Chapter 14THE BEHAVIOR OF GASES

Properties of Gases

Compressibility – a measure of how much the volume of matter decreases under pressure

Gases are easily compressed because of the space between the particles in a gas

Factors Affecting Gas Pressure

1. The amount of gas

2. Volume

3. Temperature

1. Amount of Gas

When a gas is pumped into a container:

pressure increases

Number of collisions increase

2. Volume

When volume decreases, pressure increases (inverse relationship)

If volume is doubled, pressure is halved

3. Temperature (Kelvin)

As temperature increases, pressure increases (proportional)

If temperature (Kelvin) is doubled, pressure is doubled

Standard Temperature and Pressure (STP)

The Gas Laws

1. Boyle’s Law: Pressure and Volume

2. Charles’s Law: Volume and Temperature

3. Gay-Lussac’s Law: Pressure and Temperature

4. The Combined Gas Law

1. Boyle’s Law:Pressure and Volume

As the pressure increases, volume decreases, if temperature is constant

Inverse relationship

Table T

P1 x V1 = P2 x V2

Boyle’s Law

Graphs based on Boyle’s Law

Volume versus pressure

Sample Exercise A balloon contains 30.0 L of helium gas at 103 kPa. What is the

volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (temperature remains constant)

Answer: 124 Liters

Practice Exercise

Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?

Answer: 6.48 Liters

2. Charles’s Law:Volume and Temperature

As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant

Direct relationship

V1 = V2

T1 T2

Illustration of Charles’s Law

Volume of an enclosed gas as a function of temperature at constant pressure

The dashed line is an extrapolation to temperatures at which the substance is no longer a gas

Sample Exercise

A balloon, inflated in an air-conditioned room at 27C, has a volume of 4.0L. The balloon is then heated to a temperature of 57C. What is the new volume of the balloon if the pressure remains constant?

Answer: 4.4 liters

Practice Exercise

If a sample of gas occupies 6.8L at 327C, what will its volume be at 27C if the pressure does not change?

Answer: 3.4 Liters

3. Gay-Lussac’s Law:Pressure and Temperature As the temperature of a gas increases, pressure

increases, if volume is constant

Direct relationship

P1 = P2

T1 T2

Sample Exercise

A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K ?

Answer: 2.58 kPa

Practice Exercise

The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure is 225 kPa. What is the temperature of air in the tire? Assume that the volume is constant.

Answer: 341 Kelvin

4. The Combined Gas Law

Sample Exercise

A 5.00 L air sample has a pressure of 107 kPa at a temperature of -50°C. If the temperature is raised to 102°C and the volume expands to 7.00 L, what will the new pressure be?

Answer : 129 kPa

Sample Exercise

The volume of a gas filled balloon is 30.0 L and 313 K and 153 kPa pressure. What would the volume be at standard temperature and pressure?

Answer : 39.5 Liters

Diffusion – the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout

Effusion – a gas escapes through a tiny hole in its container

Gases with a lower molar mass (g/mol) diffuse and effuse faster than a gas with a higher molar mass.

Ideal Gases and Real Gases1. Ideal Gases Particles have no volume There is no attraction between molecules

Ideal gases do not exist (kind of: H2 and He behave Ideally)

Needs high temperature and low pressure

2. Real Gases Have volume There are attractions between molecules (can

condense) Needs low temperature and high pressure

Ideal Gases

Calculates the number of moles (n) of a contained gas

PV = nRT

Ideal gas constant (R) = 8.31

Sample Exercise

A deep underground cavern contains 2.24 x 106

L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain?

Practice Problems

A child’s lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37°C? Use a molar mass of 29 grams (per mole) for air, which is about 20% O2 (32 g/mol) and 80% N2 (28 g/mol)