P₁V₁/T₁ = P₂V₂/T₂
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Temperatures converted to kelvin before solving. Methodology & sources →
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For a fixed amount of gas, this single relationship contains the simpler gas laws. Hold temperature constant and it becomes Boyle's law (P₁V₁ = P₂V₂); hold pressure constant for Charles's law (V₁/T₁ = V₂/T₂); hold volume constant for Gay-Lussac's law (P₁/T₁ = P₂/T₂). To bring in the amount of gas, use the Ideal Gas Law.
Worked Example — Combined Gas Law with Changing P, V, and T
Question: A gas sample has a volume of 4.25 L at 25.6°C and 748 mmHg. What is its volume at 26.8°C and 742 mmHg?
Step 1 — convert both temperatures to kelvin: T₁ = 298.75 K, T₂ = 299.95 K
Step 2 — rearrange P₁V₁/T₁ = P₂V₂/T₂ for V₂: V₂ = V₁ × (P₁/P₂) × (T₂/T₁)
Step 3 — substitute (pressures are both in mmHg, so no conversion needed): V₂ = 4.25 × (748/742) × (299.95/298.75) = 4.32 L
Answer: 4.32 L.
Common Mistakes
- Temperature must be in kelvin, even though pressure and volume can stay in whatever consistent units they're given in — the combined gas law is a ratio, so units cancel for P and V but not for T (because 0°C ≠ 0 K).
- Mixing pressure units between states. P₁ and P₂ must use the same unit as each other (both mmHg, or both atm) — but that unit doesn't have to be atm.
- Using the wrong simplified law. If temperature is constant, this reduces to Boyle's law (P₁V₁=P₂V₂); if pressure is constant, it reduces to Charles's law (V₁/T₁=V₂/T₂). The combined law works for all cases, including when only n is held constant.
Frequently Asked Questions
P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas — it combines Boyle's, Charles's and Gay-Lussac's laws.
Because the law uses a ratio of absolute temperatures. Add 273.15 to a Celsius value; choose °C above and the calculator converts for you.
Boyle's law (P1V1 = P2V2) applies when temperature is constant. Charles's law (V1/T1 = V2/T2) applies when pressure is constant. The combined gas law (P1V1/T1 = P2V2/T2) covers both cases and any situation where P, V, and T all change but the amount of gas (n) stays fixed — it's the more general tool.
No — only temperature must be in kelvin. Pressure and volume can be in any unit, as long as P1 and P2 share a unit, and V1 and V2 share a unit. The ratios cancel the units out.