Chapter 7 Gases 7.6 The Combined Gas Law

Summary of Gas Laws The gas laws can be summarized as follows:

Combined Gas Law The combined gas law uses Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law (n is constant). P1 V1 = P2V2 T1 T2

Combined Gas Law Calculation 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 constant)? Step 1 Set up data table: Conditions 1 Conditions 2 P1 = 0.800 atm P2 = 3.20 atm V1 = 0.180 L (180 mL) V2 = 90.0 mL T1 = 29 °C + 273 = 302 K T2 = ?

Combined Gas Law Calculation (continued) STEP 2 Solve for T2 P1 V1 = P2 V2 T1 T2 T2 = T1 x P2 x V2 P1 V1 STEP 3 Substitute values to solve for unknown. T2 = 302 K x 3.20 atm x 90.0 mL = 604 K 0.800 atm 180. mL T2 = 604 K  273 = 331 °C

Learning Check A gas has a volume of 675 mL at 35 °C and 0.850 atm pressure. What is the volume (mL) of the gas at -95 °C and a pressure of 802 mmHg (n constant)?

Solution STEP 1 Set up data table Conditions 1 Conditions 2 T1 = 308 K T2 = -95 °C + 273 = 178 K V1 = 675 mL V2 = ? P1 = 646 mmHg P2 = 802 mmHg STEP 2 Solve for V2 V2 = V1 x P1 x T2 P2 T1 STEP 3 Substitute values to solve for unknown. V2 = 675 mL x 646 mmHg x 178 K = 314 mL 802 mmHg x 308 K