UNIT 4GAS LAWS

Chemistry

CDO High School

Important Characteristics of Gases

1) Gases are highly compressible An external force compresses the gas sample and decreases its volume, removing the external force allows the gas volume to increase.2) Gases are thermally expandable When a gas sample is heated, its volume increases, and when it is cooled its volume decreases.3) Gases have high viscosity Gases flow much easier than liquids or solids.4) Most Gases have low densities Gas densities are on the order of grams per liter whereas liquids and solids are grams per cubic cm, 1000 times greater.5) Gases are infinitely miscible

Gases mix in any proportion such as in air, a mixture of many gases.

THE NATURE OF GASES

Three basic assumptions of the kinetic theory as it applies to gases:

1. Gas is composed of particles- usually molecules or atomsSmall, hard spheresInsignificant volume; relatively far apart from each other

No attraction or repulsion between particles

THE NATURE OF GASES

2. Particles in a gas move rapidly in constant random motionMove in straight paths, changing direction only when colliding with one another or other objects

Average speed of O2 in air at 20 oC is an amazing 1660 km/h! (1.6km=1mile)

THE NATURE OF GASES

3. Collisions are perfectly elastic- meaning kinetic energy is transferred without loss from one particle to another- the total kinetic energy remains constant

THE KINETIC THEORY OF GASES

Gas consists of large number of particles (atoms or molecules)

Particles make elastic collisions with each other and with walls of container

There exist no external forces (density constant)

Particles, on average, separated by distances large compared to their diameters

No forces between particles except when they collide

Remember the assumptions

VARIABLES THAT DESCRIBE A GASThe four variables and their common

units:

1. pressure (P) in kilopascals

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. amount (n) in moles

1. PRESSURE OF GAS

a measure of the force exerted by the gas on the walls of a container

The greater the number of collisions between gas particles and the wall the greater the pressure

PRESSURE CONVERSIONS

1 atm = 101.3 kPa = 760 mmHg = 760 torr

The pressure in Tucson 668 mmHg, what is that pressure in:

atmkPatorr

2. AMOUNT OF GASIncreasing the number of gas particles increases the number of collisionsthus, the pressure increases

PRESSURE AND THE NUMBER OF MOLECULES ARE DIRECTLY RELATED Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into

3. VOLUME OF GASAs volume decreases, pressure increases.

Thus, volume and pressure are inversely related to each other

4. TEMPERATURE OF GAS

Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related)

DENSITY OF GAS AT STP One mole of any gas at STP occupies 22.4 L.

The mass of one mole of a substance can be used with the molar volume to calculate the density of the gas as a g/L value.

What is the density of SO2 gas at STP, in g/L?

PRACTICE

What is the density, in g/L, of C2H6 at STP?

PRACTICE

What is the molar mass of a gas that has a density of 0.890 g/L at STP?

THE GAS LAWS

#1. BOYLE’S LAW

Gas pressure is inversely proportional to the volume, when temperature is held constant.

#2. CHARLES’S LAW

The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.

CONVERTING CELSIUS TO KELVIN

•Gas law problems involving temperature will always require that the temperature be in Kelvin.

Kelvin = C + 273

°C = Kelvin - 273

and

#3. GAY-LUSSAC’S LAW •The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.

#5. THE COMBINED GAS LAW

The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

P1 = Initial PressureV1 = Initial Volume T1 = Initial Temperature in KelvinP2 = Final PressureV2 = Final VolumeT2 = Final Temperature in Kelvin

The combined gas law contains all the other gas laws!

If the temperature remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Boyle’s Law

The combined gas law contains all the other gas laws!

If the pressure remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Charles’s Law

The combined gas law contains all the other gas laws!

If the volume remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Gay-Lussac’s Law

EXAMPLES

The volume of some amount of a gas was 1.00 L when the pressure was 10.0 atm; what would the volume be if the pressure decreased to 1.00 atm?

The volume of some amount of a gas was 1800 mL when the pressure was 98 kPa; what would the volume be if the pressure decreased to 400 mmHg?

A gas occupied a volume of 6.54 mL at 25°C what would its volume be at 100°C?

A gas occupied a volume of 3.2 L at 90oC what would be the temperature of the gas if the volume is increased to 5.0L ?

• A gas has a pressure of 750 torr at 15oC. If the pressure is increased 1025 torr, what is the new temperature?

A gas has a pressure of 250 kPa at 100 K. If the pressure is increased 3.5 atm, what is the new temperature?

A 1.00 L balloon at 25.0oC has a pressure of 750 mmHg. If the temperature is increased to 37.0oC and the pressure is decreased to 740 mmHg, what is the new volume?

0.85 L of a gas 125.0oC has a pressure of 1.25 atm. If the temperature is increased to 237.0oC and the pressure is decreased to 0.85 atm, what is the new volume?

AVOGADRO'S LAW The amount of gas, in moles, is directly

related to the volume of the gas.

n1 = Initial amount of gas in molesn2 = Final amount of gas in moles

1.75 mol of gas occupies a volume of 1.5 L what would be the volume if the amount of gas is decreased to 0.68 mol?

3.5 mol of gas occupies a volume of 300 mL what would be the volume if the amount of gas is increased to 5.8 mol?

#6. THE IDEAL GAS LAW #1

Equation: PV = nRTIdeal Gas Constant (R)

R = 0.08206 (L atm) / (mol K)

The other units must match the value of the constant, in order to cancel out.

#7. IDEAL GAS LAW 2

PVmm = gRT

g = mass, in gramsmm = molar mass, in g/mol

IDEAL GAS EQUATION #3

Density is mass divided by volume

PMr = dRT

d = densityMr= Molar Mass

#8 DALTON’S LAW OF PARTIAL PRESSURES

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

• P1 represents the “partial pressure”, or the contribution by that gas.

•Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.

Collecting a gas over water – one of the experiments in this unit involves this.

Connected to gas generator

If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3:

2 atm + 1 atm + 3 atm = 6 atm

Sample Problem 14.6, page 434

1 2 3 4

IDEAL GASES DON’T EXIST, BECAUSE:

1. Molecules do take up space

2. There are attractive forces between particles

- otherwise there would be no liquids formed

REAL GASES BEHAVE LIKE IDEAL GASES...

When the molecules are far apart.

The molecules do not take up as big a percentage of the spaceWe can ignore the particle

volume.This is at low pressure

REAL GASES BEHAVE LIKE IDEAL GASES…

When molecules are moving fastThis is at high temperature

Collisions are harder and faster.Molecules are not next to each other very long.

Attractive forces can’t play a role.

DIFFUSION IS:

Effusion: Gas escaping through a tiny hole in a container.

Both of these depend on the molar mass of the particle, which determines the speed.

Molecules moving from areas of high concentration to low concentration.Example: perfume molecules spreading across the room.

•Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

•Molecules move from areas of high concentration to low concentration.

•Fig. 14.18, p. 435

Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire…

Diffusion and effusion are explained by the next gas law: Graham’s