Combined Gas Law
Relates two states of a fixed amount of gas.
Formula
Variables
Example
A gas at 1 atm, 300 K, 2 L heated to 600 K at 2 atm occupies (1·2·600)/(300·2) = 2 L.
How it works
The combined gas law links pressure, volume, and absolute temperature for a fixed amount of gas, showing how a gas changes when none of the gas is added or removed. It comes from combining Boyle’s law, Charles’s law, and Gay-Lussac’s law into one relationship, so it works best when the number of moles stays constant and the gas behaves approximately ideally. The temperatures must be in kelvin because the law depends on absolute temperature, not Celsius.
When to use it
Use this formula when a gas sample is taken from one set of conditions to another and you know the initial and final values for some of pressure, volume, and temperature. It is common in chemistry, physics, and lab calculations involving sealed containers, pistons, balloons, or gas syringes.
Worked example, step by step
A gas has an initial pressure of 95 kPa, volume of 4.0 L, and temperature of 290 K. It is changed to a pressure of 140 kPa and a temperature of 350 K. Find the final volume. P1V1/T1 = P2V2/T2 (95 × 4.0) / 290 = (140 × V2) / 350 380 / 290 = 140V2 / 350 1.3103 = 0.4V2 V2 = 1.3103 ÷ 0.4 V2 = 3.28 L
Common mistakes to avoid
- using Celsius instead of converting temperatures to kelvin
- mixing up initial and final values in the formula
- solving for the wrong variable or forgetting to rearrange the equation before calculating
Did You Know?
The combined gas law is why a sealed bag of chips puffs up on an airplane as cabin pressure drops.
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