 × 10−2 (d) 2 × 10−4
k = 2.303 log10 (a a x) ; t = 2 × 102 sec , a = 800mol / dm3 , (a − x) = 50mol / dm3
t −
k = 2.303 log10 800 = 1.386 × 10−2 sec −1
2 × 102 50
Example : 10 The rate of a gaseous reaction is halved when the volume of the vessel is doubled. The order of reaction is
(a) 0 (b) 1 (c) 2 (d) 3
R k a n
2 2
Solution : (b) (i) R = k an (ii) =
Dividing (i) by (ii), 2 = 2n . Hence n = 1 .
Example : 11 The first order rate constant for the decomposition of N2O5 is 6.2 × 10−4 sec−1 . The half-life period for this
decomposition in seconds is [MNR 1991; MP PET 1997; UPSEAT 2000]
(a) 1117.7 (b) 111.7 (c) 223.4 (d) 160.9
Solution : (a) t1 / 2 = 0.693 = 0.693 = 1117.7 sec
k 6.2 × 10−4
Example : 12 A substance ' A' decomposes by a first order reaction initially with (a) = 2.00mol and after
200 min, (a − x) = 0.15mol . For this reaction what is the value of k [AIIMS 2001]
(a) 1.29 × 10−2 min−1 (b) 2.29 × 10−2 min−1 (c) 3.29 × 10−2 min−1 (d) 4.40 × 10−2 min−1
Solution : (a) Given [a] = 2.00mol, t = 200minute and (a − x) = 0.15mol
k = 2.303 log10 (a a x) = 2.303 log10 2.00 = 1.29 × 10−2 min−1
t − 200 0.15
Example : 13 The half-life for the reaction, N 2O5 ⇌ 2NO2 + 1 O2 in 24 hrs. at 30o C . Starting with 10g of N 2O5 how
2
many grams of N2O5 will remain after a period of 96 hours [KCET 1992]
(a) 1.25g (b) 0.63g (c) 1.77g (d) 0.5g
Solution : (b) k = 0.693 = 0.69 = 2.303 log 10 (a 1 Or log 10 = 1.2036 or 1 − log(a − x) = 1.2036
t1/ 2 24 96 − x) (a − x)
Or log(a − x) = −0.2036; (a − x) = 0.6258g
Example : 14 Thermal decomposition of a compound is of the first order. If 50% of a sample of the compound is
decomposed in 120 minutes, how long will it take for 90% of the compound to decompose [Roorkee 1988]
(a) 399 min (b) 2.99 min (c) 39.9 min (d) 3.99 min
Solution : (a) Half life of reaction =120 min
k = 0.693 = 0.693 = 5.77 × 10−3 min −1
t1/ 2 120
Applying first order reaction equation, t= 2.303 log10 (a a x) ; If a = 100, x = 90 or (a − x) = 10
k −
So, t = 2.303 . log 10 10 = 2.303 = 399 min
5.77 × 10−3 5.77 × 10−3
Example: 15 For a reaction A + 2B → C + D , the following data were obtained [AIIMS 1990]
Expt. Initial concentration Initial Rate of formation of D
(moles litre–1) (moles litre–1 min–1)
S. No. [A] [B]
1. 0.1 0.1 6.0 × 10 −3
2. 0.3 0.2 7.2 × 10 −2
3. 0.3 0.4 2.88 × 10 −1
4. 0.4 0.1 2.4 × 10 −2
(c) Rate = k[A]2[B]2
The correct rate law expression will be
(a) Rate = k[A][B] (b) Rate = k[A] [B]2 (d) Rate = k[A]2[B]
Solution: (b) From 1 and 4, keeping [B] constant, [A] is made 4 times, rate also becomes 4 times. Hence rate ∝ [A] . From
2 and 3 keeping [A] constant, [B] is doubled, rate becomes 4 times. Hence rate ∝ [B]2 . Overall rate law will
be : rate = k[A][B]2 .
Example: 16 The rate of elementary reaction, A → B , increases by a 100 when the concentration of A is increased ten
folds. The order of the reaction with respect to A is [CPMT 1985]
(a) 1 (b) 10 (c) 2 (d) 100
Solution: (c) R = k[A]n ; Also, 100R = k[10 A]n ; 1 = 1 n ; ∴ n = 2
100 10
Molecularity of Reaction.
“It is the sum of the number of molecules of reactants involved in the balanced chemical equation”.
Or
“It is the minimum number of reacting particles (Molecules, atoms or ions) that collide in a rate determining
step to form product or products”.
• Molecularity of a complete reaction has no significance and overall kinetics of the reaction depends upon the
rate determining step. Slowest step is the rate-determining step. This was proposed by Van't Hoff.
Example : NH 4 NO2 → N 2 + 2H 2O (Unimolecular)
NO + O3 → NO2 + O2 (Bimolecular)
2NO + O2 → 2NO2 (Trimolecular)
• Molecularity of a reaction can't be Zero, negative or fractional.
• Molecularity of a reaction is derived from the mechanism of the given reaction.
• Molecularity can not be greater than three because more than three molecules may not mutually collide with
each other.
A2 + 3 B2 → A2 B3
2
Mechanism
Step I : 2A → A2 (Bimolecular)
Step II : (Trimolecular)
A2 + 1 B2 → A2 B
2
Step III : A2 B + B2 → A2 B3 (Bimolecular)
Example : Decomposition of H 2O2
(Overall reaction Mechanism)
2H2O2 → 2H2O + O2 (Slow)
H2O2 → H2O + O (Fast)
H2O2 + O → H2O + O2
Rate = K[H 2O2 ] ; The reaction is unimolecular
(1) Pseudo Unimolecular Reaction : Reaction whose actual order is different from that expected using rate
law expression are called pseudo-order reaction. For example, RCl + H 2O → ROH + HCl
Expected rate law : Rate = k[RCl][H 2O] ; Expected order = 1 + 1 = 2
Actual rate law : Rate = k[RCl] ; Actual order =1
Because of water is taken in excess amount; therefore, its concentration may be taken constant. The reaction
is therefore, pseudo first order. Similarly the acid catalysed hydrolysis of ester, viz.,
RCOOR′ + H 2O ⇌ RCOOH + R′OH (follow first order kinetic) : Rate = k[RCOOR′]
Those reactions which may have order of reaction as one while molecularity of reaction 2 or more than two
are as follows :
Examples : (i) 2N 2O5 → 4 NO2 + O2 ; Order = 1; molecularity = 2
(ii) CH 3COOC2 H 5 + H 2O H+ → CH 3COOH + C2 H 5 OH ; r = k[CH 3COOC2 H5 ]
Order =1 , Molecularity = 2
(iii) inversion of cane sugar : C12 H 22O11 + H 2O H+ → C6 H12O6 + C6 H12O6
Sucrose glucose fructose
Order = 1, Molecularity = 2
(iv) (CH 3 )3 CCl + OH − → (CH 3 )3 COH + Cl − Order = 1, Molecularity = 2
(v) 2H 2O2 Pt, → 2H 2O + O2 Order = 1, Molecularity = 2
Difference between Molecularity and Order of reaction
Molecularity Order of Reaction
It is the number of molecules of reactants terms taking part in
elementary step of a reaction. It is sum of the power of the concentration terms
Molcularity is a theoretical value of reactants in the rate law expression.
Molecularity can neither be zero nor fractional. Order of a reaction is an experimental value
Order of a reaction can be zero, fractional for
Moleculaity has whole number values only i.e., 1, 2, 3, etc. integer.
It is assigned for each step of mechanism separately. Order of a reaction may have negative value.
It is independent of pressure and temperature. It is assigned for overall reaction.
It depends upon pressure and temperature.
Theories of Reaction rate. Fraction of molecules
capable of bringing
Some theories, which explain the reaction rate, are as follows:
effective collisions
(1) Collision theory
(i) The basic requirement for a reaction to occur is that the reacting species Fraction of
must collide with one another. This is the basis of collision theory for molecules
reactions.
Energy E
(ii) The number of collisions that takes place per second per unit volume of
the reaction mixture is known as collision frequency (Z). The value of Distribution of energies at a
definite temperature
collision frequency is very high of the order of 10 25 to 10 28 in case of binary collisions.
(iii) Every collision does not bring a chemical change. The collisions that actually produce the product are
effective collisions. The effective collisions, which bring chemical change, are few in comparison to the total
number of collisions. The collisions that do not form a product are ineffective elastic collisions, i.e., molecules
just collide and disperse in different directions with different velocities.
(iv) For a collision to be effective, the following two barriers are to be cleared.
(a) Energy barrier : “The minimum amount of energy which the colliding molecules must possess as to make
the chemical reaction to occur, is known as threshold energy”.
• In the graph 'E' corresponds to minimum or threshold energy for effective collision.
• There is an energy barrier for each reaction. The reacting species must be provided with sufficient energy to
cross the energy barrier.
(b) Orientation barrier : The colliding molecules should also have proper orientation so that the old bonds
may break and new bonds are formed. For example, NO2(g) + NO2(g) → N 2O4 (g). During this reaction, the
products are formed only when the colliding molecules have proper orientation at the time of collisions. These are
called effective collisions.
O O OO OO
NN
N N Molecules N N Bond
OO
approach Formation N2O4
O O OO
NO2 + NO2 Collision Product
(a) Properly oriented collisions form products
O O OO
N NN
ON Molecules N O N Molecules
O approach Separate
NO2
O OO OO
+ NO2 Collision NO2 produNctO2
No
(b) Collisions not properly oriented
(v) Thus, the main points of collision theory are as follows,
(a) For a reaction to occur, there must be collisions between the reacting species.
(b) Only a certain fraction of the total number of collisions is effective in forming the products.
(c) For effective collisions, the molecules should possess sufficient energy as well as orientation.
(vi) The fraction of effective collisions, under ordinary conditions may vary from nearly zero to about one for
ordinary reactions. Thus, the rate of reaction is proportional to :
(a) The number of collisions per unit volume per second (Collision frequency, Z) between the reacting species
(b) The fraction of effective collisions (Properly oriented and possessing sufficient energy), f
i.e., Rate = − dx = f × Z ; Where f is fraction of effective collision and Z is the collision frequency.
dt
(vii) The physical meaning of the activation energy is that it is the minimum relative kinetic energy which the
reactant molecules must possess for changing into the products molecules during their collision. This means that the
fraction of successful collision is equal to e −Ea / RT called Boltzmann factor.
(viii) It may be noted that besides the requirement of sufficient energy, the molecules must be properly
oriented in space also for a collision to be successful. Thus, if Z AB is the collision frequency, P is the orientation
factor (Steric factor) then, k = PZ AB .e −Ea / RT . If we compare this equation with Arrhenius equation. k = A e −Ea / RT
We know that pre-exponential form 'A' in Arrhenius equation is, A = PZ AB .
Concept of activation energy
(i) The excess energy (Over and above the average energy of the reactants) which must be supplied to the
reactants to undergo chemical reactions is called activation energy (Ea ), Ea = E −(Threshold energy) E(Reactants)
Activation energy = Threshold energy – Average kinetic energy of the reacting molecules.
(a) Zero activation energy = Fraction of effective collision (f) will be very large = Very fast reaction
(Instantaneous reaction).
(b) Low activation energies = Fraction of effective collision (f) will be large = Fast reactions.
(c) High activation energies = Fraction of effective collision (f) will be small = Slow reaction.
(ii) When the colliding molecules possess the kinetic energy equal to activation energy, the atomic
configuration of species formed at this stage is different from the reactants as well as products. This stage is called
the activated state or transition state and specific configuration of this state is called activated complex. In
other words, we can say that, A collision between high energy molecules overcomes the forces of repulsion and
brings the formation of an unstable molecule cluster called the activated complex. The life span of an activated
complex is very small. Thus, the activated complex breaks either into reactants again or new substances, i.e.,
products.
