Gas Laws Lesson 2

Boyle’s Law States that the volume of a given amount of gas held at a constant temperature varies inversely with the pressure. P1V1 = P2V2 Example problem A 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?

Charles’s Law States that the volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure. V1/T1 = V2/T2 TK = 273 + TC Example Problem A 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?

Gay-Lussac’s Law States 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 problem The 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?

Practice Problems Page 422 - # 1-5 Page 425 - #6-8 Page 427 - #9-13

The Combined Gas Law States the relationship among pressure, volume, and temperature for a fixed amount of gas. P1V1/T1 = P2V2/T2 It is a combination of Boyle’s, Charles’s and Gay-Lussac’s laws. Example Problem A 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 19-23 on page 430.

Avogadro’s Principle States 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 22.4 L.

Example Problems Calculate the volume that 0.881 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.

The Ideal Gas Law Can 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 Law 0.0821 when pressure is in atm 8.314 when pressure is in kPa 62.4 when pressure is in mm Hg

PV = mRT/M where m = mass and M = molar mass PV = nRT or PV = mRT/M where m = mass and M = molar mass Molar mass can be determined using the equation M = mRT/PV

Example Problem Calculate 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 Unknowns V = 3.0 L n = ? Mol T = 300 K P = 1.50 atm R = 0.0821 Practice problems 41-45 page 437

Example Problem What is the molar mass of a pure gas that has a density of 1.40 g/L at STP? Known Unknown Mass = 1.40 g M = ? g/mol Volume = 1.0 L Temperature = 273 K Pressure = 1.00 atm R = 0.0821 Practice Problems 46-50 page 438