Gases
Gases
The forces of attraction between gas
molecules are very small
 Each molecule moves randomly;
 Each molecule moves freely and essentially
independently of other molecules.
gas and vapor
Gases-the molecules are relatively far apart



A gas expands spontaneously to fill its
container. the volume of a gas equals the
volume of its container.
Gases also are highly compressible: When
pressure is applied to a gas, its volume
readily decreases.
Two or more gases form a homogeneous
mixture regardless of the identities or
relative proportions of the gases
Pressure of a gas


SI unit of pressure: Pascal (Pa) 1 Pa = 1 N/m2
Barometer: measuring the atmospheric pressure.
Standard atmospheric pressure:
1 atm = 760 mmHg
=760 torr
= 101,325 Pa
=101.325 kPa
= 1.01325 bar

Manometer: measuring the pressure of
gases other than the atmospheric
The gas laws

Boyle’s law

Charles’s and Gay-Lussac’s law, or simply
Charles’s law

Avogadro’s law
The gas laws: Boyle’s law

PV = k, (一定量气体，恒T)
The volume of a fixed quantity of gas maintained at
constant temperature is inversely proportional to the
pressure.

P1V1=P2V2
The gas laws: Boyle’s law

A sample of N2 has a volume of 1.5 L at a
pressure of 600 torr. Calculate the volume of
the gas if the pressure is changed to 760 torr
at a constant temperature.
The gas laws: Charles’s law (Charles’s and
Gay-Lussac’s law)

V =bT （一定量气体，恒P）
The volume of a fixed amount of gas maintained at
constant pressure is directly proportional to its
absolute temperature.

Absolute zero on the Kelvin scale:

0 K = -273℃
V1
V2
=
T1
T2
10 ℃ = ? K
The gas laws: Avogadro’s principle
Volume (V) and moles (n):V = k n(恒温恒压)
The volume of a gas maintained at constant temperature
and pressure is directly proportional to the number of
moles of the gas.


V1 = V2
n1
n2
The ideal gas law
An ideal gas:
 (a) the molecules of an ideal gas do not interact
with one another
 (b) the combined volume of the molecules is
much smaller than the volume the gas occupies; for
this reason, we consider the molecules as taking up
no space in the container.
The ideal gas law
The ideal gas equation: PV = nRT
 R : gas constant, 0.0821 L atm mol-1 K-1,
or 8.314 m3 Pa mol-1 K-1
 T: K
 standard temperature and pressure (STP): 0℃ and
1atm
At STP, molar volume of a gas = 22.4 L

Gas Densities(d) and Molar Mass(M)
Questions :
The density of a gas is 3.38 g/L at 40 ℃ and
1.97 atm. What is its molar mass?
Exercise

(A)
(B)
(C)
(D)
(E)
What is the density of a gas at 76 torr and
37℃ (molar mass = 25 g/mol)
0.1 g/L
0.8 g/L
22.4 g/L
75 g/L
633 g/L
A
Gas stoichiometry
Gas mixtures and partial pressure


The total pressure of a mixture of gases equals the sum
of the pressures that each would exert if it were present
alone.
The pressure exerted by a particular component
of a mixture of gases is called the partial
pressure of that component.
Dalton’s law of partial pressures

Ptotal = P1 + P2 + …
partial pressure

The mole fraction: Xi= ni/ntotal

Pi= XiPtotal
Dalton’s law of partial pressures

A mixture of gases contains 2.00 mol of O2,
3.00 mol of N2, and 5.00 mol of He, the total
pressure of the mixture is 850 torr. What is
the partial pressure of each gas?
Exercise
(A) Boyle’s law

(B) Charles’s law

(C) Avogadro’s law

(D) Ideal gas law

(E) Dalton’s law
1. Total pressure of a gaseous mix is equal to the sum
of the partial pressure.
2. Volume is inversely proportional to pressure.
3. Volume is directly proportional to temperature
4. All gases have the same number of moles in the
same volume at constant temperature and pressure


Oxygen gas generated by the decomposition of
potassium chlorate is collected. The volume of oxygen
collected at 24°C and atmospheric pressure of 762
mmHg is 128 mL. Calculate the mass (in grams) of
oxygen gas obtained. The pressure of the water vapor
at 24°C is 22.4 mmHg.
The kinetic molecular theory of gases
5 assumptions:
 The volume occupied by the atoms or molecules in a
gas is negligibly small.
 The attractive or repulsive forces between the atoms
or molecules in a gas are negligible.
 Gases consist of molecules or atoms in continuous
random motion.
 Collision between these molecules or atoms in a gas
are elastic.
 The average kinetic energy of a molecule or atom in
a gas is directly proportional to the Kelvin
temperature of the gas. Any two gases at the same
temperature will have the same average kinetic energy.
The kinetic molecular theory of gases

Distribution of molecular speed (one gas at
different temperature)

the peak of
the curve
represents
the most
probable
speed, ump
root-mean square (rms) speed, urms, of the molecules: the
speed of a molecule possessing a kinetic energy identical
to the average kinetic energy of the sample. The rms
speed is not quite the same as the average speed, uav.
The kinetic molecular theory of gases

Distribution of molecular speed (different
gases at T)
The kinetic molecular theory of
gases

One of the results of the kinetic theory of gases is
that the total kinetic energy of a mole of any gas
equals 3/2RT.

Root -mean- square speed (urms):

3RT
urms 
M
The most probable speed of a gas molecule:
Gas diffusion and effusion :

effusion, which is the escape of gas
molecules through a tiny hole
diffusion, which is the spread of one
substance throughout a space or
throughout a second substance.

Graham’s law:

rates of effusion of the two gases are r1 and r2
and molar masses are ℳ1 and ℳ2
Gas diffusion and effusion :
Question: He leaks through a very small hole into a
vacuum at a rate of 3.22×10-5 m/s , how fast will
O2 effuse through the same hole under the same
conditions?
Deviation from ideal behavior

Real gases
At low temperature and/or high pressure, the
distances between the particles decrease
dramatically, the real volumes and forces can no
longer be ignored.
Deviation from ideal behavior

Real molecules, however, do have finite volumes and do
attract one another
van der Waals equation:
(P+an2/V2)(V-bn) = nRT
(P+an2/V2)(V-bn) = nRT
C
A
A
E

(A)
(B)
(C)
(D)
When a gas is collected over water, the
pressure is corrected by
Adding the vapor pressure of water
Multiplying by the vapor pressure of water
Subtracting the vapor pressure of water at
that temperature
Subtracting the temperature of the water
from the vapor pressure.
C