H I HI HI
+ I
HI HI
H Activated complex Products
Reactants
(iii) The activation energy (Ea ) depends upon the nature of chemical bonds undergoing rupture and is
independent of enthalpies of reactants and products.
(iv) According to the concept of activation energy, the reactants do not change directly into the products. The
reactant first absorb energy equal to activation energy and form activated complex. At this state, the molecules must
have energy at least equal to the threshold energy. This means that the reaction involves some energy barrier which
must be overcome before products are formed. The energy barrier is known as activation energy barrier.
Chemical Kinetics
Energy barrier
Lower energy Threshold Activated
location complex
E energy (Et) Energy barrier
A t (activation energy)
Ea
Er Reactants Energy of the
E (Er) ∆E reaction
p Products (Ep)
B
Potential-energy barrier figure Progress of reaction
Note : The activation energy is found to increase with the lowering of temperature i.e., at lower
temperatures the activation energy tends to increase.
(2) Transition state theory
(i) According to transition state theory the activated complex is supposed to be in equilibrium with the reactant
molecules.
(ii) Once the transition state is formed it can either return to the initial reactants or proceeds to form the
products.
(iii) Assuming that once formed the transition state proceeds to products we can say that rate is proportional
to concentration of transition state. Mathematically, Rate ∝ Transition state; Rate= Constant × Transition state
(iv) The activation energy for the forward reaction, (Eaf ) and the activation energy for the reverse reaction
(Ear ) are related to the enthalpy (∆H)of the reaction by the equation ∆H = Eaf − Ear .
(a) For endothermic reactions, ∆H > 0, so that Ear < Eaf
(b) For exothermic reaction, ∆H < 0, so that Ear > Eaf .
Note : Exothermic reaction requires less activation energy than the endothermic reaction. Therefore
an exothermic reaction proceeds at a faster rate than the endothermic reaction.
Kinetic stability of fuels : Combustion of fuels is highly exothermic reaction yet these can be safely
stored in contact with oxygen or air. The stability of fuels is due to high activation energy of these
combustion reactions.
Ea cannot be zero (if suppose Ea =0 then according to Arrhenius equation k = A i.e., every collision
between molecules leads to be chemical reaction. This is not true.)
Dependence of reaction rate on temperature.
A general approximate rule or the effect of temperature on reaction rates is that the rate of a reaction becomes
almost double for every 10o C rise in temperature. This is also called temperature coefficient.
Temperature coefficient : Temperature coefficient of a reaction is defined as the ratio of rate constants at
two temperatures differing by (generally 25°C and 35°C) 10.
Temperature coefficient = k at (t + 10o C) = k35o C Or Temperature coefficient = kt + 10
k at toC k25o C kt
The temperature coefficient for most of the reactions lies between 2 and 3 i.e. the rate of reaction increase by
a factor of 2 to 3, for every 10o C rise in temperature.
Arrhenius equation and Calculation of activation energy.
Arrhenius proposed a quantitative relationship between rate constant and temperature as,
k = A e − Ea / RT …..(i)
The equation is called Arrhenius equation in which constant A is known as frequency factor. This factor is
related to number of binary molecular collision per second per litre. Ea is the activation energy. T is the absolute
temperature and R is the gas constant. Both A and Ea are collectively known as Arrhenius parameters. Taking
logarithm equation (i) may be written as,
log k = log A − Ea RT …..(ii)
2.303
The value of activation energy (Ea ) increases, the value of k decreases and therefore, the reaction rate
decreases. When log k plotted against 1 , we get a straight line. The intercept of
T
this line is equal to log A and slope equal to − Ea R . Therefore log k
2.303
Ea = −2.303 R × slope . Slope = − Ea
Rate constants for the reaction at two different temperatures T1 and T2 , 2.303R
1/T
log k2 = Ea 1 − 1 …..(iii)
k1 2.303R T1
T2
where k1 and k2 are rate constant at temperatures T1 and T2 respectively (T2 > T1) .
Note : Generally rate of reaction increases with increase in temperature but remember for the
reaction
2NO + O2 → 2NO2; the rate decreases slightly with increase in temperature because it has small
negative temperature coefficient.
When Ea= 0, the rate of reaction becomes independent of temperature (Ea= activation energy)
Example : 17 In the Arrhenius equation for a certain reaction, the values of A and Ea are 4 × 1013 sec −1 and 9.86 kJ mol −1
respectively. If the reaction is of first order, at what temperature will its half life period be 10 minute
(a) 311.34 K (b) 31.134 K (c) 411.34 K [IIT 1990]
(d) 41.134 K
Solution : (a) According to Arrhenius equation, k = Ae − Ea / RT or log k = − Ea × 1
A RT 2.303
k = 0.693 = 0.693 = 1.155 × 10−3
t1/ 2 10 × 60
log 1.155 × 10 −3 98.6 × 103 or − 16.54 98600
4 × 1013 8.314 × T × 2.303 8.314 × 2.303
∴ = − = − T
or T = 98600 = 311.34 K.
8.314 × 2.303 × 16.54
Example : 18 A first order reaction is 50% completed in 30 minutes at 27°C and in 10 minutes at 47°C. Calculate the
activation energy of the reaction.
(a) 46.8 kJ mol −1 (b) 43.8 kJ mol −1 (c) 50.8 kJ mol −1 (d) 60.8 KJ mol −1
Solution : (b) Let us first calculate k1 and k2 at temperatures 27°C and 47°C. We know that t1/ 2 = 0.693 or k = 0.693
k t1/ 2
At 27°C, t1/ 2 = 30 min ; k1 = 0.693 = 0.0231
30
At 47°C, t1/ 2 = 10 min ; k2 = 0.693 = 0.0693
10
Now, log k2 = Ea 1 − 1 ; log 0.0693 = Ea 1 − 1
k1 2.303R T2 0.0231 2.303 × 8.314 300 320
T1
log 3 = Ea 20 ⇒ 0.4771 = Ea × 20
2.303 × 8.314 300 × 320 2.303 × 8.314 × 300 × 320
or Ea = 0.4771× 2.303 × 8.314 × 300 × 320 = 43848Jmol −1 or 43.8 kJ mol −1 .
20
Example : 19 The rate of reaction becomes 2 times for every 10o C rise in temperature. How the rate of reaction will
increases when temperature is increased from 30o C to 80o C
(a) 16 (b) 32 (c) 64 (d) 128
Solution: (b) kt + 10 = rt + 10 = 2.
kt rt
For an increase of temperature to 50o C , i.e., 5 times, the rate increases by 25 times, i.e., 32 times.
Example : 20 The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at 25o C are
3.0 × 10−4 s−1, 104.4 kJ mol−1 and 6.0 × 1014 s−1 respectively. The value of the rate constant as T → ∞ is
[IIT 1996]
(a) 2.0 × 1018 s−1 (b) 6.0 × 1014 s−1 (c) Infinity (d) 3.6 × 1030 s−1
Solution: (b) k= Ae −Ea / RT ; At T →∞ i.e., 1 →0; k = A = 6 × 1014 sec −1
T
Example : 21 The activation energy of a reaction is 9kcal / mole . The increase in the rate constant when its temperature is
raised from 295 to 300 K is approximately [Pb. CET 1988]
(a) 10% (b) 50% (c) 100% (d) 28.8%
Solution: (d) log k2 = Ea R T2 − T1 = 9000 2 300 − 295 = 0.1103
k1 2.303 T1 T2 2.303 × 295 × 300
Hence k2 = 1.288 or k2 = 1.288 k1 i.e., increase = 28.8%.
k1
Mechanism of the reaction.
• The study of reaction pathway or mechanism of a reaction is very important aspect of kinetics of reaction.
• In some reactions, intermediates formed which accumulate during the early period of the reaction, reach to
the maximum concentration and then react and give the final products.
• The necessary condition for a mechanism is that it must lead to the correct law.
(1) Reaction involving first order consecutive reactions
(i) In such reactions, the reactions form a stable intermediate compound before they are finally converted into
the products.
(ii) For example, reactants (R) are first converted to intermediate (I) which is then converted to product (P) as
R k1 → I k2 → P ; Therefore, the reaction takes place in two steps, both of P
which are first order i.e.,
Concentration
Step I : R k1 → I I
Step II : I k2 → P R
This means that I is produced by step I and consumed by step II. In these
reactions, each stage will have its own rate and rate constant the reactant Time
concentration will always decrease and product concentration will always increase as
shown in fig. Concentration profile of reactants
(R), intermediate (I) and products (P)
as a function of time
(2) Reaction involving slow step : When a reaction occurs by a sequence of steps and one of the step is
slow, then the rate determining step is the slow step. For example in the reaction
R k1 → I ; I k2 → P , if k1 << k2 then I is converted into products as soon as it is formed, we can say that
− d[R] = d[P] = k1 [R]
dt dt
(3) Parallel reactions : In such type of reactions the reactants are more reactive, which may have different
orders of the reactions taking place simultaneously. For example, in a system containing NO2 and SO2 , NO2 is
consumed in the following two reactions, 2NO2 k1 → N 2O4 ; NO2 + SO2 k2 → NO + SO3
The rate of disappearance of NO2 will be sum of the rates of the two reactions i.e.,
− d[NO2 ] = 2k1[NO2 ]2 + k2[NO2 ][SO2 ]
dt
Photochemical reactions:
Absorption of radiant energy by reactant molecules brings in photophysical as well as photochemical changes.
According to Einstein's law of photochemical equivalence, the basic principle of photo processes, each reactant
molecule is capable of absorbing only one photon of radiant energy. The absorption of photon by a reactant
molecule may lead to any of the photo process.
Reactant molecule
Absorption of photon (As per Einstein law)
Excitation of electronic level Knock out the electron from
the reactant species
Excited molecule Photoelectric effect
Photophysical process Photochemical process
(i) Fluorescence (i) Oxidation
(ii) Phosphorescence (ii) Reduction
(iii) Dissociation
(iv) Double decomposition
(v) Isomeric transformation
(vi) Photosensitization
The chemical reactions, which are initiated as a result of absorption of light, are known as photochemical
reactions. In such cases, the absorbed energy is sufficient to activate the reactant molecules to cross the energy
barrier existing between the reactants and products or in other words, energy associated with each photon supplies
activation energy to reactant molecule required for the change.
(1) Characteristics of photochemical reactions
(i) Each molecule taking part in a photo process absorbs only one photon of radiant energy thereby increasing
its energy level by hv or hc
λ
(ii) Photochemical reactions do not occur in dark.
(iii) Each photochemical reaction requires a definite amount of energy which is characteristic of a particular
wavelength of photon. For example, reactions needing more energy are carried out in presence of UV light (lower
λ , more E/Photon). A reaction-taking place in UV light may not occur on exposure to yellow light (lower λ and
lesser E/Photon)
(iv) The rate of photochemical reactions depend upon the intensity of radiation’s absorbed.
(v) The ∆G values for light initiated reactions may or may not be negative.
(vi) The temperature does not have marked effect on the rate of light initiated reactions.
(2) Mechanism of some photochemical reactions
(i) Photochemical combination of H2 and Cl2 : A mixture of H 2 and Cl2 on exposure to light give rise to
the formation of HCl, showing a chain reaction and thereby producing 106 to 108 molecules of HCl per photon
absorbed.
H 2 + Cl 2 sunlight → 2HCl
The mechanism leading to very high yield of HCl as a result of chemical change can be as follows. Chlorine
molecules absorb radiant energy to form an excited molecule which decomposes to chlorine free radicals (Cl) to
give chain initiation step.
Light absorption step : Cl2 hv → Cl2* (Excited molecule) ........(i)
Chain initiation step : Cl 2* → Cl • + Cl • ........(ii)
The chlorine free radical then combines with H 2 molecule to form HCl and H • free radical. The H • free
radical so formed again combines with another Cl2 molecule to give HCl and Cl • free radical back resulting into
chain propagation step.
