C8 REACTION KINETICS

• The equation can take the form of a linear equation

ln k   - Ea  1   ln A
R  T 

y= m x +c

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• From the equation, the graph of ln k versus 1/T
can be plotted as a linear graph :
Gradient  - Ea
R
ln k Interception on the y axis  ln A

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Example :

The rate constants for the decomposition of dinitrogen
pentoxide at different temperature are given below.

Temperature (K) K (s-1)
298 3.55 x 10-5
308 1.26 x 10-4
318 2.8 x 10-4
328 1.41 x 10-3
338 2.82 x 10-3

By using a graphical method, calculate

(a) the activation energy (Ans : 102.5 kJmol-1)

(b) The Arrhenius constant (Ans : 3.31 x 1013 s-1)

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ANSWER

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ANSWER

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ANSWER

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• The rate constant of a reaction varies with temperature.

If the rate constant at temperature T1 is given, the rate

constant at T2 can be calculated by using the Arrhenius

equation. Ea
RT1
ln k1  ln A -

ln k 2  ln A - Ea
RT2

ln k1 - ln k 2  Ea  1 - 1 
R T2 T1

ln k1  Ea  1 - 1 
k2 R T2 T1

• This equation can be used to calculate Ea if rate 107
constant at two different temperatures are known

Example:
Consider the following reaction:

2HI(g)  H2(g)  I2 (g)

At 227oC the rate constant of the reaction is
5.71 x 10-7 dm3mol-1min-1 . At 327oC the rate
constant is 6.6 x 10-4 dm3mol-1min-1 . Calculate the
activation energy for this reaction.

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ANSWER

ln k1 = E ( 1 − 1 )
k2 R T2 T1

ln 5.71 × 10−7 = E ( 1 − 1 )
6.6 × 10−4 8.314 600.15 500.15

E = 176.00 kJ mol−1

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