Charles’ Law T V In Real Life A football inflated inside and then taken outdoors on a winter day shrinks slightly. A slightly underinflated rubber life raft left in bright sunlight swells up. Boyle’s Law P V The bubbles exhaled by a scuba diver grow as the approach the surface of the ocean. Deep sea fish die when brought to the surface. Gay-Lussac’s Law P T Gun powder heated behind a bullet causes pressure to build up and fire. Bad things happen if you leave an aerosol can in your car on a hot day.

Boyle’s Law When pressure increases, volume decreases. Let’s think about the math. P1 V1 = P2 V2

P2 P1 V1 = P2 V2 Boyle’s Law V2 As pressure increases… Volume decreases! P2 P1 V1 = P2 V2 V2

Boyle’s Law As pressure increases… Volume decreases! P1 V1 V2 = P2

P1 V1 V2 = P2 3 4 = * * 3 4 = 2 6 ? * * Boyle’s Law What if we change P2 to 2? What happens to V2? 3 4 = 2 6 ? * *

Boyle’s Law Example: A tank of nitrogen has a volume of 14 Boyle’s Law Example: A tank of nitrogen has a volume of 14.0 L and a pressure of 760.0 mmHg. Find the volume of the nitrogen when its pressure is changed to 400.0 mmHg.

Charles’ Law When temperature increases, volume increases. Let’s think about the math. V1 V2 = T1 T2

Charles’ Law When the top of the fraction on the right side increases, the bottom must also. 4 3 1 2 = = = 1 2 3 4

V2 T2 V1 V2 = T1 T2 Charles’ Law When temperature increases… Volume ALSO increases! V2 V1 V2 = T2 T1 T2

Charles’ Law Example: Find the final temperature of a 2000 Charles’ Law Example: Find the final temperature of a 2000.00 mL gas sample at 20.00C cooled until it occupies a volume of 500 mL.

If I initially have a gas at a pressure of 12 atm, a volume of 23 liters and a temperature of 200oK, and then I raise the pressure to 14 atm and increase the temperature to 300oK, what is the new volume of gas?

P1V1 P2V2 = T1 T2 Combined Gas Law Sometimes we need to account for more than one change… Enter, the combined gas law! T1 P1V1 P2V2 = T2

Combined Gas Law: If I initially have a gas at a pressure of 12 atm, a volume of 23 liters and a temperature of 200oK, and then I raise the pressure to 14 atm and increase the temperature to 300oK, what is the new volume of gas?

500. 0 liters of a gas are prepared at 1. 00atm and 200. 0 °C 500.0 liters of a gas are prepared at 1.00atm and 200.0 °C. The gas is placed into a tank under high pressure. When the tank cools to 20.0 °C, the pressure of the gas is 30.0 atm. What is the volume of the gas?