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 – –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 m 3 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 0  C and 1 atm or 273 K and kPa

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

P 1 V 1 = P 2 V 2 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

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 V 1 = V 2 T 1 T 2 Temperature MUST be in KELVIN when doing gas law problems A balloon is inflated in a room at 24  C 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

P 1 = P 2 T 1 T 2 Gay-Lussac’s Law The gas in a used aerosol can is at a pressure of 103 kPa at 25  C. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928  C?

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

P 1 x V 1 = P 2 x V 2 T 1 T 2 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 = atm  L/mol  K

R = 8.31 L  kPa/K  mol R = L  atm/K  mol 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 10 3 kPa. How many moles of helium does the sphere contain? A deep underground cavern contains 2.24 x 10 6 L of methane gas (CH 4 ) at a pressure of 1.50 x 10 3 kPa and a temperature of 315 K. How many kilograms of CH 4 does the cavern contain?

R = 8.31 L  kPa/K  mol R = L  atm/K  mol 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 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 P total = P 1 + P 2 + P 3 + ….

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

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

Rate A =  molar mass B Rate B molar mass A Practice Problem: Compare the rates of effusion of nitrogen to helium. Which travels faster and by approximately how much? Graham’s Law of Effusion