How to Use the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂): Formula & Examples

Use P₁V₁/T₁ = P₂V₂/T₂ to find final pressure, volume, or temperature. Convert °C to kelvin, keep units consistent, and verify every answer with a free combined gas law calculator.

What the Combined Gas Law Means

The combined gas law connects two states of the same gas sample when the amount of gas stays fixed. In symbols: P₁V₁/T₁ = P₂V₂/T₂. Pressure, volume, and absolute temperature on one side balance the same trio on the other.

It merges Boyle’s law (P and V at fixed T), Charles’s law (V and T at fixed P), and Gay-Lussac’s law (P and T at fixed V) into one homework-friendly ratio. Most worksheet mistakes come from Celsius temperatures or mismatched units — not from the algebra.

If you already have five known values and only need a checked unknown, open the free combined gas law calculator first, then return here for Kelvin traps and worked examples.

The Formula P₁V₁/T₁ = P₂V₂/T₂

Rearrangements that cover almost every problem:

P₂ = (P₁ × V₁ × T₂) / (T₁ × V₂) — final pressure.

V₂ = (P₁ × V₁ × T₂) / (T₁ × P₂) — final volume.

T₂ = (P₂ × V₂ × T₁) / (P₁ × V₁) — final temperature in kelvin.

When one quantity is unchanged, cancel it mentally: fixed volume → P/T constant; fixed pressure → V/T constant; fixed temperature → PV constant.

Kelvin First — Always

Absolute temperature is required:

T(K) = T(°C) + 273 (common school form) or + 273.15.

Never put °C or °F directly into T₁ or T₂.

After solving for T₂ in kelvin, convert back to °C only if the question asks for Celsius.

Trap: 27 °C looks “small,” but the gas law sees 300 K. Using 27 in the denominator shrinks T and warps every other unknown.

Units That Stay Consistent

Pressure: keep both states in kPa, atm, or torr — do not mix without converting.

Volume: both in L, or both in mL (1 L = 1000 mL).

Temperature: both in kelvin after conversion from °C.

The calculator defaults (kPa, L, K) match many school labs. If your paper uses atm, convert both P₁ and P₂ the same way.

Worked Examples

Example 1: find final pressure

A gas at 100 kPa, 2.0 L, and 300 K is heated to 360 K at the same volume. P₂ = (100 × 2.0 × 360) / (300 × 2.0) = 120 kPa. Rough check: temperature rose 20%, so pressure rose 20%.

Example 2: °C conversion before solving

Initial: 1.0 atm, 5.0 L, 27 °C. Final: 2.0 atm, 2.5 L, find T₂. First T₁ = 27 + 273 = 300 K. T₂ = (2.0 × 2.5 × 300) / (1.0 × 5.0) = 300 K (still 27 °C). Skipping the conversion and using 27 would be wrong.

Example 3: find final volume (Boyle check)

P₁ = 200 kPa, V₁ = 3.0 L, T₁ = 250 K → P₂ = 100 kPa at the same T. V₂ = (200 × 3.0 × 250) / (250 × 100) = 6.0 L. Halving pressure at fixed T doubles volume.

Combined Gas Law vs Ideal Gas Law

Use the combined law when you compare two states of the same sample and n is constant. Use PV = nRT when moles matter, or when you need one absolute state from P, V, n, and T instead of a before/after pair.

For mole-based problems, open the ideal gas law calculator.

Common Mistakes

Leaving temperature in °C inside P₁V₁/T₁ = P₂V₂/T₂.

Mixing atm with kPa or mL with L between state 1 and state 2.

Assuming the law still holds when gas is added or removed (n changes).

Reporting T₂ in kelvin when the question asked for °C — or the reverse.

Sanity check: absolute temperatures near room conditions are roughly 270–310 K, not 20–40.

Check With the Free Calculator

The combined gas law calculator rearranges P₁V₁/T₁ = P₂V₂/T₂ with visible steps so you can verify homework unknowns.

Combined gas law calculator — P₂, V₂, or T₂.

Ideal gas law calculator — PV = nRT.

Pressure calculator — force over area context.

Learn P₁V₁/T₁ = P₂V₂/T₂ with kelvin temperatures, then confirm every answer on the calculator.

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