Chain propagation step : Cl • + H 2 → HCl + H • ........(iii)
H • + Cl2 → HCl + Cl •
The combination of two Cl • free radicals leads to chain terminating step.
Chain terminating step : Cl • + Cl • → Cl2 ........(iv)
(ii) Photochemical combination of H2 and Br2 : The combination of H2 and Br2 to form HBr in presence
of light is also an example of chain reaction like photochemical combination of H2 and Cl2 . Here two Br2
molecules absorb photon, however, inspite of chain reaction only one molecule of HBr is formed for each 100
photon absorbed by 100 molecules of Br2 . The mechanism of reaction is given below.
H2 + Br2 light → 2HBr
Mechanism :
Light absorption step : Br2 + hv → Br2* ........(i)
Chain initiation step : Br2* → Br • + Br • ........(ii)
Chain propagation step : Br * + H 2 → HBr + H • ........(iii)
H * + Br2 → HBr + Br • ........(iv)
Chain termination step : Br • + Br • → Br2 ........(v)
The lower values of HBr formation per photon of light absorbed has been attributed to the fact that step (III) is
highly endothermic and thus before step (III) can take place most of the bromine free radicals recombine as per step
(V) to give Br2 molecule and thus providing less feasibility for step (IV) i.e. steps regenerating free radicals. Also the
decomposition of HBr increases with increase in temperature.
(3) Quantum yield (or quantum efficiency) : The quantum efficiency or yield (φ ) of a photochemical
reaction may be expressed as, φ = No. of molecules reacted or product formed
No. of photon absorbed
(4) Application of photochemistry : Photochemistry has significant role in our daily life. Some of the
photochemical reactions commonly known as cited below,
(i) Photosynthesis in plants (ii) Photography
(iii) The formation and destruction of ozone layer (iv) Photoetching in electronic industry
(v) Many polymerization reactions. (vi) Modern printing technology
(vii) Free radical combinations to obtain many compounds.
(5) Damaging effect of photochemistry : As already discussed, the destruction of ozone layer by chloro-
fluorocarbon is due to photochemical decomposition of these compounds. The fading away of colours in coloured
fabrics is due to the photochemical decomposition of colouring material (i.e. dyes) used in printing technology.
Note : Generally ultraviolet or visible radiation’s are used for carrying out such type of reactions
because their photons possess energies approximately of the order of 420 kJ per mol which is
comparable to mole of the bond energy. Thus UV radiation energy is capable of breaking the bonds.
On the other hand IR radiation’s are generally not used because their photons possess energy of the
order of 60 kJ per mole which is quite less for breaking the bonds.
Destruction of ozone layer : The formation and dissociation of ozone keeps a balance of ozone and
oxygen in the ozone layer. However the diffusion of chloro-fluorocarbon such as CFCl3 and CF2Cl2
into the ozone layer are destroying the ozone. Cl 2 + hν → CF2 C•l+ C•l ; C• l+ O3 → • O 2 ;
ClO+
• + O3 → • 2O2 . Chloro-fluorocarbons are used as aerosol repellents and as refrigerants.
Cl O Cl +
Hence, ozone layer which acts as an umbrella for earth is being continuously destroying by the
harmful UV radiation's coming from the sun.
Study of fast reactions.
Rates of chemical reactions differ form very slow to very fast. The rates of moderate speed reactions lying in
between these two extreme reactions. However, rates of some instantaneous reactions are so fast that they occur
within 10−12 second or in even less time. For example,
• Neutralization reactions have half life of 10−10 sec ; H(+aq.) + OH(−aq.) → H2O(l)
• Photosynthesis has half life of 10−12 sec ; 6CO2 + 6H2O chlorophyll → C6 H12O6 + 6O2
hv
• Some precipitation reactions have very short half life; AgNO3 + KCl → AgCl ↓ +KNO3
• Isomerisation of retinal in vision has half life of 10−12 sec
Rates of such reactions cannot be studied by ordinary methods because change in concentration cannot be
measured during this short interval of time. However, modern techniques such as flow methods, relaxation
methods, flash photolysis, laser technique and spectrophotometric methods are used to study such fast reactions.
(1) Photosynthesis in plants : Plants obtain their food for growth by the combination of CO2 and H2O in
presence of chlorophyll and light (a fast reaction) which leads to the preparation of carbohydrate and this
phenomenon is known as photosynthesis. The studies on photosynthesis involve flash photolysis technique. The
following mechanism has been proposed for photosynthesis. First step of the reaction mechanism involves the
excitation of chlorophyll molecule by absorbing photon of red light. The excited chlorophyll molecule transfers its
energy in the form of an electron to nearby reactant molecule A within 10−12 second. The reactant molecule which
accepts this energy is known as electron acceptor.
Chlorophyll hv → Chlorophyll* ; Chlorophyll* + A → Chlorophyll + A− + Energy
(Excited molecule) ( A is CO2 or H 2O)
The electron acceptor (A) transfer this electron to another electron acceptor molecule (B). A– + B → A + B− + E
The process leads to release of energy which is used for the series of reaction to yield the synthesis of energy
rich molecule of carbohydrates from CO2 and water. 6CO2 + 6H 2O Energy → C6 H12O6 + 6O2
(2) Isomerisation of retinal in vision : The mechanism involves two steps
(i) The retinal molecule (a light sensitive molecule present in the retina of eye) gets excited on exposure to
light and undergoes geometrical isomerization and the energy absorbed is stored as chemical energy. The process
takes place within 10−12 sec .
(ii) As soon as the first step gets completed, the retinal is converted back into its original form within 10−12 sec
and the energy released is used to send signals to the brain which ultimately causes the sensation of vision.
Differences between Photochemical and Thermochemical reactions
Photochemical reactions Thermochemical reactions
These reactions are initiated by light radiation. These reactions are initiated by heat energy.
They cannot occur in dark. They do occur in dark.
Temperature does not have any significant effect on the rates of The temperature does have a marked effect on the rates of these
such reactions and temperature coefficient is low. reactions and temperature coefficient is generally high.
The value of ∆G may be +ve or – ve. ∆G is – ve for such reactions.
Important tips
Chemiluminiscence : It is the emission of light in chemical reaction at ordinary temperature e.g., the light emitted by
glow worms (fire flies) is due to the oxidation of a protein Luciferin present in them.
Fluorescence and Phosphorescence : There are some substances which when exposed to light or radiation, absorbs
light and immediately start re-emitting the energy. The glow continue as long as the source of light is there. Such substances
are called fluorescent substances and phenomenon as fluorescence e.g., fluorite (CaF2), fluorescein dye etc.
On the other hand, there are some substances which continue to glow for some time even after the source of light is cut off.
Such substances are called phosphorescent substances and phenomenon as phosphorescence e.g., Zinc sulphide and
sulphides of other alkaline earth metals.
Bioluminiscence : Certain living organisms emit light and show the phenomenon of chemiluminiscence. It is known as
Bioluminiscence e.g., light emission in fire flies.
Example of fourth order reaction, 4KClO3 ⇌ 3KClO4 + KCl
Grothus-Draper law : When light falls on a substance, a part of light is absorbed, a part is reflected and a part is
transmitted. Only that part of light which is absorbed causes a particular reaction to occur.
Stark's Einstein law of photochemical equivalence : According to this law, every atom or molecule taking part in a
photochemical reaction absorbs only one quantum of radiation. (E = hν ) . The energy absorbed by one mole of reacting
molecules is known as one Einstein.
Free energy (∆G) for thermochemical reactions is always negative but remember, ∆G for photochemical reactions may not
always be negative. It is because a part of the light energy absorbed by the reactants is converted into free energy of the
products. In the following photochemical reactions for which ∆G is positive and still they are spontaneous
(a)Ozanisation of oxygen (b) Synthesis of carbohydrates (c) Decomposition of HCl to H2 and Cl2
There are some substances which when added to a reaction mixture helps to start the photochemical reaction but do not undergo
any chemical change are called photosensitizer and this process is called photosensitization. A photosensitizer simply acts as a
carrier of energy. For example (i) Dissociation of H2 in the presence of mercury vapours. (ii) Photosynthesis in presence of
chlorophyll.
***
Surface chemistry
“The branch of physical chemistry, which deals the nature of surfaces and also with the chemical and
physical processes which takes place on the surfaces, is called surface chemistry”.
In surface chemistry, we study the phenomenon of adsorption, catalysis and colloidal properties.
Adsorption.
(1) Definition : The phenomenon of attracting and retaining the molecules × ×× ××× × ×× ×× Substance
of a substance on the surface of a liquid or solid resulting in to higher ×× × molecule
concentration of the molecules on the surface is called adsorption. ×
× × Solid (liquid)
(2) Causes of adsorption : Unbalanced forces of attraction or free × × surface
valencies which is present at the solid or liquid surface, have the property to ×
attract and retain the molecules of a gas or a dissolved substance on to their × × × ××
surfaces with which they come in contact. × ××
×× × × × ×
Adsorption
Example : (i) Ammonia gas placed in contact with charcoal gets adsorbed on the charcoal whereas ammonia
gas placed in contact with water gets absorbed into water, giving NH4OH solution of uniform concentration.
(ii) If silica gel is placed in a vessel containing water vapours, the latter are adsorbed on the former. On the
other hand, if anhydrous CaCl2 is kept in place of silica gel, absorption takes places as the water vapours are
uniformly distributed in CaCl2 to form hydrated calcium chloride (CaCl2 . 2H 2O) .
Some basic terms which are used in adsorption
Interface : Any surface is a plane which separates any Adsorbate and Adsorbent : The substance which
two phases in contact with each other. The plane which gets adsorbed on any surface is called adsorbate for
separates any two phase is generally called an interface example, if a gas gets adsorbed on to the surface of a solid,
between the two phases. then the gas is termed as the adsorbate.
Solid-air The substance on the surface of which adsorption takes
interface Phase 2 place is called adsorbent.
(air)
Adsorbent may be a Adsorbate
Phase 1 (gas or
(solid) solid or a liquid metal solute)
Interface powders. Powdered Adsorbent
(solid)
charcoal, animal
charcoal silica powder
etc. are commonly used Adsorbent and adsorbate
as adsorbents.
Desorption : The removal of the adsorbed substance Absorption : When the molecules of a substance are
from a surface is called desorption. uniformly distributed throughout the body of a solid or
Removal of liquid. This phenomenon is called absorption.
adsorbate
×××××××××××A×××d(×s×soo××lri×b×d×e)××n××t××××××××× × ×× ×× × Substance
× ×× × × molecules
×××× Body of
× ×× × × solid (liquid)
×××××
Desorption ××××× ×
×××× ×
Absorption
Sorption : The phenomenon in which adsorption and Occlusion : When adsorption of gases occur on the
absorption occur simultaneously is called sorption. surface of metals this is called occlusion.
Mc. Bain introduced a general term sorption describeing
both the processes, however adsorption is instantaneous
i.e. a fast process while absorption is a slow process.
×××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××× Substance × × × × × × ××××× × Adsorption of
molecules ×× gas
Sorption
Body of × × Metal surface
solid (liquid) ×
×
××
××
× × ×o×cc×lu×si×o×n××××
Difference between adsorption and absorption
Adsorption Absorption
It is a surface phenomenon. It concerns with the whole mass of the absorbent.
It implies that a substance is uniformly distributed, through the
In it, the substance is only retained on the surface and does not body of the solid or liquid.
go into the bulk or interior of the solid or liquid.
In it the concentration is low.
In it the concentration of the adsorbed molecules is always
greater at the free phase.
It is rapid in the beginning and slows down near the equilibrium. It occurs at the uniform rate.
