Gas Laws

What are gas laws??? What are gas laws??? Study of the relationships between pressure, volume, temperature, and amount of gases in a system Study of the relationships between pressure, volume, temperature, and amount of gases in a system

Boyles Law If the pressure of a gas is increased, the volume is decreased If the pressure of a gas is increased, the volume is decreased This is an inverse relationship This is an inverse relationship P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2

Boyles Law P 1 V 1 = P 2 V 2 Example: 16.0 L of hydrogen gas exerts a pressure of mm Hg at standard temperature. At what volume will the gas exert a pressure of mm Hg? (Be sure your units of volume and pressure agree!) Example: 16.0 L of hydrogen gas exerts a pressure of mm Hg at standard temperature. At what volume will the gas exert a pressure of mm Hg? (Be sure your units of volume and pressure agree!) (740.0)(16.0) = (550.0)(V 2 ) V 2 = 21.5 L

Charles Law If the temperature of a gas increases, the volume of a gas increases If the temperature of a gas increases, the volume of a gas increases This shows a direct relationship between V and T This shows a direct relationship between V and T Temperature must be in Kelvin! (Celsius + 273) Temperature must be in Kelvin! (Celsius + 273) V 1 = V 2 T 1 T 2 V 1 = V 2 T 1 T 2

Charles Law V 1 = V 2 T 1 T 2 Example: 16.0 L of oxygen gas occupies a gas cylinder at 0.00ºC. What will be the volume of the gas if the temperature is increased to 35.0ºC? (Hint: Celsius Kelvin) Example: 16.0 L of oxygen gas occupies a gas cylinder at 0.00ºC. What will be the volume of the gas if the temperature is increased to 35.0ºC? (Hint: Celsius Kelvin) _16.0_ 273 _V 2 _ 308 = V 2 = 18.1 L

Gay-Lussacs Law If the temperature of a gas increases, the pressure also increases If the temperature of a gas increases, the pressure also increases This is a direct relationship between T and P This is a direct relationship between T and P P 1 = P 2 T 1 T 2 P 1 = P 2 T 1 T 2

Gay-Lussacs Law P 1 = P 2 T 1 T 2 Example: If a gas at 25.0ºC and 1.00 atm is heated to 45.0ºC, then what is the new pressure? Assume constant volume Example: If a gas at 25.0ºC and 1.00 atm is heated to 45.0ºC, then what is the new pressure? Assume constant volume __1.00__ 298 _P 2 _ 318 = P 2 = 1.10 atm

Combined Gas Law Puts Boyle, Charles, and Gay- Lussacs Laws together Puts Boyle, Charles, and Gay- Lussacs Laws together P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2

Ideal Gas Law PV = nRT PV = nRT P = pressure P = pressure V = volume (use only L) V = volume (use only L) n = number of moles of gas n = number of moles of gas R = constant (.0821 atm-L/mol-K or 62.4 mmHg-L/mol-K) R = constant (.0821 atm-L/mol-K or 62.4 mmHg-L/mol-K) T = temperature in Kelvin T = temperature in Kelvin

Daltons Law of Partial Pressures The sum of the pressures of all gases present in a system equals the total pressure of the system The sum of the pressures of all gases present in a system equals the total pressure of the system P 1 + P 2 + P 3 + … = P t P 1 + P 2 + P 3 + … = P t

Grahams Law The rates of diffusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses The rates of diffusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses Normal language: lighter gases move through the air faster than heavier gases Normal language: lighter gases move through the air faster than heavier gases Example: helium moves faster than radon Example: helium moves faster than radon