The Gaseous State of Matter - Columbia University

The Gaseous State
of Matter

Preparation for College Chemistry
Columbia University
Department of Chemistry

Chapter Outline

KMT
Gas Laws
Ideal Gas Equation
Gas Stoichiometry
Air Pollution

Preliminary Observations

Molar mass of water: 18g /mole
6.02x1023 molecules weigh 18g
Density of water: 1g/cc
18 g liquid water occupies 18mL
18 g gaseous water occupies 22,400mL

Kinetic Molecular Theory of Gases

KE = 1 m c 2= p 2 p=mc 1 mc2 = 3 kT
2 2m 22

v=+10cm/s -x +x
c=10cm/s
{v=-10cm/s
c=10cm/s

Wall

Kinetic Molecular Theory of Gases

Distribution of Molecular Speeds
Maxwell-Boltzmann Distribution

# Molecules 1.4 O2 at 25°C

1.2

1.0 O2 at 1000°C

0.8
0.6

0.4

0 200 600 1000 1400 1800

Molecular Speed (ms-1)

Graham’s Law of Effusion

At the same T and P, the rates of Effusion of
two gases are inversely proportional to their
densities or molar masses.

RategasA = d B = MB
RategasB d A M A

Naturally occurring Uranium : U-235 / U238 = 1 / 140

1st step: U + 6 F 235 UF6 238 UF6 (g)

R =235 -UF6 m =238 -UF6 352 = 1.0043
R238 -UF6 m235 -UF6 349

2nd step: Diffusion through thousands of membranes (cascades)

Gas Vacuum

3rd step: 235 UF6 235 U Fully enriched weapons-grade Uranium

State Variables

V = volume (liters, cm3, m3)
T = temperature (in K)
P = pressure (atmospheres, mmHg, kPa)

Torricelli’s barometer

760 torr
760 mmHg
76 cmHg
101.325 mbar
29.9 in. Hg
14.7 lb/in2 (PSI)
1 atm

At sea level

Hg height 150 km
air

Atmospheric Pressure

Boyle’s Law At Constant T
For an Ideal Gas
7

Pressure (atm) 6 P1 V1 = P2 V2

5 PV = C P1 = P2
V2 V1
4
T2 > T1
3

2 T2

1 T1 3 5 79
0 Volume (L)
1
0

Boyle’s Law At Constant T
For an Ideal Gas

Pressure (atm) 7 P = C Ê 1 ˆ
ËÁ V ¯˜
6
5 3 5 79 T2 > T1
4 1/V (L-1)
3
2

1
0

01

Boyle’s Law At Constant T
For an Ideal Gas
PV 7
T2 > T1
6 3 57
5 P 9
4
3
2

1
001

Charles’ Law At Constant P for an Ideal Gas

7 V1 = T1
V2 T2

Volume (L) 6

5 Vµ T

4

3 Absolute zero
2 -273°C

1

0 -300 -100 100 300 500
T (°C)

Gay-Lussac’s Law P1 = P2
T1 T2
At Constant V for an Ideal Gas Pµ T

7

6

Pressure (atm) 5 P = CT

4

3

2
1

0 -300 -100 100 300 500
T (°C)

Combined Gas Laws

Charles’ Boyle’s

V1 = V2 P1 V1 = P2 V2
T1 T2 P2 V2
T2
P1 V1 =
T1

V2 = V1 P1 T2
P2 T1

STP Conditions

Reference Points for T and P for comparison
Standard Temperature: 273.15 K= 0°C
Standard Pressure: 1 atm

Dalton’s Law of Partial Pressures

Ptot = P1 + P2 + P3 + ...

where P1 is the partial pressure of gas 1, etc...
Pn = XnPtotal

Xn = nn Molar fraction of gasn

n1 + n2 + n3 + ...