Examples : (i) Water vapours adsorbed by silica gel. Examples : (i) Water vapours absorbed by anhydrous
CaCl2
(ii) NH3 is adsorbed by charcoal.
(iii) N2 is adsorbed on mica. (ii) NH3 is absorbed in water forming NH4OH
(iv) O2 is adsorbed on tungsten surface
(v) Decolourisation of sugar solution by
activated or animal charcoal.
(vi) Ink is adsorbed by blotting paper.
(3) Surface forces : Only the surface atoms of an adsorbent play an active Balanced force New
role in adsorption. These atoms posses unbalanced forces of various types such as, unbalanced
Vander Waal’s forces and chemical bond forces. × × Breaking × + ×
Thus, the residual force-field on a free surface which is responsible for × ×× ×
adsorption is produced. For example, when a solid substance is broken into two No. of No. of
pieces, two new surfaces are formed and therefore, the number of unbalanced forces unbalanced unbalanced
becomes more. As a result the tendency for adsorption become large.
(4) Reversible and Irreversible adsorption : The adsorption is reversible, if the adsorbate can be easily
removed from the surface of the adsorbent by physical methods.If the adsorbate can not be easily removed from
the surface of the adsorbent is called irreversible adsorption.
(i) Example for Reversible adsorption: A gas adsorbed on a solid surface can be completely removed in vacuum.
(ii) Example for Irreversible adsorption: Adsorption of O2 on tungusten adsorbent.
(5) Characteristics of adsorption
(i) Adsorption refers to the existence of a higher concentration of any particular component at the surface of a
liquid or a solid phase.
(ii) Adsorption is accompanied by decrease in the ∆G (free energy charge) of the system when ∆G = 0 ,
adsorption equilibrium is said to be established.
(iii) Adsorption is invariably accompanied by evolution of heat, i.e. it is an exothermic process. In other words,
∆H of adsorption is always negative.
(iv) When a gas is adsorbed, the freedom of movement of its molecules becomes restricted. On account of it
decrease in the entropy of the gas after adsorption, i.e. ∆S is negative.
Adsorption is thus accompanied by decrease in enthalpy as well as decrease in entropy of the system and ∆G
also decreases.
(v) For a process to be spontaneous, the thermodynamic requirement is that ∆G must be negative, i.e.
there is decrease in free energy. On the basis of Gibb’s Helmholtz equation, ∆G = ∆H − T∆S , ∆G can be
negative if ∆H has sufficiently high negative value and T∆S has positive value.
Note : When adsorbents are porous, the adsorbate is actually condensed in the pores. This is called
capillary condensation.
Classification of Adsorption.
Adsorption can be classified into two categories as described below.
(1) Depending upon the concentration : In adsorption the concentration of one substance is different at
the surface of the other substance as compared to adjoining bulk or interior phase.
(i) Positive adsorption : If the concentration of adsorbate is more on the surface as compared to its
concentration in the bulk phase then it is called positive adsorption.
Example : When a concentrated solution of KCl is shaken with blood charcoal, it shows positive adsorption.
(ii) Negative adsorption : If the concentration of the adsorbate is less than its concentration in the bulk then
it is called negative adsorption.
Example : When a dilute solution of KCl is shaken with blood charcoal, it shows negative adsorption.
(2) Depending upon the nature of force existing between adsorbate molecule and adsorbent
(i) Physical adsorption : If the forces of attraction existing between adsorbate and adsorbent are Vander
Waal’s forces, the adsorption is called physical adsorption. This type of adsorption is also known as physisorption
or Vander Waal’s adsorption. It can be easily reversed by heating or decreasing the pressure.
(ii) Chemical adsorption : If the forces of attraction existing between adsorbate particles and adsorbent are
almost of the same strength as chemical bonds, the adsorption is called chemical adsorption. This type of adsorption
is also called as chemisorption or Langmuir adsorption. This type of adsorption cannot be easily reversed.
Comparison between physisorption and chemisorption
Physisorption (Vander Waal's adsorption) Chemisorption (Langmuir adsorption)
Low heat of adsorption usually in range of 20-40 High heat of adsorption in the range of 50-400
kJ/mol kJ/mol
Force of attraction are Vander Waal's forces. Forces of attraction are chemical bond forces.
It is reversible It is irreversible
It is usually takes place at low temperature and It takes place at high temperature.
decreases with increasing temperature.
It is related to the case of liquefication of the gas. It is not related.
It forms multimolecular layers. It forms monomolecular layers.
It does not require any activation energy. It requires high activation energy.
High pressure is favourable. Decrease of pressure High pressure is favourable. Decrease of pressure
causes desorption does not cause desorption.
It is not very specific. It is highly specific.
Note : Adsorption of gases on animal charcoal and adsorption of water vapours on silica gel is physical
adsorption.
The behavior of adsorption of N2 on iron clearly distinguishes between physisorption and
chemisorption. At 83 K, nitrogen is physisorbed on iron surface as N2 molecules. The amount of
N2 adsorbed decreases rapidly as the temperature increases at room temperature, practically, there is
no adsorption of N2 on iron. However at 773 K and above, nitrogen is chemisorbed on the iron
surface as nitrogen atoms.
Due to formation of multilayers physical adsorption decreases after some times.
Chemisorption and physisorption both are exothermic.
Adsorption of gases on solids.
• Whenever a clean surface is exposed to a gas, the gas molecules get adsorbed on the free surface.
However, if the surface is already having a weakly held adsorbate on it, the same is displaced by the substance
which has a tendency to get adsorbed more strongly.
• When the activated charcoal used in the gas masks is already exposed to the atmospheric air, the gases
and the water vapours in the air are adsorbed on its surface. But when it is exposed to chlorine atmosphere, these
gases are displaced by chlorine, Thus we find that the substances which get strongly adsorbed can easily displace
the weakly adsorbed adsorbate.
• Almost all solids adsorb gases to some extent.
• Charcoal adsorbs many gases. It even adsorbs polluting gases present in air in small concentration.
• Gases such as H2, N2, O2 and CO are adsorbed by finely divided transition metal such as Ni, Pt, Pd, Fe,
Co, etc.
Factors which affect the extent of adsorption on solid surface : The following are the factors which
affect the adsorption of gases on solid surface.
(1) Nature of the adsorbate (gas) and adsorbent (solid)
(i) In general, easily liquefiable gases e.g., CO2, NH3, Cl2 and SO2 etc. are adsorbed to a greater extent than
the elemental gases e.g. H2, O2, N2, He etc. (while chemisorption is specific in nature.)
(ii) Porous and finely powdered solid e.g. charcoal, fullers earth, adsorb more as compared to the hard non-
porous materials. Due to this property powdered charcoal is used in gas masks.
(2) Surface area of the solid adsorbent
(i) The extent of adsorption depends directly upon the surface area of the adsorbent, i.e. larger the surface
area of the adsorbent, greater is the extent of adsorption.
(ii) Surface area of a powdered solid adsorbent depends upon its particle size. Smaller the particle size, greater
is its surface area.
(iii) The surface area per gram of the adsorbent is called specific surface area of the adsorbent.
(3) Effect of pressure on the adsorbate gas Extent of adsorption Adsorption tends to
(i) An increase in the pressure of the adsorbate gas increases the extent of reach limiting value
adsorption.
Adsorption increases
(ii) At low temperature, the extent of adsorption increases rapidly with rapidly at the beginning
pressure. Pressure
(iii) Small range of pressure, the extent of adsorption is found to be directly
proportional to the pressure.
(iv) At high pressure (closer to the saturation vapour pressure of the gas), the
adsorption tends to achieve a limiting value.
(4) Effect of temperature
(i) As adsorption is accompanied by evolution of heat, so according to the Le-Chatelier’s principle, the
magnitude of adsorption should decrease with rise in temperature.
(ii) The relationship between the extent of adsorption and P - Constant P - Constant
temperature at any constant pressure is called adsorption x/m x/m
isobar.
Temperature Temperature
(iii) A physical adsorption isobar shows a decrease in x/m Physical adsorption Chemical adsorption
(where ‘m’ is the mass of the adsorbent and ‘x’ that of
adsorbate) as the temperature rises.
(iv) The isobar of chemisorption show an increase in the
beginning and then decrease as the temperature rises.
(5) Activation of adsorbent
(i) Activation of an adsorbent means, increase in the adsorbing power of the adsorbent.
(ii) This can be achieved by increasing the surface area of the adsorbent.
(iii) This can be done by making the surface of adsorbent rough or by breaking it into small pieces.
(iv) If the particle are made of then interparticle space will be too small hence the extent of adsorption may
decrease.
(v) The active sites (clear surface) can be actually free from the adsorbed gases by heating in very high
vacuum ( 10−10 or 10−11 mm Hg)
Adsorption isotherms.
• A mathematical equation which describes the relationship between pressure (p) of the gaseous adsorbate
and the extent of adsorption at any fixed temperature is called adsorption isotherms.
• The extent of adsorption is expressed as mass of the adsorbate adsorbed on one unit mass of the
adsorbent.
• Thus, if x g of an adsorbate is adsorbed on m g of the adsorbent, then
Extent of adsorption = x
m
Various adsorption isotherms are commonly employed in describing the adsorption data.
(1) Freundlich adsorption isotherm
(i) Freundlich adsorption isotherm is obeyed by the adsorptions where the adsorbate forms a
monomolecular layer on the surface of the adsorbent.
x = 1 (Freundlich adsorption isotherm) or log x = log k + 1 log p where, x is the weight of the gas
m m n
kp n
adsorbed by m gm of the adsorbent at a pressure p, thus x/m represents the amount of gas adsorbed by the
adsorbents per gm (unit mass), k and n are constant at a particular temperature and for a particular adsorbent and
adsorbate (gas), n is always greater than one, indicating that the amount of the gas adsorbed does not
increase as rapidly as the pressure.
(ii) At low pressure, the extent of adsorption varies linearly with pressure. x ∝ p'
m
(iii) At high pressure, it becomes independent of pressure. x p0
m∝
(iv) At moderate pressure x depends upon pressure raised to powers x ∝ 1
m m
pn
x ∝ p1 x ∝ p0
m m
log (x/m) slope = 1
n
x/m
x
m ∝ p1/ n intercept = log k
p log p
Freundlich adsorption isotherm Plot of log x/m against log p for the
: plot of x/m against p adsorption of a gas on a solid
Note : Equation log x = log k + 1 log p is similar to the equation of a straight line y = c + mx . Therefore, the
m n
plot of log (x/m) against log p should be a straight line with an intercept equal to log k and slope 1 .
n
(2) The Langmuir - adsorption isotherms
(i) One of the drawbacks of Freundlich adsorption isotherm is that it fails at high pressure of the gas. Irving
Langmuir in 1916 derived a simple adsorption isotherm, on theoretical considerations based on kinetic
theory of gases. This is named as Langmuir adsorption isotherm.
(ii) The main points of Langmuir’s theory of adsorption are as follows,
(a) Adsorption takes place on the surface of the solid only till the whole of the surface is completely covered
with a unimolecular layer of the adsorbed gas.
(b) Adsorption consists of two opposing processes, namely Condensation of the gas molecules on the solid
surface and Evaporation (desorption) of the gas molecules from the surface back into the gaseous phase.
(c) The rate of condensation depends upon the uncovered (bare) surface of the adsorbent available for
condensation. Naturally, at start when whole of the surface is uncovered the rate of condensation is very high and
as the surface is covered more and more, the rate of condensation progressively decreases. On the contrary, the rate
of evaporation depends upon the covered surface and hence increases as more and more of the surface is covered
ultimately an equilibrium will be set up at a stage when the rate of condensation becomes equal to the rate of
evaporation (adsorption equilibrium).
(d) The rate of condensation also depends upon the pressure of the gas since according the kinetic theory of
gases, the number of molecules striking per unit area is proportional to the pressure.
