Chapter 11 · Gases
11.6The Combined Gas Law: Pressure, Volume, and Temperature
10 min · two checks
Predict
What stays constant in the combined gas law?
The idea
- Solve the combined gas law for any one variable.
- Recover Boyle or Charles as special cases.
If pressure, volume, and temperature all may change, and moles do not, use P₁V₁/T₁ = P₂V₂/T₂. Temperature is again in kelvin. If pressure is constant, the P terms cancel and you have Charles’s law. If temperature is constant, you have Boyle’s law. If volume is constant, P₁/T₁ = P₂/T₂: pressure is proportional to absolute temperature. That last case is sometimes called Amontons’s or Gay-Lussac’s law.
Algebra first: isolate the unknown, then substitute. A common mess is forgetting to convert one temperature and converting the other. Convert both. Then size-check each change separately in your head: heating tends to increase P or V, squeezing tends to increase P or decrease V.
Keep these
- P₁V₁/T₁ = P₂V₂/T₂ at constant n.
- Kelvin for every T.
- Constant volume: pressure proportional to kelvin temperature.
Worked path
A sample is 1.20 L at 98.0 kPa and 25 °C. Find the volume at 110 kPa and 80 °C.
Observe
T₁ = 298 K, T₂ = 353 K. n is constant.