2Boyle’s LawStates that the volume of a given amount of gas held at a constant temperature varies inversely with the pressure.P1V1 = P2V2Example problemA sample of helium gas in a balloon is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L?
3Charles’s LawStates that the volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure.V1/T1 = V2/T TK = TCExample ProblemA gas sample at 40.0oC occupies a volume of 2.32 L. If the temperature is raised to 75.ooC, what will the volume be, assuming the pressure remains constant?
4Gay-Lussac’s LawStates that the pressure given a mass of gas varies directly with the Kelvin temperature when the volume remains constant.P1/T1 = P2/T2 Temperature must be in Kelvins!!Example problemThe pressure of a gas in a tank is 3.20 atm at 22.0oC. If the temperature rises to 60.0oC, what will be the gas pressure in the tank?
6The Combined Gas LawStates the relationship among pressure, volume, and temperature for a fixed amount of gas.P1V1/T1 = P2V2/T2It is a combination of Boyle’s, Charles’s and Gay-Lussac’s laws.Example ProblemA gas at 110 kPa and 30.0oC fills a flexible container with an initial volume of 2.00 L. If the temperature is raised to 80.0oC and the pressure increased to 440 kPa, what is the new volume?Do practice problems on page 430.
7Avogadro’s PrincipleStates that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.Molar volume for a gas is the volume that one mole of gas occupies at 0.00oC and 1.00 atm pressure.0.00oC and 1 atm are known as standard temperature and pressure (STP)Avogadro found that at STP, 1 mole of any gas occupies L.
8Example ProblemsCalculate the volume that mol of gas at standard temperature and pressure (STP) will occupy.Calculate the volume that 2.0 kg of methane gas (CH4) will occupy at STP.
9The Ideal Gas LawCan be used to determine volume, pressure, temperature, and the number of moles of a gas.An ideal gas constant (R) is equal to PV/nT, where P is pressure, V is volume, n is the number of moles, and T is the temperature.There are three ideal gas constants that can be used in the Ideal Gas Lawwhen pressure is in atm8.314 when pressure is in kPa62.4 when pressure is in mm Hg
10PV = mRT/M where m = mass and M = molar mass PV = nRT orPV = mRT/M where m = mass and M = molar massMolar mass can be determined using the equationM = mRT/PV
11Example ProblemCalculate the number of moles of gas contained in a 3.0 L vessel at 3.00 x 102K with a pressure of 1.50 atm.Knowns UnknownsV = 3.0 L n = ? MolT = 300 KP = 1.50 atmR =Practice problems page 437
12Example ProblemWhat is the molar mass of a pure gas that has a density of 1.40 g/L at STP?Known UnknownMass = 1.40 g M = ? g/molVolume = 1.0 LTemperature = 273 KPressure = 1.00 atmR =Practice Problems page 438