Mathematically, x = 1 ap , where a and b are constants and their value depends upon the nature of gas
m + bp
(adsorbate), nature of the solid adsorbent and the temperature. Their values can be determined from the
experimental data.
(iii) Limitation of Langmuir theory
(a) Langmuir’s theory of unimolecular adsorption is valid only at low pressures and high temperatures.
(b) When the pressure is increased or temperature is lowered, additional layers are formed. This has led to the
modern concept of multilayer adsorption.
Note : The Langmuir adsorption isotherm is restricted to the formation of unimolecular layer of gas
molecules on the surface of solids. However, it was suggested that there is possibility of
multimolecular layer of gas molecules on the surface of the solids rather than single layer. On this
basis, Brunauer, Emmett and Teller proposed a new theory known as B.E.T theory.
Adsorption from Solutions.
(1) The process of adsorption can take place from solutions also.
(2) In any solution, there are two (or more) components ; solute and solvent. The solute may be present in
the molecular or ionic form.
(3) The extent of adsorption from solution depends upon the concentration of the solute in the solution, and
can be expressed by the Freundlich isotherm.
(4) The Freundlich adsorption isotherm for the adsorption from solution is, x = 1 where, x is the mass of
m
kc n
the solute adsorbed, m is the mass of the solid adsorbent, c is the equilibrium concentration of the solute in the
solution, n is a constant having value greater than one,
k is the proportionality constant, (The value of k depends upon the nature of solid, its particle size,
temperature, and the nature of solute and solvent etc.)
(5) The plot of x/m against c is similar to that Freundlich adsorption isotherm. The above equations may be
written in the following form, log x = log k + 1 log c where c, is the equilibrium concentration of the solute in the
m n
solution.
Note : Adsorption Isostere : Degree of adsorption depends on Temperature Pressure
temperature as well as on pressure. When temperature increases
the extent of adsorption decreases. A linear relationship should exist
between temperature and pressure with a certain amount of
adsorption. The plot of temperature versus pressure for a given
amount of adsorption is called adsorption isostere.
Application of Adsorption.
The phenomenon of adsorption finds a number of applications. Important applications are given as follows.
(1) Production of high vacuum : A bulk of charcoal cooled in liquid air is connected to a vessel which has
already been exhausted as for as possible by a vacuum pump. The remaining traces of air are adsorbed by the
charcoal. Then a very high vacuum is produced.
(2) In Gas masks : It is a device which consists of activated charcoal or a mixture of adsorbents. This
apparatus is used to adsorb poisonous gases (e.g. Cl2, CO, oxide of sulphur etc.) and thus purify the air for
breathing.
(3) For desiccation or dehumidification : Certain substances have a strong tendency to absorb water such
as silica and alumina (Al2O3 ) . These substances can be used to reduce/remove water vapours or moisture present
in the air. Silica gel is also used for dehumidification in electronic equipment.
(4) Removel of colouring matter from solution : (i) Animal charcoal removes colours of solutions by
adsorbing coloured impurities. (ii) Animal charcoal is used as decolouriser in the manufacture of cane sugar.
(5) Heterogeneous catalysis : Mostly heterogeneous catalytic reactions proceed through the adsorption of
gaseous reactants on solid catalyst. For example,
(i) Finely powdered nickel is used for the hydrogenation of oils.
(ii) Finely divided vanadium pentaoxide (V2O5 ) is used in the contact process for the manufacture of
sulphuric acid.
(iii) Pt, Pd are used in many industrial processes as catalyst.
(iv) Manufacture of ammonia using iron as a catalyst.
(6) Separation of inert gases : Due to the difference in degree of adsorption of gases by charcoal, a
mixture of inert gases can be separated by adsorption on coconut charcoal at different low temperatures.
(7) Softening of hard water
(i) The hard water is made to pass through a column packed with zeolite (sodium aluminium silicate)
(ii) Ca++, Mg++ ions which are responsible for hardness, get adsorbed on zeolite, exchanging sodium ions.
Na2 Al2Si2O8 + CaCl 2 → CaAl 2Si2O8 + 2NaCl
(iii) The exhausted zeolite is regenerated with 10% of sodium chloride solution.
CaAl 2Si2O8 + 2NaCl → Na2 Al2Si2O8 + CaCl 2
(8) De-ionisation of water
(i) Water can be de-ionised by removing all dissolved salts with the help of cation and anion-exchanger resin.
(ii) Cation-exchanger is an organic synthetic resin such as polystyrene-containing a macroanion
(R − SO3− etc.) which has adsorbed H+ ions.
(iii) A resin containing a basic group (R3 N + etc.) which has adsorbed OH − ions acts as anion exchanger.
(9) In curing diseases : A number of drugs are adsorbed on the germs and kill them or these are adsorbed
on the tissues and heat them.
(10) Cleaning agents : Soap and detergents get adsorbed on the interface and thus reduce the surface
tension between dirt and cloth, subsequently the dirt is removed from the cloth.
(11) Froth floatation process
(i) A low grade sulphide ore is concentrated by separating it from silica and other earthy matter by this
method.
(ii) The finely divided ore is added to water containing pine oil and foaming agent.
(iii) The air is bubbled through the mixture.
(iv) The foam formed rises to the surface on which mineral particles wetted with oil are adsorbed while earthy
matter settle down at the bottom.
(12) In adsorption indicators
(i) Surface of certain precipitates such as silver halide, have the property of adsorbing some dyes like eosin,
fluorescein etc.
(ii) In this case of precipitation titrations (for example AgNO3 Versus NaCl) the indicator is adsorbed at the
end point producing a characteristic colour on the precipitate.
(13) Chromatographic analysis
(i) The phenomenon of adsorption has given an excellent technique of analysis known as chromatographic
analysis.
(ii) The technique finds a number of applications in analytical and industrial fields.
(iii) Chromatographic technique based on differential adsorption of different constituents of a mixture.
(14) In dyeing : Many dyes get adsorbed on the cloth either directly or by the use of mordants.
Catalysis.
“Catalyst is a substance which speeds up and speeds down a chemical reaction without itself being used up.”
‘or’
“A catalyst is a foreign substance the addition of which into the reaction mixture accelerates or retards the
reaction.”
• Berzelius (1836) introduced the term catalysis and catalyst.
• Ostwald (1895) redefined a catalyst as, “A substance which changes the reaction rate without affecting
the overall energetics of the reaction is termed as a catalyst and the phenomenon is known as catalysis.”
Types of catalysis.
Catalytic reactions can be broadly divided into the following types,
(1) Homogeneous catalysis : When the reactants and the catalyst are in the same phase (i.e. solid, liquid
or gas). The catalysis is said to be homogeneous. The following are some of the examples of homogeneous
catalysis.
(i) Oxidation of sulphur dioxide into sulphur trioxide with oxygen in the presence of oxides of nitrogen as the
catalyst in the lead chamber process. 2SO2 (g) + O2 (g) NO(g) → 2SO3 (g)
The reactants, products and catalyst all are in gaseous state i.e. same phase.
(ii) Hydrolysis of methyl acetate is catalysed by H+ ions furnished by hydrochloric acid .
CH 3COOCH 3 (l) + H 2O(l) HCl(l) → CH 3COOH(l) + CH 3OH(l)
(iii) Hydrolysis of sugar is catalysed by H+ ions furnished by sulphuric acid.
C12 H 22O11 (l) + H 2O(l) H2SO4(l) → C6 H12O6 (l) + C6 H12O6 (l)
(Sucrose solution) (Glucose solution) (Fructose solution)
(2) Heterogeneous catalysis : The catalytic process in which the reactants and the catalyst are in different
phases is known as heterogeneous catalysis. Some of the examples of heterogeneous catalysis are given below.
(i) Oxidation of sulphur dioxide into sulphur trioxide in the presence of platinum metal or vanadium
pentaoxide as catalyst in the contact process for the manufacture of sulphuric acid. The reactants are in gaseous
state while the catalyst is in solid state. 2SO2 (g) + O2 (g) Pt(s) → 2SO3 (g)
(ii) Combination between nitrogen and hydrogen to form ammonia in the presence of finely divided iron in
Haber’s process.
N 2 (g) + 3H 2 (g) Fe(s) → 2NH 3 (g)
(iii) Oxidation of ammonia into nitric oxide in the presence of platinum gauze as a catalyst in Ostwald’s
process.
4 NH 3 (g) + 5O2 (g) Pt(s) → 4 NO(g) + 6H 2O(g)
(iv) Hydrogenation of vegetable oils in the presence of finely divided nickel as catalyst.
Vagetable oils(l) + H 2 (g) Ni(s) → Vegetable Ghee(g)
(3) Positive catalysis : When the rate of the reaction is accelerated by the foreign substance, it is said to be
a positive catalyst and phenomenon as positive catalysis. Some examples of positive catalysis are given
below.
(i) Decomposition of H 2O2 in presence of colloidal platinum. 2H 2O2 (l) Pt → 2H 2O(l) + O2(g)
(ii) Decomposition of KClO3 in presence of manganese dioxide. 2KClO3 (s) MnO2(s) → 2KCl(s) + 3O2 (g)
270o C
(iii) Oxidation of ammonia in presence of platinum gauze. 4 NH 3 (g) + 5O2 (g) Pt(s) → 4 NO(g) + 6H 2O(g)
300o C
(iv) Oxidation of sulphur dioxide in presence of nitric oxide. 2SO2 (g) + O2 (g) NO(g) → 2SO3 (g)
(v) Oxidation of sulphur dioxide in presence of platinised asbestos or vanadium pentaoxide.
2SO2 (g) + O2 (g) V2O5 (s) → 2SO3 (g)
or Pt(s)
(vi) Oxidation of hydrochloric acid into chlorine by Deacon’s process in presence of CuCl2 .
4 HCl(g) + O2 (g) CuCl2(s) → 2Cl 2 (g) + 2H 2O(g)
450o C
(vii) Formation of methane in presence of nickel. CO(g) + 3H 2 (g) Ni(s) → CH 4 (g) + H 2O(g)
(viii) Synthesis of ammonia by Haber’s process in presence of a mixture of iron and molybdenum.
N 2 (g) + 3H 2 (g) Fe(s)&Mo(s) → 2NH 3 (g)
450−500o C
(ix) Hydrogenation of vegetable oil in presence of nickel. Vegetable oil (l)+ H 2(g) Ni(S) → Ghee(s)
(x) Manufacture of methyl alcohol in presence of ZnO / Cr2O3 . CO(g) + 2H 2 (g) ZnO(g)2500C → CH 3 OH(g)
Cr2O3 (s)
Note : Positive catalyst increases the rate by lowering activation energy of reaction. Catalyst changes
the mechanism by changing the intermediate i.e. intermediate of low energy is formed. It increases
the rate by converting some inactive molecule into active one.
(4) Negative catalysis : There are certain, substance which, when added to the reaction mixture, retard the
reaction rate instead of increasing it. These are called negative catalyst or inhibitors and the phenomenon is
known as negative catalysis. Some examples are as follows.
(i) The oxidation of sodium sulphite by air is retarded by alcohal. Alcohol acts as a negative catalyst
2Na2SO3 (s)O2 (g) Alcohol(l) → 2Na2SO4 (s)
(ii) The oxidation of chloroform by air is retarded it some alcohol is added to it.
2CHCl3(l) + O2(g) Alcohol(l) → 2COCl2(g) + 2HCl(g)
(iii) The oxidation of benzaldehyde is retarded if some diphenyl amine is added. It acts as a negative catalyst.
2C6 H 5 CHO(l) + O2 (g) Diphenyl → 2C6 H 5 COOH(l)
amine(l )
(iv) Addition of small amount of acetanilide or glycerine slow down the decomposition of hydrogen peroxide.
