Physical Chemistry I(TKK-2246)

13/14 Semester 2

Instructor: Rama OktavianEmail: rama.oktavian86@gmail.comOffice 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 gases1. 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 fastGas molecules are too far apartIntermolecular 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 gasesPressure and molecular speed relation

2

31 nMcpV (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:

212vc (2)

Kinetic theory of gasesPressure and molecular speed relation

Justification

Consider the movement of gas

the momentum before collision isxmv

the momentum after collision isxmv

the change in momentum is the difference between final and initial momentum

xmv2

Kinetic theory of gasesPressure and molecular speed relation

JustificationThe distance that molecule can travel along the x-axis in an interval ∆t is written as

if the wall has area A, then all the particles in a volume

tvx

tAv x will reach the wall

Kinetic theory of gasesPressure and molecular speed relation

JustificationThe number density of particles is

where n is the total amount of molecules in the container of volume V and NA is Avogadro’s constant

VnN A

The number of molecules in the volume tAv x

VnN A x tAv x

Kinetic theory of gasesPressure and molecular speed relation

JustificationAt any instant, half the particles are moving to the right and half are moving to the left

Therefore the number of molecules will become

VtAvnN xA 21

The total momentum change within interval Δt is

VtAvnN xA

2

x xmv2

Kinetic theory of gasesPressure and molecular speed relation

JustificationThe total momentum change within interval Δt is

VtAvnN xA

2

x xmv2

VtnMAv

VtvnmAN xxA

22

Where M = mNA

Kinetic theory of gasesPressure and molecular speed relation

JustificationRate of change of momentum can be written as total momentum divided by time interval

VnMAv x

2

rate of change of momentum is equal to the force (by Newton’s second law of motion)

Kinetic theory of gasesPressure and molecular speed relation

Justificationthe 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 gasesPressure and molecular speed relation

JustificationTo 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

2222zyx vvvv

212vc 22222zyx vvvvc

because the molecules are moving randomly, all three averages are the same, it follows

22 3 xvc

Kinetic theory of gasesPressure and molecular speed relation

Justification 22 3 xvc

22

31 cvx

2

31 nMcpV

Kinetic theory of gasesPressure and molecular speed relation

2

31 nMcnRT

Using Boyle’s Law and ideal gas Law

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 gasesPressure and kinetic energy relation

2

21 mc

Kinetic energy of molecule is defined as

2

31 nMcpV M = mNA

AnNpV32

N = nNA

NpV32

Kinetic theory of gasesPressure and kinetic energy relation

NnRT32

Using Boyle’s Law and ideal gas Law

ANRT

23

kT23

k is Boltzmann constant

k = 1.3806488 × 10-23 m2 kg s-2 K-1

Kinetic theory of gasesThe 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

kT23

Kinetic theory of gasesDalton’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