9.5 Combined Gas Law
Notes
The combined gas law joins Boyle's, Charles's and Gay-Lussac's laws for a fixed amount of gas.
- $\displaystyle \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, with $T$ in kelvins.
- Cross out any variable that stays constant to get the simpler laws.
- Solved for $V_2$: $\displaystyle V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}$.
- Example: 10.0 L at 1.20 atm and 300 K changes to 0.800 atm and 400 K. $\displaystyle V_2 = 10.0 \times \frac{1.20}{0.800} \times \frac{400}{300} = 20.0$ L.
Practice
A gas occupies 5.00 L at 1.00 atm and 273 K. What volume does it occupy at 2.00 atm and 546 K?
$\displaystyle V_2 = 5.00 \times \frac{1.00}{2.00} \times \frac{546}{273} = 5.00$ L. The two changes cancel.
A 2.00 L sample of gas is at 0.500 atm and 250 K. What is its pressure if it is changed to 1.00 L at 500 K?
$\displaystyle P_2 = 0.500 \times \frac{2.00}{1.00} \times \frac{500}{250} = 2.00$ atm.
A gas at STP (273 K, 1.00 atm) occupies 22.4 L. What is its volume at 25 °C and 1.00 atm?
$\displaystyle V_2 = 22.4 \times \frac{298}{273} = 24.5$ L.
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