GAS LAWS

Behavior of Gases

• Gases can expand to fill their container

• Gases can be compressed– Because of the space between

gas particles

• Compressibility: A measure of how much the volume of matter decreases under pressure

At room temp, the distance

between particles in an

enclosed gas is about 10

times the diameter of the

particle

Behavior of Gases• Gasses move in a

straight line path until they collide with other particles or the walls of the container

• The motion of gasses is constant and random

• There are no forces of attraction or repulsion between particles so gasses move freely

• Gasses take the shape of their container

Gas Pressure• Results from the collisions of gas particles with the walls

of their container– The more collisions taking place, the greater the

pressure– http://phet.colorado.edu/en/simulation/gas-properties – Units of Pressure: kPa, atm or mm Hg

Lower Pressure Higher Pressure

Factors that Affect Pressure

• Volume: The amount of space the gas occupies– Unit: Liters or m3

• Temperature: The average kinetic energy of the particles– Unit: Kelvin or C

• Number of Moles: The amount of particles present– Unit: mol (may have to convert g to mol)

Standard Temperature & Pressure

0C and 1 atm

or

273 K and 101.3 kPa

Boyle’s Law

Boyle’s Law

• The volume of a gas varies inversely with the pressure of a gas at constant temperature– At constant

temperature• As volume decreases,

pressure increases• As volume increases,

pressure decreases

P1V1 = P2V2

Boyle’s Law

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

CHARLES’ LAW

CHARLES’ LAW

• The temperature and volume of a gas are directly proportional if the pressure is held constant– At constant pressure

• As temperarure decreases, volume decreases

• As temperature increases, volume increases

CHARLES’ LAW

V1 = V2

T1 T2

Temperature MUST be in KELVIN when

doing gas law problems

A balloon is inflated in a room at 24C has a volume of 4.00 L. The balloon is then heated to a temperature of 58 C . What is the new volume if the pressure remains constant?

Gay-Lussac’s Law

• The pressure of a gas is directly proportional to the Kelvin temperature if the volume is constant– If temperature

increases, pressure increases

– If temperature decreases, pressure decreases

P1 = P2

T1 T2

Gay-Lussac’s Law

The gas in a used aerosol can is at a pressure of 103 kPa at 25C. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928C?

Combined Gas Law

• The law that describes the relationship among the pressure, temperature and volume of an enclosed gas

P1 x V1 = P2 x V2

T1 T2

Combined Gas Law

IDEAL GAS LAW

• The gas law that includes all four variables– Pressure, Volume, Temperature & Amount of

Gas

• Ideal Gas: Follows the gas laws at all conditions of pressure and temperature

IDEAL GAS LAW

PV = nRT

(1 atm)(22.4 L) = (1 mol)(R)(273 K)

R = 0.082 atmL/mol K

R = 8.31 LkPa/K mol R = 0.0821 Latm/Kmol

PV = nRT

IDEAL GAS LAW

When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain?

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?

R = 8.31 LkPa/K mol R = 0.0821 Latm/Kmol

PV = nRT

5) Calculate the number of moles of oxygen in a 12.5 L tank if the pressure is 25,325 kPa and the temperature is 22ºC.

6) Calculate the mass of nitrogen dioxide present in a 275 mL container if the pressure is 240.0 kPa and the temperature is 28ºC.

IDEAL GAS LAW

• Ideal Gas: No volume and no attraction between particles

• Does not exist• At most conditions of pressure &

temperature a real gas behaves like an idea gas

–Differ only at low temperatures or high pressures

IDEAL GAS LAW

Dalton’s Law of Partial Pressure

• At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases

• Ptotal = P1 + P2 + P3 + ….

Graham’s Law of Effusion

• States that the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass

http://www.youtube.com/watch?v=GRcZNCA9DxE

• 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 of lower molar mass diffuse and effuse

faster than gases of higher molar mass

Graham’s Law of Effusion

RateA = molar massB

RateB molar massA

Practice Problem: Compare the rates of effusion of nitrogen to helium. Which travels faster and by approximately how much?

Graham’s Law of Effusion