13/14 Semester 2
Physical Chemistry I
(TKK-2246)
Instructor: Rama Oktavian
Email: rama.oktavian86@gmail.com
Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11
Outlines
1. Gas structure
2. Kinetic theory of gas
3. Calculation of the gas pressure
4. Dalton’s law in kinetic theory of
gas
Learning check
Molar mass of gas
In an experiment to measure the molar mass of a gas, 250 cm3
of the gas was confined in a glass vessel. The pressure was 152
Torr at 298 K and, after correcting for buoyancy effects, the mass
of the gas was 33.5 mg. What is the molar mass of the gas?
Learning check
Dalton’s partial pressure
A gas mixture consists of 320 mg of methane, 175 mg of argon,
and 225 mg of neon. The partial pressure of neon at 300 K is 8.87
kPa. Calculate
(a) the volume and (b) the total pressure of the mixture.
Learning check
Dalton’s partial pressure
A vessel of volume 22.4 dm3 contains 2.0 mol H2and 1.0 mol N2 at 273.15 K
initially. All the H2 reacted with sufficient N2 to form NH3. Calculate
the partial pressures and the total pressure of the final mixture.
Gas structure
1. In gases, the particles are very spread out
2. They are moving very quickly in different directions
3. They are not arranged in any pattern
4. They are changing places all of the time.
Gas structure
1. A gas will fill the whole volume of its container.
2. A gas is easily compressed.
3. The speed of the particles in a gas increases as the temperature increases
Kinetic theory of gases
•
Kinetic theory of gas observes molecular motion in gases
•
In the kinetic model of gases we assume that the only contribution to the energy
of the gas is from the kinetic energies of the molecules
The pressure that a gas exerts is caused
by the collisions of its molecules with the
walls of the container.
Kinetic theory of gases
1. Gases are made of tiny particles far apart relative to
their size:
Volume occupied by the molecules is inconsequential
Volume is mostly space
Explains why gases are compressible
Kinetic theory of gases
2. Gas particles are in continuous, rapid, random
motion
As a result there are collisions with other
molecules or with the wall of the container
Creates pressure
Increase in temperature increases the
movement of the molecules and thus the
pressure exerted by the gas
Kinetic theory of gases
3. There are no attractive forces between molecules under normal
conditions of temperature and pressure
Gas molecules are moving too fast
Gas molecules are too far apart
Intermolecular forces are too weak
Kinetic theory of gases
4. Collisions between gas particles and between particles and
container walls are elastic collisions.
 Collisions in which there is no net loss of total kinetic energy
 Kinetic energy can be transferred between two particles during
collisions
 Total kinetic energy remains the same as long as temperature
remains the same
Kinetic theory of gases
5. All gases at the same temperature have the same average
kinetic energy. The energy is proportional to the
absolute temperature.
Absolute temperature = Kelvin temp scale
Ke = ½ mv2
Ke = the kinetic energy
m = mass
v = the velocity
Kinetic theory of gases
Pressure and molecular speed relation
1
pV  nMc 2
3
(1)
Where M = mNA, the molar mass of the molecules, and c is the root mean
square speed of the molecules, the square root of the mean of the squares of the
speeds, v, of the molecules:
c v
2 12
(2)
Kinetic theory of gases
Pressure and molecular speed relation
Justification
Consider the movement of gas
the momentum before collision is
the momentum after collision is
mvx
 mvx
the change in momentum is the difference between final and initial momentum
 2m vx
Kinetic theory of gases
Pressure and molecular speed relation
Justification
The distance that molecule can travel along the x-axis in
an interval ∆t is written as
vx t
if the wall has area A, then all the particles
in a volume
will reach the wall
Avx t
Kinetic theory of gases
Pressure and molecular speed relation
Justification
The number density of particles is
nNA V
where n is the total amount of molecules in the
container of volume V and NA is Avogadro’s
constant
The number of molecules in the volume
nNA V
x
Avx t
Avx t
Kinetic theory of gases
Pressure and molecular speed relation
Justification
At any instant, half the particles are moving to the right
and half are moving to the left
Therefore the number of molecules will become
1
nN A Av x t V
2
The total momentum change within interval Δt is
nN A Av x t
x
2V
2m vx
Kinetic theory of gases
Pressure and molecular speed relation
Justification
The total momentum change within interval Δt is
nN A Av x t
x
2V
2m vx
nm ANAvx2 t nMAvx2 t


V
V
Where M = mNA
Kinetic theory of gases
Pressure and molecular speed relation
Justification
Rate of change of momentum can be written as total
momentum divided by time interval
2
x
nMAv
V
rate of change of momentum is equal to the force
(by Newton’s second law of motion)
Kinetic theory of gases
Pressure and molecular speed relation
Justification
the pressure, the force divided by the area, is
rate of change of momentum is equal to the force
(by Newton’s second law of motion)
Not all the molecules travel with the same velocity, so
the detected pressure, p, is the average (denoted ... )
of the quantity just calculated
Kinetic theory of gases
Pressure and molecular speed relation
Justification
To write an expression of the pressure in terms of the root
mean square speed, c, we begin by writing the speed of a
single molecule, v, as
v2  vx2  vy2  vz2
c v
2 12
c 2  v 2  v x2  v y2  v z2
because the molecules are moving randomly, all three averages are the same,
it follows
c 2  3 v x2
Kinetic theory of gases
Pressure and molecular speed relation
Justification
c 2  3 v x2
v
2
x
1 2
 c
3
1
pV  nMc 2
3
Kinetic theory of gases
Pressure and molecular speed relation
Using Boyle’s Law and ideal gas Law
1
nRT  nMc 2
3
the root mean square speed of the molecules in a gas at a temperature T must
be
the higher the temperature, the higher the root mean square speed of the
molecules, and, at a given temperature, heavy molecules travel more slowly than
light molecules
Kinetic theory of gases
Pressure and kinetic energy relation
Kinetic energy of molecule is defined as
1 2
  mc
2
1
pV  nMc 2
3
2
pV  nN A
3
M = mNA
N = nNA
2
pV  N
3
Kinetic theory of gases
Pressure and kinetic energy relation
Using Boyle’s Law and ideal gas Law
2
nRT  N
3
3 RT

2 NA
3
  kT
2
k is Boltzmann constant
k = 1.3806488 × 10-23 m2 kg s-2 K-1
Kinetic theory of gases
The Speed of Molecules in Air
Air is primarily a mixture of nitrogen N2 (molecular mass = 28.0 g/mol) and
oxygen O2 (molecular mass = 32.0 g/mol). Assume that each behaves as an
ideal gas and determine the speeds of the nitrogen and oxygen molecules when
the temperature of the air is 293 K and determine the kinetic energy contained
in that molecule
3
  kT
2
Kinetic theory of gases
Dalton’s law of partial pressure
In a mixture of gases the total pressure is the sum of the forces per unit
area produced by the impacts of each kind of molecule on a wall of a
container