1. Chapter 7 Gases
7.6 The Combined Gas Law

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

3. 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
T T2

4. Combined Gas Law Calculation
A sample of helium gas has a volume of L, a pressure of 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 = atm P2 = 3.20 atm
V1 = L (180 mL) V2 = 90.0 mL
T1 = 29 °C = 302 K T2 = ?

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

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

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