(v) Tetra ethyl lead (TEL) is added to petrol to retard the ignition of petrol vapours on compression in an
internal combustion engine and thus minimise the knocking effect.
(5) Auto-catalysis : In certain reactions, one of the product acts as a catalyst. In the initial stages the reaction
is slow but as soon as the products come into existences the reaction rate increases. This type of phenomenon is
known as auto-catalysis. Some examples are as follows,
(i) The rate of oxidation of oxalic acid by acidified potassium permanganate increases as the reaction
progresses. This acceleration is due to the presence of Mn2+ ions which are formed during reaction. Thus
Mn2+ ions act as auto-catalyst. 5H 2C2O4 + 2KMnO4 + 3H 2SO4 → 2MnSO4 + K 2SO4 + 10CO2 + 8H 2O
(i) When nitric acid is poured on copper, the reaction is very slow in the beginning, gradually the reaction
becomes faster due to the formation of nitrous acid during the reaction which acts as an auto-catalyst.
(iii) In hydrolysis of ethyl acetate, acetic acid and ethyl alcohol are formed. The reaction is initially very slow
but gradually its rate increases. This is due to formation of acetic acid which acts as an auto-catalyst in this reaction.
(6) Induced catalysis : When one reaction influences the rate of other reaction, which does not occur under
ordinary conditions, the phenomenon is known as induced catalysis. Some examples are as follows,
(i) Sodium arsenite solution is not oxidised by air. If, however, air is passed through a mixture of the solution
of sodium arsenite and sodium sulphite, both of them undergo simultaneous oxidation. The oxidation of sodium
sulphite, thus, induces the oxidation of sodium arsenite.
(ii) The reduction of mercuric chloride (HgCl 2 ) with oxalic acid is very slow, but potassium permanganate is
reduced readily with oxalic acid. If, however, oxalic acid is added to a mixture of potassium permanganate and
HgCl 2 both are reduced simultaneously. The reduction of potassium permanganate, thus, induces the reduction of
mercuric chloride.
(7) Acid-base catalysis : According to the Arrhenius and Ostwald H+ or H– ion act as a catalyst.
(i) For example, Hydrolysis of an ester, CH 3COOC2 H5 (l) + H 2 O(l) H +or → CH 3 COOH(l) + C 2 H 5 OH(l)
OH −
(ii) Inversion of cane sugar, C12 H 22O11(l) + H 2O H+ → C6 H12O6 (l)+ C6 H12O6 (l)
Sugar Fructose Glucose
(iii) Conversion of acetone into diacetone alcohol,
CH 3COCH 3 (l) + CH 3COCH 3 (l) OH− → CH 3COCH 2 .C(CH 3 )2 OH(l)
(iv) Decomposition of nitramide, NH 2 NO2 (l) OH− → N 2O(g) + H 2O(l)
Note : All Bronsted acids and bases act as acid base catalysts.
Catalytic converter for an automobile : The catalytic converter in the exhaust systems of cars,
which converts polluting exhaust gases into non-toxic gases contains a heterogeneous catalyst.
Mixtures of transition metals and their oxides embedded in inert supports act as catalyst. When the gases
are passed through the catalyst bed, carbon monoxide (CO) and unburnt petrol are oxidised to carbon
dioxide and water while nitric oxide (NO) is reduced to N 2 as,
2CO + O2 Catalyst → 2CO2 ; Hydrocarbons Catalyst → CO2 + H2O ; 2NO Catalyst → N 2 + O2
O2
(Unburnt petrol)
Characteristics of catalysis.
The following are the characteristics which are common to must of catalytic reactions.
(1) A catalyst remains unchanged in mass and chemical composition at the end of the reaction.
(2) A small quantity of the catalyst is generally sufficient to catalyses almost unlimited reactions
(i) For example, in the decomposition of hydrogen peroxide, one gram of colloidal platinum can catalyses
108 litres of hydrogen peroxide.
(ii) In the some reaction the rate of the reaction is proportional to the concentration of the catalyst. For
example the acid and alkaline hydrolysis of an ester, the rate of reaction is proportional to the concentration of
H + or OH − ions. RCOOR' (l) + H 2O(l) H +or → RCOOH(l) + R ' OH(l)
OH −
(iii) In Friedel – craft’s reaction, anhydrous aluminium chloride is required in relatively large amount to the
extent of 30% of the mass of benzene, C6 H6 + C2 H5Cl AlCl3 → C6 H5C2 H5 + HCl
(iv) In certain heterogeneous reactions, the rate of reaction increases with the increase of area of the catalytic
surface.
(3) The catalyst can not initiate the reaction: The function of the catalyst is to alter the speed of the
reaction rather than to start it.
(4) The catalyst is generally specific in nature: A substance, which acts as a catalyst for a particular
reaction , fails to catalyse the other reaction , different catalysts for the same reactant may for different products.
Examples : Al 2 O3 C2 H 4 (g) + H 2O(g) Cu CO2 (g) + H 2 (g)
C2 H 5 OH(l) Al 2 O3
(Dehydration) HCOOH(l) (Dehydrogenation)
Cu CH 3CHO(g) + H 2 (g) CO(g) + H2O(g)
(Dehydrogenation) (Dehydration)
(5) The catalyst can not change the position of equilibrium : The catalyst catalyse both forward and
backward reactions to the same extent in a reversible reaction and thus have no effect on the equilibrium constant.
(6) Catalytic promoters : Substances which themselves are not catalysts, but when mixed in small quantities
with the catalysts increase their efficiency are called as promoters or activators.
(i) For example, in Haber’s process for the synthesis of ammonia, traces of molybdenum increases the activity
of finely divided iron which acts as a catalyst.
(ii) In the manufacture of methyl alcohol from water gas (CO + H 2 ), chromic oxide (Cr2O3 ) is used as a
promoter with the catalyst zinc oxide (ZnO) .
(iii) In the hydrogenation of oils, the activity of the catalyst nickel increases on adding small amount of copper.
(7) Catalytic poisons : Substances which destroy the activity of the catalyst by their presence are known as
catalytic poisons.
(i) For example, the presence of traces of arsenious oxide (As2O3 ) in the reacting gases reduces the activity of
platinized asbestos which is used as catalyst in contact process for the manufacture of sulphuric acid.
(ii) The activity of iron catalyst is destroyed by the presence of H 2S or CO in the synthesis of ammonia by
Haber’s process.
(iii) The platinum catalyst used in the oxidation of hydrogen is poisoned by CO .
Note : The poisoning of the catalyst is probably due to the preferential adsorption of poison on the
surface of the catalyst, thus reducing the space available for the adsorption of reacting molecules.
(8) Change of temperature alters the rate of catalytic reaction as it does for the same reaction in
absence of catalyst : By increasing the temperature, there is an increase in the catalytic power of a catalyst but
after a certain temperature its power begins to decrease. A catalyst has thus, a particular temperature at which its
catalytic activity is maximum. This temperature is termed as optimum temperature.
(9) A positive catalyst lowers the activation energy
(i) According to the collision theory, a reaction occurs on account of effective collisions between the reacting
molecules.
(ii) For effective collision, it is necessary that the molecules must possess a minimum amount of energy known
as activation energy (Ea).
(iii) After the collision molecules form an activated complex which dissociate to yield the product molecules.
(iv) The catalyst provides a new pathway involving lower amount of activation energy. Thus,
Ea Ea ⇒ – Ea ⇒ e–Ea/RT ⇒ k
⇒ RT RT Increases ⇒ Reaction speeds up
Decreases Increases Increases
Decreases
larger number of effective collisions occur in the presence of a catalyst in comparison to effective collisions at
the same temperature in absence of a catalyst. Hence the presence of a catalyst makes the reaction to go faster.
(v) Figure shows that activation energy Ea , in absence of a catalyst is higher than the activation energy Ea, in
presence of a catalyst.
(vi) ER and Ep represent the average energies of reactants and products. The difference gives the value of
∆G , i.e., ∆G = ER − EP Uncatalysed
complex
Chemical potential energy Energy Catalysed
barrier complex
Ea
E′a
ER Reactants ∆G° of
Initial (A+B) reaction
state
EP Products (C + D)
Final state
Reaction sequence
Theories of catalysis.
There are two theories of catalysis which is described as follows.
(1) Intermediate compound theory
(i) This theory was proposed by Clement and Desormes in 1806. According to this theory, the desired
reaction is brought about by a path involving the formation of an unstable intermediate compound, followed by its
decomposition into the desired end products with the regeneration of the catalyst.
(ii) The intermediate compund may be formed in either of two ways
(a) When the intermediate compound is reactive and reacts with the other reactants.
AB + X → BX + A
intermediate
BX + C → CB + X …….(i)
(b) When the intermediate is unstable and decomposes to give the final product.
A + B + X → ABX → AB + X …….(ii)
intermediate
Where, A, B and C are the reactant molecules and X is the molecule of the catalyst. The first type of
reaction sums up to, AB + C → CB + A
While the second to, A + B → AB in many cases, the intermediate compounds postulated to be formed
are known compounds and often their presence is detected.
(2) Adsorption theory
(i) This theory is applicable to reactions between gases in the presence of a solid catalyst. Some typical
examples are as follows.
(ii) The contact process for the oxidation of SO2 to SO3 with atmospheric oxygen in the presence of
platinum as the catalyst.
(iii) The Haber’s process for the synthesis of ammonia with iron as the catalyst.
(iv) Adsorption results in the loosening of the chemical bonds in the reactant molecules, so that their rupture
becomes easier. This is confirmed by the observed lower activation energies for heterogeneous catalytic reactions in
the presence of the catalysts as compared to that for the same reaction in the absence of the catalyst.
(v) The metals copper and nickel are found particularly suitable for reactions involving hydrogen gas. These
metals are known to strongly chemisorb hydrogen gas. Typical example includes the dehydrogenation of ethandol
vapours when passed over heated metal at 350o C . CH 3 CH 2 OH Ni → CH 3 CHO + H 2
350o C
(vi) Aluminium oxide in some physical forms is a good adsorbent for water vapour. It is also a useful catalyst
for reactions involving dehydration processes (i.e. processes involving the removal of water from molecules). For
example, formation of ethene from ethyl alcohol, CH 3CH 2OH Al2O3 → CH 2 = CH 2 + H2O
ethanol 350o C ethene
Mechanism of surface reactions.
(1) Heterogeneous catalytic reactions generally proceed via adsorption of reactants on the surface of the
catalyst.
(2) Mechanism of such surface reactions may be explained in terms of diffusion theory of catalysis. This
theory postulates the following sequence for gaseous reactions on a solid surface.
Step: (i) Diffusion of the reactants to the surface.
Step: (ii) Adsorption of the reactant molecules onto the surface.
Step: (iii) Actual chemical reaction on the surface.
Step: (iv) Desorption of the products from the surface.
Step: (v) Diffusion of the products away from the surface.
In generally, Step (iii) determines the rate of reaction. However step (ii) and (iv) may be rate determining.
(3) According to Langmuir-Hinshelwood, the rate of a catalytic reaction is proportional to the
concentration of the reacting species on the surface. For this, the reacting species must get adsorbed on the
neighboring sites.
(4) Another way in which two reacting molecules may react on a solid surface is that one of them gets
adsorbed and then the adsorbed molecules reacts with a molecule in the gas phase. This mechanism is called
Rideal mechanism.
Uncatalysed reaction + 2 Slow 2
Surface catalysed reaction
1. Diffusion to 2.Surface Reaction 3.Desorption of one 4. Desorption of other
the surface product molecule product molecule
Mechanisms for the surface reactions
Enzyme catalysis.
(1) Enzymes are complex nitrogenous substances secreted by low forms of vegetable animal organism.
(2) Enzymes are actually protein molecules of higher molecular mass.