Pgas = Ptotal – PH2O (table 11.3 p. 387)

wtehmepreerPatHu2rOei.sMthoestvoafptoern pressure of water at the specified
used in collection of insoluble gases

over water. In open systems, Ptotal = Patm

1809

Gay-Lussac’s Law of combining volumes

“When measured at the same T and P, the ratios of the V
of reacting gases are small whole numbers”

1811

Avogadro’s Law

“Equal volumes of different gases at the same T and P contain
the same number of molecules”

Consequences of Avogadro’s Law

1. Explanation of Gay-Lussac’s combining volumes
law. Diatomic nature of elemental gases.

2. Method for determining molar masses of gases.
The molar Volume.

3. Firm foundation of KMT: gases consists of
microscopic particles

d= m Density of Gases dT,P
V gas
But V = f (P, T)

Gas STP Gas M(g/mol) STP
M(g/mol) d(g/L) d(g/L)
H2 H2S 34.09
CH4 2.016 0.900 HCl 36.46 1.52
NH3 F2 38.00 1.63
C2 H2 16.04 0.716 CO2 1.70
17.03 0.760 C3 H8 44.01
HCN O3 44.09 1.96
CO 26.04 1.16 SO2 48.00
N2 Cl2 1.97
air 27.03 1.21 64.07 2.14
O2 2.86
28.01 1.25 70.90 3.17

28.02 1.25

28.9 1.29
32.00 1.43

Ideal Gas Equation Equation of State

Vµ 1 V µ= R nT PV = nRT
P P

Vµ n

Vµ T M = mRT d= PM
PV = m RT PV RT
M

For one mole of a gas at STP, R constant:

(1 atm)(22.4L) L-atm
R=
= 0.082

273K mol-K

Ideal Gas Equation

The ideal gas constant has energy/mol degrees dimensions

[R] [pressure][Volume] [force][volume]

= =

[temperature][mol] [area][temperature][mol]

[force][length] [energy]

[R] = =

[temperature][mol] [temperature][mol]

R = 8.134 J mol-1 K-1 ~ 2 Cal mol -1 K-1

Gas Stoichiometry

Concentrated nitric acid acts on copper and produces nitrogen
dioxide and dissolved copper. 6.80 g Cu is consumed and NO2 is
collected at a pressure of .970atm and a temperature of 45°C
(318 K) . Calculate the volume of NO2 produced.

Cu(s) + 4H+ + 2NO3- (aq) Cu+2 (aq) + 2NO2 (aq) + 2H2O

6.80 g Cu x 1 mol Cu 2 mol NO2 = 0.214 mol NO2
x
63.55 g Cu 1 mol Cu

V = n R T = 5.76 L NO2
P

Real Gases

Follow the ideal gas law at sufficiently low densities
o Gas molecules attract one another
o Gas molecules occupy a finite volume

Both factors increase in importance when the
molecules are close together (high P. low T).

Deviations from ideality are quantified by

the Compressibility factor z z = PV
nRT

Real Gases

Compressibility factor Intermolecular Forces N2 H2
2.0
1.5

1.0 Ideal Gas
0.5 CH4

0
0 200 400 600 800
P (atm)

Nitrogen at several T

Compressibility factor 2.0 25 °C
1.5
1.0 600 °C
0.5 Ideal Gas
00
-100 °C

200 400 600 800
P (atm)

Van der Waals Equation (1873)

Ê P + a n2 ˆ (V - nb) = nRT
ËÁÁ V2 ¯˜˜

b = constant representing volume excluded per mole
of molecules

a = depends on the strength of attractive forces

n 2 Proportional to reduction of wall collisions
V 2 due to cluster formation.

Air Pollution

Upper and Lower Atmosphere Ozone
Sulfur Dioxide
Nitrogen Oxides
Green House Effect

Upper atmosphere Ozone

O2 hn 2O Allotropic Transformation
O2 + O O3

O3 hn O2 + O + heat Ozone shield

CCl3F hn CCl2F .+ Cl . Ozone Layer Destruction

Cl . + O3 ClO . + O2 Chain propagation
ClO . + O O2 + Cl .