Boyle’s Law The volume of a fixed mass of gas varies inversely with the pressure at constant temperature. PV = k P 1 V 1 = P 2 V 2 Episode 902

Kinetic Theory and Boyle’s Law Pressure of a gas is caused by the molecules of the gas striking the walls of the container. If the gas is compressed to half the volume it had, twice as many molecules are present in any given volume. – Twice as many impacts per second on the walls of the container – Pressure of the gas will double Episode 902

Example 1 A balloon filled with helium has a volume of 457 mL at standard atmospheric pressure. After the balloon is released, it reaches an altitude of 6.3 km where the pressure is only 65.5 kPa. What is the volume of the balloon at this altitude? Given: – V 1 = 457 mL – P 1 = kPa – P 2 = 65.5 kPa – V 2 = ? P 1 V 1 = P 2 V 2 (457 mL)(101.3 kPa) = (65.5 kPa)V 2 V 2 = 707 mL Episode 902

Example 2 Under a pressure of 623 mm Hg, a confined gas has a volume of 335 mL. If the pressure is increased until the volume is 252 mL, what is the new pressure, assuming the temperature remains constant? Given: – V 1 = 335 mL – P 1 = 623 mm Hg – V 2 = 252 mL – P 2 = ? P 1 V 1 = P 2 V 2 (335 mL)(623 mm Hg) = P 2 (252 mL) P 2 = 828 mm Hg Episode 902

Charles’s Law For a fixed mass of gas, as long as the pressure is held constant, the volume varies directly with the Kelvin temperature. V/T = k V 1 /T 1 = V 2 /T 2 Episode 902

The Kelvin Temperature Scale Absolute zero – Lowest possible temperature – Never been reached 0 Kelvin = absolute zero 0 Kelvin = ⁰ C K = ⁰ C Episode 902

Example 1 A quantity of gas occupies a volume of 506 cm 3 at a temperature of 147 ⁰ C. Assuming the pressure stays constant, at what temperature will the volume of the gas be 604 cm 3 ? Given: – V 1 = 506 cm 3 – T 1 = 147 ⁰ C – V 2 = 604 cm 3 – T 2 = ? V 1 /T 1 = V 2 /T cm 3 /420 K = 604 cm 3 /T 2 T 2 = 501 K or 501 – 273 = 228 ⁰ C Remember to convert temperature to Kelvin (420 K) Episode 902

Kinetic Molecular Theory and Charles’s Law Doubling the Kelvin temperature of a gas doubles the average kinetic energy of its molecules. Faster moving molecules – Strike the walls of the container more often – Strike the walls of the container with more force From Boyle’s law we derive that the volume would have to double if the Kelvin temperature is doubled so that the pressure would remain constant. Episode 902