(3) Enzymes form colloidal solutions in water and are very effective catalysts. They catalyse numerous
reactions, especially those connected with natural processes.
(4) Numerous reactions occur in the bodies of animals and plants to maintain the life process. These reactions
are catalysed by enzymes. The enzymes are thus, termed as bio-chemical catalysts and the phenomenon is
known as bio-chemical catalysis.
(5) Nitrogenase an enzyme present in bacteria on the root nodules of leguminous plants such as peas and
beans, catalyses the conversion of atmospheric N 2 to NH3 .
(6) In the human body, the enzyme carbonic anhydrase catalyses the reaction of CO2 with H 2O ,
CO2 (aq) + H 2O(l) H + (aq.) + HCO3− (aq.)
The forward reaction occurs when the blood takes up CO2 in the tissues, and the reverse reaction occurs when the
blood releases CO2 in lungs.
Catalysts in industry
Process Catalyst
Haber’s process for the manufacture ammonia. Finely divided iron. Molybdenum as promoter and
200 atmospheric pressure and 450-500oC temperature.
N2(g) + 3H2(g) 2NH 3 (g) Platinised asbestos and temperature 300o C.
Ostwald’s process for the manufacture of nitric acid.
4 NH3(g) + 5O2(g) → 4 NO(g) + 6H2O(g) Nitric oxide
2NO(g) + O2(g) → 2NO2(g) Platinised asbestos or vanadium pentoxide (V2O5 ) .
Temperature 400-4500 C.
4 NO2(g) + 2H2O(l) + O2(g) → 4HNO3(l)
Lead chamber process for the manufacture of Cupric chloride (CuCl 2 ) . Temperature 500o C.
sulphuric acid. Ferric oxide (Fe2O3 ) + chromic oxide as a promoter.
2SO2(g) + O2(g) 2SO3 (g) Temperature 400-600o C.
SO3(g) + H2O(l) → H2SO4(l)
Contact process for the manufacture of sulphuric
acid.
2SO2 (g) + O2 (g) 2SO3 (g)
SO3 (g) + H 2SO4 (l) → H 2S2O7 (l)
oleum
H 2 S2O7 (l) + H 2O(l) → 2H 2 SO4 (l)
Deacon’s process for the manufacture of chlorine.
4HCl(g) + O2 (g) → 2H 2O(l) + 2Cl2 (g)
Bosch’s process for the manufacture of hydrogen.
CO+ H2 + H2O(g) → CO2(g) + H2O(g)
water gas
Synthesis of methanol. Zinc oxide (ZnO) +chromic oxide as promoter. Pressure
200 atmopheres and temperature 250o C.
CO(g) + 2H 2 (g) → CH 3OH(l)
Nickel (finely divide). Temperature 150-200oC. High
Hydrogenation of vegetable oils. pressure.
Oil(l) + H 2 (g) → Vanaspati ghee (s) Invertase enzyme and zymase (yeast) enzyme.
Temperature 25-30o C. Conversion occurs in 2 or 3 days.
Manufacture of ethyl alcohol by fermentation of
molasses (sugar solution).
C12 H 22O11(l) + H 2O(l) Invertase →
C6 H12O6 (l)+ C6 H12O6 (l)
glucose fructose
C6 H12O6 (l) Zymase → 2C2 H 5 OH(l) + 2CO2 (l) Germinated barley (diastase enzyme). Temperature 50-
Manufacture of ethyl alcohol from starch. 60o C. Yeast (maltase and zyamase enzymes).
(a) Starch (l) Diastase → Maltose (l) Temperature 25-300 C.
(b) Maltose Maltase → Glucose Zyamase → Alcohol Mycoderma aceti. Temperature 25-30o C.
Manufacture of acetic acid from ethyl alcohol
Ferric oxide (Fe2O3 ) . Temperature 475oC and pressure
C2 H5OH(l) + O2 (g) → CH 3COOH(l) + H 2O(l) 200 atmosphere.
Bergius process for the synthesis of petrol from coal.
Coal + H 2 (g) → Mixture of hydrocarbons
Activity and selectivity.
(1) Activity : Activity is the ability of catalysts to accelerate chemical reaction, the degree of acceleration can
be as high as 1010 times in certain reactions. For example reaction between H 2 and O2 to form H 2O in presence of
platinum as catalyst takes place with explosive violence.
In absence of catalyst, H 2 and O2 can be stored indefinitely without any reaction.
(2) Selectivity : Is the ability of catalysts to direct reaction to yield particular products (excluding other).
CH 3
O
||
Example : (i) n − heptane Pt → (ii) CH3CH = CH2 BiMoO4 → CH2
= CHCH
Acrolein
toluene
Zeolite (shape selective catalysis).
(1) Zeolite are alumino–silicates of the general formula, M x / n[AlO2]x .(SiO2)y.mH2O , where, M may be simple
cation like Na + , K + or Ca 2+ , n is the charge on the simple cation, m is the number of molecules of water of crystallization.
(2) Some well known zeolites are as follows,
Erionite → Na2K2CaMg(AlO2)2(SiO2)2.6H2O
Gemelinite → Na2Ca(AlO2)2(SiO2)4.6H2O
Faujasite (natural) → Na56(AlO2)56(SiO2)136.250H2O
ZSM-5 → Hx[(AlO2)x(SiO2)96−x ].16H2O
Linde-A (synthetic) →[Na12(AlO2)12(SiO2)12.27H2O]8
(3) The characteristic feature of zeolites is the openness of the structure, which permits cavities of different sizes.
(4) The open structure is provided by silica in which aluminium occupies x/(x+y) fraction of the telrahedral sites.
(5) The negative charge of the aluminosilicate framework is neutralized by the replaceable cations.
(6) The void space forms more than 50% of the total volume, which is occupied by water molecules.
(7) The reaction- selectivity of zeolites depends upon the size of cavities (cages), pores (apertures) and the
distribution of pores in the structure. The pore size in zeolites generally varies from 260 pm to 740 pm.
(8) The building block of zeolites is a truncated octahedron. This is also called the sodalite cage (or β - cage).
(9) Tetrahedral atom denoted by open circles in fig (a) are present at the corners of polygons with the oxygen
atoms approximately half way between them.
(a) (b) (c)
(a) The sodalite (or β -) cage, (b) zeolite-A, (c) Faujasite.
(10) Zeolite have high porosity due to the presence of one, two, or three dimensional networks of
interconnected channels and cavities of molecular dimensions.
(11) Accordingly zeolite - A is formed by linking sodalite cages through double four-membered rings, Faujasite
(Zeolite X and Y) is formed by linking the sodalite cages through double six-membred rings.
(12) Many Zeolites occur in nature and they can be readily prepared in laboratories.
(13) There is a new class of highly siliceous zeolites with an optimal pore diameter of 550pm. ZSM-5 is one
such zeolite having the formula. [H x (AlO2 )x .(SiO2 )96−x ].16H 2O
(14) The zeolite catalyst ZSM-5 converts alcohols to gasoline (petrol) by dehydrating the alcohol and
producing a mixture of wide variety of hydrocarbons. The shape selectivity of this catalyst is demonstrated by data
given in table.
Input stock Input stock
Product (in %) methanol n-heptyl alcohol Product (in %) methanol n-heptyl alcohol
Methane i- Pentane
Ethane 1.0 0.0 Benzene 7.8 8.7
i-butane Toluene
n-butane 0.6 0.3 Xylenes 1.7 3.7
18.7 19.3 10.5 14.3
5.6 11.3 17.2 11.6
Colloidal state.
(1) The foundation of colloidal chemistry was laid down by an English scientist, Thomas Graham, in 1861.
The credit for the various advances in this field goes to eminent scientists like Tyndall, Hardy, Zsigmondy, N.R.
Dhar, S.S. Bhatnagar and others.
(2) Thomas Graham classified the soluble substances into two categories depending upon the rate of
diffusion through animal and vegetable membranes or parchment paper.
(i) Crystalloids : They have higher rate of diffusion and diffused from parchment paper.
Examples : All organic acids, bases and salts and organic compounds such as sugar, urea etc.
(ii) Colloids (Greek word, kolla, meaning glue-like) : They have slower rate of diffusion and can not diffused
from parchment paper. Examples : Starch, gelatin, gums, silicic acid and hdemoglobin etc.
(3) The above classification was discarded i.e., the terms colloid does not apply to a particular class of
substances but is a state of matter like solid, liquid and gas. Any substance can be brought into colloidal state.
(4) The colloidal state depends on the particle size. If is regarded as intermediate state between true solution
and suspension.
• True solution : In true solutions the size of the particles of
solute is very small and thus, these can not be
detected by any optical means and freely diffuse through
membranes. It is a homogenous system.
• Suspension : The size of particles is large and, thus it can True solution Colloidal solution Suspension
be seen by naked eye and do not pass through Size < 1 nm Size between Size > 100 nm
1-100 nm
filter paper. It is a heterogeneous system.
The size of different solutions are sometimes expressed in other Three types solutions
units also as given below :
Size (diameter) of particles in particles in different units
True solutions Colloids Suspensions Relation
<10–9m 10–9 m to 10–7m > 10 −7 m 1 nm = 10–9 m
<1nm 1 nm - 100 nm > 100 nm 1 Å = 10–10 m
<10 Å 10 Å – 1000 Å > 1000 Å 1 pm = 10–12 m
<1000 pm 1000 pm –105 pm >105 pm
The important distinguishing features of the three types of solutions
Property Suspension Colloid solution True solution
Nature Heterogeneous Heterogeneous Homogeneous
Particle size > 100 nm 1 nm – 100 nm < 1 nm
Separation by
Possible Not possible Not possible
(i) Ordinary filtration Possible Not possible
(ii) Ultra- filtration Settle under gravity Possible Do not settle
Settling of particles
Opaque Settle only on Transparent
Appearance Shows Does not show
Tyndall effect Does not diffuse centrifugation Diffuses rapidly
Diffusion of particles May show
Brownian movement Generally transparent Negligible
Shows
Diffuses slowly
Shows
(5) Roughly speaking the colloidal state is a heterogeneous dispersion of solute particles of size between true
solution and suspension.
Note : Colloidal particles do not settle down under the force of gravity even an long keeping.
The surface area of colloidal particle is very large in comparison to suspension.
Phases of colloids and their classification.
(1) Phases of colloids : We know that a colloidal solution is of heterogeneous nature. It consists of two
phases which are as follows
(i) Internal phase or Dispersed phase (Discontinuous phase) : It is the component present in small
proportion and is just like a solute in a solution. For example in the colloidal solution of silver in water (silver acts as
a dispersed phase)
(ii) External phase or Dispersion medium (continuous phase) : It is Dispersed phase
(Ag)
generally component present in excess and is just like a solvent in a solution. For
Dispersion
example, in the colloidal solution of silver in water. Water act as a dispersion medium (water)
A colloidal solution of silver in water
medium.
Note : When dispersion medium is a gas, the colloidal system is
called aerosol. When it is a liquid system is called solution
(hydrosol for water, alcosol for alcohol, benzosol for benzene)
Colloidal system is a two phase system. Colloidal system = Dispersed phase + Dispersion medium
(2) Classification of colloids : The colloids are classified on the basis of the following criteria
(i) Classification based on the physical state of the dispersed phase and dispersion medium
Depending upon the physical state of dispersed phase and dispersion medium whether these are solids, liquids or
gases, eight types of colloidal systems are possible.
