Two Dials at Once: The Gas Equation
Combine Boyle and Charles with P₁V₁/T₁ = P₂V₂/T₂ — and meet S.T.P.
What this lesson covers
Why it matters
A weather balloon climbs into the sky, and the air around it grows colder AND thinner at the same time. Two dials — pressure and temperature — are turning at once, so neither Boyle nor Charles alone can predict its volume. For that you need their laws combined.
Predict first
A gas at S.T.P. has its pressure doubled while its temperature is raised from 273 K to 546 K. What happens to its volume?
Doubling the kelvin temperature would double the volume; doubling the pressure would halve it. Together they cancel: by P₁V₁/T₁ = P₂V₂/T₂, V₂ = V₁ × (546/273) × (760/1520) = V₁. The gas equation handles both dials at once.
- It stays exactly the same — the two changes cancel out — correct
- It doubles — heating always expands a gas
- It halves — extra pressure always squashes a gas
What you do
A numerical gives you a gas at one set of conditions and asks about another. Arrange the solution steps in the order a careful chemist works — one step here saves more marks than any other!
Check yourself
A gas occupies 572 cm³ at 13°C and 725 mm Hg. What is its volume at 24°C and 792 mm Hg?
Convert first: T₁ = 286 K, T₂ = 297 K. Then P₁V₁/T₁ = P₂V₂/T₂ gives V₂ = (725 × 572 × 297) ÷ (286 × 792) = 543.75 cm³. The higher pressure shrinks the gas more than the small warming expands it.
The standard temperature and pressure (S.T.P.) for gases are…
Standard temperature = 0°C = 273 K; standard pressure = 760 mm Hg = 76 cm Hg = 1 atm. Both values together are called S.T.P.
Why are gas volumes usually reduced to S.T.P.?
The same mass of gas fills wildly different volumes under different conditions, so stating a volume means nothing unless you also state P and T. Reducing every volume to S.T.P. (273 K, 760 mm Hg) puts all gases on the same footing.
- 543.75 cm³ — correct
- 966.7 cm³
- 594 cm³
- 0°C (273 K) and 760 mm Hg (1 atm) — correct
- 25°C and 760 mm Hg
- 0 K and 76 cm Hg
- A gas's volume changes with temperature and pressure, so volumes are only comparable at agreed standard conditions — correct
- Gases obey the gas laws only at S.T.P.
- Gas volumes cannot be measured at other temperatures