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
2
mc =
2
p2
p=mc
2m
1
3
2
mc  kT
2
2
v=+10cm/s
-x
c=10cm/s
+x
{
v=-10cm/s
c=10cm/s
Wall
Kinetic Molecular Theory of Gases
# Molecules
Distribution of Molecular Speeds
O2 at 25°C
1.4
1.2
1.0
O2 at 1000°C
0.8
0.6
0.4
0
200
600
1000
1400
1800
Molecular Speed
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

RategasB
dB

dA
MB
MA
Naturally occurring Uranium : U-235 / U238 = 1 / 140
1st step: U + 6 F
R235UF6

R238UF6
235 UF
6
m238UF6
m235UF6
238 UF
6 (g)
352

 1.0043
349
2nd step: Effusion through thousands of membranes (cascades)
Vacuum
Gas
3rd step:
235
UF
6
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
150 km
Hg height
air
Atmospheric Pressure
Boyle’s Law
At Constant T
For an Ideal Gas
7
6
Volume (L)
5
PxV=k
P1 x V1 = P2 x V2
4
3
P1
2
V2
1
0
0 1
3
5
9
7
Pressure (atm)
=
P2
V1
Charles’ Law
At Constant P for an Ideal Gas
V1
V T
T1
7
Volume (L)
6
5
V = kT
4
3
Absolute zero
2
-273°C
1
0
-300
-100
100
300
500
T (°C)
=
V2
T2
Gay-Lussac’s Law
At Constant V for an Ideal Gas
P T
7
P1
T1
Pressure (atm)
6
5
P = kT
4
3
2
1
0
-300
-100
100
300
500
T (°C)
=
P2
T2
Combined Gas Laws
Charles’
V1
T1
=
Boyle’s
V2
P1 V1 = P2 V2
T2
P1 V1
T1
V2
=
P2 V2
T2
=
V1 P1 T2
P2 T1
STP Conditions
Reference Points for T and P for comparison
Standard Temperature: 273.15 K= 0.00°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 = Xn Ptotal
Xn =
nn
Molar fraction of gasn
n1 + n2 + n3 + ...
Pgas = Ptotal – PH2O
where PH2O is the vapor pressure of water at the specified
temperature. Most often 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
V
 cons tan t
n
“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
Density of Gases
d=
m
T,P
gas
d
But V = f (P, T)
V
Gas
H2
CH4
NH3
C2 H2
HCN
CO
N2
air
O2
STP
M(g/mol) d(g/L)
0.900
2.016)
16.04
17.03
26.04
27.03
28.01
28.02
28.9
32.00
0.716
0.760
1.16
1.21
1.25
1.25
1.29
1.43
Gas
M(g/mol)
STP
d(g/L)
H2 S
HCl
F2
34.09
36.46
38.00
1.52
1.63
1.70
CO2
44.01
44.09
48.00
1.96
C3 H8
O3
SO2
Cl2
64.07
70.90
1.97
2.14
2.86
3.17
Ideal Gas Equation Equation of State
1
nT
V  nT
P
V =R
nT
PV = nRT
P
PV = m RT
M
mRT
=
M
PV
d=
For one mole of a gas at STP, R constant:
R =
(1 atm)(22.4L)
273K
= 0.082
L-atm
mol-K
PM
RT
Ideal Gas Equation
The ideal gas constant has energy/mol degrees dimensions
[R] =
[pressure][Volume]
[temperature][mol]
[R] =
[force][length]
[temperature][mol]
=
[force][volume]
[area][temperature][mol]
=
[energy]
[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)
6.80 g Cu x
Cu+2 (aq) + 2NO2 (aq) + 2H2O
1 mol Cu
63.55 g Cu
V =
x
nRT
2 mol NO2
1 mol Cu
= 0.214 mol NO2
= 5.76 L NO2
P
http://www.sp.uconn.edu/~terry/229sp98/Ncycleanim.html
Real Gases
Follow the ideal gas law at sufficiently low densities

Gas molecules attract one another

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
PV
z =
nRT
Real Gases Intermolecular Forces
Compresibility ratio
2.0
N2
1.5
H2
Ideal Gas
1.0
CH4
0.5
0
0
200
400
600
800
P (atm)
Nitrogen at several T
Compresibility ratio
2.0
25 °C
1.5
600 °C
Ideal Gas
1.0
-100 °C
0.5
0
0
200
400
600
800
P (atm)
Van der Waals Equation

n2 

P  a 2 
V  nb  nRT

V 
b = constant representing volume excluded per mole
of molecules
a = depends on the strength of attractive forces
2
n Proportional to reduction of wall collisions
2
V due to cluster formation.
Air Pollution
O2
l
2O
O3
O2 + O
O3
l
CCl3F
Allotropic Transformation
O2 + O + heat
l
CCl2F +
Cl .
Cl . + O3
ClO . + O2
ClO . + O
O2 + Cl .
Ozone shield
Ozone destruction