Different types of colloidal systems
Dispersed phase Dispersion Colloidal System Examples
Medium
Liquid Gas Aerosol of liquids Fogs, clouds, mists, fine insecticide sprays
Solid Gas Aerosol of solids Smoke, volcanic dust, haze
Gas Liquid Foam or froth Soap lather. Lemonade froth, foam, whipped cream, soda
water
Liquid Liquid Emulsions Milk, emulsified oils, medicines
Solid Liquid Sols Most paints, starch in water, proteins, gold sol, arsenic
sulphide sol, ink
Gas Solid Solid foam Pumice stone, styrene rubber, foam rubber
Liquid Solid Gels Cheese, butter, boot polish, jelly, curd
Solid Solid Solid sols (coloured Ruby glass, some gem stones and alloys
glass)
Note : A colloidal system of gas in gas is not possible as gases are completely miscible and always
form homogenous true solution.
(ii) Classification based on Nature of interaction between dispersed phase and dispersion
medium: Depending upon the nature of interactions between dispersed phase and the dispersion medium, the
colloidal solutions can be classified into two types as (a) Lyophilic and (b) Lyophobic sols.
(a) Lyophilic colloids (water loving) : Substances such as proteins, starch and rubber whose molecules are
large enough to be close to the lower limit of colloidal range pass readily into colloidal state whenever mixed with
suitable solvent. Thus these colloids have strong interaction with the dispersion medium and are called lyophilic
colloids (hydrophilic when continuous phase is water)
“or”
“The colloidal solutions in which the particles of the dispersed phase have a great affinity for the dispersion
medium, are called lyophilic collodis.”
(b) Lyophobic colloids (water hateing) : Substance such as arsenic sulphide, ferric hydroxide, gold and other
metals, which are sparingly soluble and whose molecules are much smaller than the lower colloidal limit, change
into colloidal state by aggregation of many individual molecules. “These substances; therefore, do not pass into
colloidal state readily and are called lyophobic colloids (hydrophobic when continuous phase is water).”
“or”
“The colloidal solutions in which there is no affinity between particles of the dispersed phase and the
dispersion medium are called lyophobic colloids.”
Distinction between Lyophilic and Lyophobic Sols
Property Lyophilic (suspensoid) Lyophobic Sols (Emulsoid )
Surface tension Same as that of the medium
Viscosity Lower than that of the medium Same as that of the medium
Reversibility Irreversible
Stability Much higher than that of the medium Less stable
Visibility Reversible Particles can be detected under ultramicroscope.
More stable
Migration Particles migrate either towards cathode or
Particles can’t be detected even under anode in an electric field because they carry
Action of electrolyte ultramicroscope charge.
Coagulation takes place
Hydration Particles may migrate in either direction
Examples or do not migrate in an electric field No hydration
because do not carry any charge. Metals like Ag and Au, hydroxides like Al(OH)3 ,
Fe(OH)3 metal sulphides like AS2S3 etc.
Addition of smaller quantity of
electrolyte has little effect
Extensive hydration takes place
Gum, gelatin, starch, proteins, rubber
etc.
(iii) Classification based on types of particle of dispersed phase : Depending upon the type of the
particles of the dispersed phase, the colloids are classified as follows.
(a) Multimolecular colloids
• When on dissolution, atoms or smaller molecules of substances (having diameter less than 1nm) aggregate
together to form particles of colloidal dimensions, the particles thus formed are called multimolecular
colloids.
• In these sols the dispersed phase consists of aggregates of atoms or molecules with molecular size less than
1 nm.
• For example, sols of gold atoms and sulphur (S8 ) molecules. In these colloids, the particles are held
together by Vander Waal's forces. They have usually lyophilic character.
(b) Macromolecular colloids
• These are the substances having big size molecules (called macromolecules) which on dissolution form
size in the colloidal range. Such substances are called macromolecular colloids.
• These macromolecules forming the dispersed phase are generally polymers having very high molecular
masses.
• Naturally occurring macromolecules are starch, cellulose, proteins, enzymes, gelatin etc.
• Artificial macromolecules are synthetic polymers such as nylon, polythene, plastics, polystyrene etc.
• Their solutions are quite stable and resemble with true solution in many respects.
• They have usually lyophobic character.
• The molecules are flexible and can take any shape.
(c) Associated colloids
• These are the substances which on dissolved in a medium behave as normal electrolytes at low
concentration but behave, as colloidal particles at higher concentration due to the formation of
aggregated particles. The aggregates particles thus formed are called micelles.
• Their molecules contain both lyophilic and lyophobic groups.
• The colloidal behaviour of such substances is due to the formation of aggregates or clusters in solutions.
Such aggregated particles are called micelles.
Micelles
• Micelles are the cluster or aggregated particles formed by association of colloid in solution.
• The common examples of micelles are soaps and detergents.
• The formation of micelles takes place above a particular temperature called Kraft temperature (Tk ) and
above a particular concentration called critical micellization concentration (CMC).
• They are capable of forming ions.
• Micelles may contain as many as 100 molecules or more.
• For example sodium stearate (C17 H35COONa)is a typical example of such type of molecules.
• When sodium stearate is dissolved in water, it gives Na+ and C17 H35COO− ions.
C17 H35COONa C17 H35COO− + Na+ Na+ – Na+ –
Sodium stearate Stearate ion Na+ – Na+
–
The stearate ions associate to form ionic micelles of colloidal Na+ –
size.
• It has long hydrocarbon part of C17 H35 radical. Which is Na+ – Na+
lyophobic and COO− part which is lyophilic. –
• In the figure, the chain corresponds to stearate ion, – Na+
Aggregation of several ions to form ionic micelle
(C17 H35COO− ) . When the concentration of the solution is below from its CMC (10−3 mol L−1 ) , it
behaves as normal electrolyte. But above this concentration it is aggregated to behave as micelles.
• The main function of a soap is to reduce oily and greasy dirt to colloidal particles (an emulsion). Soap
therefore, are known as emulsifying agents.
• Some other examples of micelles are sodium palmitate (C15 H31COONa) , Sodium lauryl sulphate
[CH 3 (CH 2 )11 SO3O− Na + ] , Cetyl trimethyl ammonium bromide CH 3 (CH 2 )15 (CH 2 )3 N + Br − etc.
Note : Polydisperse and Monodisperse colloids : In multimolecular colloids, the colloidal
particles consist of aggregates of atoms or small molecules with diameters less than 10−9 m of 1 nm
Colloidal solutions in which colloidal particles are of different sizes are called polydisperse
colloids. For example, a gold sol may contain particles of various sizes having several atoms of
gold. The colloidal solutions in which all the colloidal particles are more or less of identical size are
monodisperse colloids.
General methods of preparation of colloids.
Lyophilic and lyophobic colloidal solutions (or sols) are generally prepared by different types of methods.
Some of the common methods are as follows.
(1) Preparation of Lyophilic colloids
(i) The lyophilic colloids have strong affinity between particles of dispersed phase and dispersion medium.
(ii) These colloidal solutions are readily formed by simply mixing the dispersed phase and dispersion medium
under ordinary conditions.
(iii) For example, the substance like gelatin, gum, starch, egg, albumin etc. pass readily into water to give
colloidal solution.
(iv) They are reversible in nature become these can be precipitated and directly converted into colloidal state.
(2) Preparation of Lyophobic colloids : Lyophobic colloids can be prepared by mainly two types of
methods.
(i) Condensation method : In these method, smaller particles of dispersed phase are condensed suitably to
be of colloidal size. This is done by the following methods.
(a) By oxidation : A colloidal solution of sulphur can be obtained by bubbling oxygen (or any other oxidising
agent like HNO3 , Br2 etc.) through a solution of hydrogen sulphide in water.
2H 2 S + O2 (or any other oxidising agent) → 2H 2O + 2S
(b) By reduction : A number of metals such as silver, gold and platinum, have been obtained in colloidal
state by treating the aqueous solution of their salts, with a suitable reducing agent such as formaldehyde, phenyl
hydrazine, hydrogen peroxide, stannous chloride etc. 2 AuCl 3 + 3SnCl2 → 3SnCl4 + 2Au
Gold sol
2 AuCl 3 + 3HCHO + 3H2O → 2Au + 3HCOOH + 6HCl
Gold sol
The gold sol, thus prepared, has a purple colour and is called purple of cassius.
(c) By hydrolysis : Many salt solutions are rapidly hydrolysed by boiling dilute solutions of their salts. For
example, ferric hydroxide and aluminium hydroxide sols are obtained by boiling solutions of the corresponding
chlorides. FeCl3 + 3H 2O → Fe(OH)3 + 3HCl
Colloidal sol
Similarly silicic acid sol is obtained by the hydrolysis of sodium silicate.
(d) By double decomposition : A sol of arsenic sulphide is obtained by passing hydrogen sulphide through a
cold solution of arsenious oxide in water. As 2O3 + 3H 2S → As 2S3 + 3H 2O
(e) By excessive cooling : A colloidal solution of ice in an organic solvent like ether or chloroform can be
prepared by freezing a solution of water in the solvent. The molecules of water which can no longer be held in
solution, separately combine to form particles of colloidal size.
(f) By exchange of solvent : Colloidal solution of certain substances such as sulphur, phosphorus, which are
soluble in alcohol but insoluble in water can be prepared by pouring their alcoholic solution in excess of water. For
example, alcoholic solution of sulphur on pouring into water gives milky colloidal solution of sulphur.
(g) By change of physical state : Sols of substances like mercury and sulphur are prepared by passing their
vapour’s through a cold water containing a suitable stabilizer such as ammonium salt or citrate.
(ii) Dispersion methods : In these methods, larger particles of a substance (suspensions) are broken into
smaller particles. The following methods are employed. Suspension
Driving Belt
(a) Mechanical dispersion
• In this method, the substance is first ground to coarse particles.
• It is then mixed with the dispersion medium to get a suspension. Discharge Discharge
• The suspension is then grinded in colloidal mill. Metal disc
Colloidal mill
• It consists of two metallic discs nearly touching each other and rotating
in opposite directions at a very high speed about 7000 revolution per minute.
• The space between the discs of the mill is so adjusted that coarse Metal ice
suspension is subjected to great shearing force giving rise to particles of electrodes
colloidal size.
Arc
• Colloidal solutions of black ink, paints, varnishes, dyes etc. are obtained
by this method. Water
(b) By electrical dispersion or Bredig’s arc method : This method is used to Bredig's arc method
prepare sols of platinum, silver, copper or gold.
• The metal whose sol is to be prepared is made as two electrodes which immerged in dispersion medium
such as water etc.
• The dispersion medium is kept cooled by ice.
• An electric arc is struck between the electrodes.
• The tremendous heat generate by this method and give colloidal solution.
• The colloidal solution prepared is stabilised by adding a small amount of KOH to it.
(c) By peptisation
• The process of converting a freshly prepared precipitate into colloidal form by the addition of suitable
electrolyte is called peptisation.
• The electrolyte is used for this purpose is called peptizing agent or stabilizing agent.
• Cause of peptisation is the adsorption of the ions of the electrolyte by the particles of the precipitate.
• Important peptizing agents are sugar, gum, gelatin and electrolytes.
• Freshly prepared ferric hydroxide can be
converted into colloidal state by shaking it with + + +
++ ++ ++
water containing Fe 3+ or OH − ions, viz. FeCl3 or Fe(OH)3 + Fe3+ + ++ ++ +
NH 4 OH respectively. ++ ++ ++
From + + +
Fe(OH)3 + FeCl3 →[Fe(OH)3 Fe]3+ + 3Cl − Precipitate electrolyte Colloidal particles
of Fe(OH)3 FeCl3
Precipitate electrolyte Colloidal sol of Fe(OH)3
• A stable sol of stannic oxide is obtained by adding Preparation of colloidal sol by peptisation
a small amount of dilute HCl to stannic oxide precipitates.
• Similarly, a colloidal solution of Al(OH)3 and AgCl are obtained by treating the corresponding freshly
prepared precipitate with very dilute solution of HCl and AgNO3 or KCl respectively.
• Gelatin stabilises the colloidal state of ice-cream.
• Lamp black is peptised by gums to form Indian ink.
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