The combined gas law describes how pressure, volume, and temperature change together for a fixed amount of gas. It matters because gases expand, compress, heat up, and cool down in predictable ways in balloons, engines, weather systems, and laboratory containers. Instead of using separate gas laws one at a time, the combined gas law lets you compare an initial state and a final state in one equation.
The law combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law by keeping the amount of gas constant. If temperature increases while pressure stays the same, volume increases, and if volume decreases while temperature stays the same, pressure increases. In calculations, temperature must always be in kelvins because gas volume and pressure are proportional to absolute temperature.
The equation is most useful when five of the six variables are known and you need to solve for the missing one.
Key Facts
- Combined gas law: P1V1/T1 = P2V2/T2
- Pressure and volume are inversely related when temperature is constant: P1V1 = P2V2
- Volume and temperature are directly related when pressure is constant: V1/T1 = V2/T2
- Pressure and temperature are directly related when volume is constant: P1/T1 = P2/T2
- Temperature must be in kelvins: K = °C + 273.15
- The combined gas law applies when the amount of gas, n, does not change.
Vocabulary
- Combined Gas Law
- A gas law that relates pressure, volume, and absolute temperature for a fixed amount of gas between two states.
- Pressure
- The force per unit area caused by gas particles colliding with the walls of their container.
- Volume
- The amount of space occupied by a gas.
- Absolute Temperature
- Temperature measured in kelvins, where 0 K represents the lowest possible thermal energy.
- Fixed Amount of Gas
- A situation where no gas particles are added or removed, so the number of moles stays constant.
Common Mistakes to Avoid
- Using Celsius instead of kelvins is wrong because gas law proportions only work with absolute temperature. Always convert °C to K before substituting into the equation.
- Mixing pressure or volume units is wrong because both sides of the equation must use consistent units. Convert units first, such as atm to kPa or mL to L, if needed.
- Forgetting the inverse relationship between pressure and volume is wrong because compressing a gas at constant temperature raises its pressure. Do not assume every variable increases together.
- Changing the amount of gas is wrong because the combined gas law assumes the number of gas particles stays constant. If gas is added or removed, use the ideal gas law instead.
Practice Questions
- 1 A gas has a pressure of 1.20 atm, a volume of 3.50 L, and a temperature of 300 K. It is changed to a pressure of 0.900 atm and a temperature of 360 K. What is the new volume?
- 2 A 2.00 L gas sample at 95.0 kPa and 25.0 °C is compressed to 1.50 L and heated to 60.0 °C. What is the final pressure in kPa?
- 3 A sealed piston contains a fixed amount of gas. The piston is pushed down while the gas is also heated. Explain why the final pressure must increase, and describe how both volume and temperature contribute to that change.