The Combined Gas Law

Review The pressure, volume, and temperature of a gas are related to each other. For ideal (or near-ideal) gases: PV = nRT If you change one aspect of a gas, you change the others.

Changes in Gases Constant temperature: Constant volume: As V increases, P decreases. As V decreases, P increases. Constant volume: As T increases, P increases. As T decreases, P decreases. Constant pressure: As T increases, V increases. As T decreases, V decreases. V P T P T V

Changes in Gases Make a card with the letters P T V. Must be in that order. Hold one of the variables constant while changing one of the others. Observe what happens to the dependent variable.

The Combined Gas Law We know that PV = nRT So nR = PV/T k = PV/T If the amount of gas stays the same, then nR = constant (k) k = PV/T The conditions of a gas can change, but k must stay the same if the amount doesn’t change: k = P1V1 / T1 k = P2V2 / T2

The Combined Gas Law P1V1 T1 = P2V2 T2 P1 = initial pressure (any suitable unit) V1 = initial volume (any suitable unit) T2 = initial temperature (K) P2 = final pressure (same unit as P1) V2 = final volume (same unit as V1) T2 = final temperature (K)

The Combined Gas Law (1.00 atm)(99.0 L) 273 K = (0.800 atm)(V2) 315 K At STP a certain gas sample occupies a volume of 99.0 L. What is the gas’s volume at 315 K and 0.800 atm? (1.00 atm)(99.0 L) 273 K = (0.800 atm)(V2) 315 K 0.363 atm*L/K = (0.00254 atm/K)V2 V2 = 143 L

The Combined Gas Law We can also employ cross-multiplication to solve CGL problems.

The Combined Gas Law (400. mmHg)(12.0 mL) 325 K = (380. mmHg)(6.80 mL) A gas sample occupies 12.0 mL at 400. mmHg and 325 K. At what temperature (in K) would the sample occupy 6.80 mL when the pressure is 380. mmHg? (400. mmHg)(12.0 mL) 325 K = (380. mmHg)(6.80 mL) T2 (400. mmHg)(12.0 mL) T2 = (380. mmHg)(6.80 mL)(325 K) (4.80x103 mmHg*mL) T2 = 8.40x105 mmHg*mL*K T2 = 175 K

The Combined Gas Law If some aspect of a gas is being held constant, we can leave that aspect out of the combined gas law: Constant temperature: P1V1 = P2V2 Boyle’s Law Constant pressure: V1/T1 = V2/T2 Charles’s Law Constant volume: P1/T1 = P2/T2 Gay-Lussac’s Law

The Combined Gas Law A gas sample’s volume is 44.0 L when its pressure is 1.00 atm. If the pressure is changed to 2.00 atm at constant temperature, what is the new volume of the gas? Predict first! Will the gas’s volume go up or down? Use the modified combined gas law to solve!

The Combined Gas Law A gas sample’s volume is 44.0 L when its pressure is 1.00 atm. If the pressure is changed to 2.00 atm at constant temperature, what is the new volume of the gas? P1V1 = P2V2 (1.00 atm)(44.0 L) = (2.00 atm) V2 44.0 atm*L = (2.00 atm) V2 V2 = 22.0 L