8.5 The Combined Gas Law Under water, the pressure on a diver is greater than the atmospheric pressure. The combined gas law comes from the pressure–volume–temperature relationships for gases that we have studied. Learning Goal Use the combined gas law to calculate the final pressure, volume, or temperature of a gas when changes in two of these properties are given and the amount of gas is constant.

The Combined Gas Law The combined gas law uses the pressure–volume–temperature relationships from Boyle’s law, Charles’s law, and Gay-Lussac’s law where n is constant.

Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35 °C and 646 mmHg pressure. What is the volume (mL) of the gas at −95 °C and a pressure of 802 mmHg (n is constant)? STEP 1 Organize the data into a table of initial and final conditions. Moles of gas remain the same. ANALYZE Conditions 1 Conditions 2 THE P1 = 646 mmHg P2 = 802 mmHg PROBLEM V1 = 675 mL V2 = ? T1 = 35 C + 273 T2 = −95 C + 273 = 308 K = 178 K

Calculations Using Combined Gas Law STEP 2 Rearrange to solve for unknown quantity V2. STEP 3 Substitute the values into the gas law equation and calculate. × × × ×

Study Check A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29 °C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n remains constant)?

Solution A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29 °C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n remains constant)? STEP 1 Organize the data into a table of initial and final conditions. Moles of gas remain the same. ANALYZE Conditions 1 Conditions 2 THE P1 = 0.800 atm P2 = 3.20 atm PROBLEM V1 = 0.180 L (180 mL) V2 = 90.0 mL T1 = 29 C + 273 T2 = ? = 302 K

Solution A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29 °C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n remains constant)? STEP 2 Rearrange to solve for unknown quantity T2. × ×

Solution A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29 °C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n remains constant)? STEP 3 Substitute the values into the gas law equation and calculate. × × -