Combined Gas Law

The combined gas law relates pressure, volume, and temperature of a fixed amount of gas. It combines Boyle's, Charles's, and Gay-Lussac's laws into one powerful equation.

The Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂

For a fixed amount of gas

Variable Definitions

P₁ = Initial Pressure

Units: atm, mmHg, Pa, kPa, torr

Pâ‚‚ = Final Pressure

Units: Same as P₁

V₁ = Initial Volume

Units: L, mL, m³, cm³

Vâ‚‚ = Final Volume

Units: Same as V₁

T₁ = Initial Temperature

Units: Kelvin (K) — MUST use Kelvin!

⚠️ Never use °C or °F

Tâ‚‚ = Final Temperature

Units: Kelvin (K)

K = °C + 273.15

When to Use Combined Gas Law

✅ Use When:

  • • Amount of gas is constant (n fixed)
  • • Both P, V, and T change
  • • Comparing two states

âš¡ Reduces To:

  • • Boyle's: T constant → P₁V₁ = Pâ‚‚Vâ‚‚
  • • Charles's: P constant → V₁/T₁ = Vâ‚‚/Tâ‚‚
  • • Gay-Lussac's: V constant → P₁/T₁ = Pâ‚‚/Tâ‚‚

❌ Don't Use If:

  • • Amount of gas changes
  • • Need to find moles (n)
  • • Use Ideal Gas Law instead

Rearranged Forms

Solve for Pâ‚‚:

P₂ = P₁V₁T₂ / (V₂T₁)

Solve for Vâ‚‚:

V₂ = P₁V₁T₂ / (P₂T₁)

Solve for Tâ‚‚:

T₂ = P₂V₂T₁ / (P₁V₁)

General Form:

PV / T = constant

Step-by-Step Example

Problem: A gas at 2.0 atm, 5.0 L, and 25°C is heated to 100°C and compressed to 3.0 L. Find the final pressure.

Given:

  • P₁ = 2.0 atm
  • V₁ = 5.0 L
  • T₁ = 25°C
  • Vâ‚‚ = 3.0 L
  • Tâ‚‚ = 100°C
  • Find: Pâ‚‚

Step 1: Convert temperatures to Kelvin

T₁ = 25 + 273.15 = 298 K
Tâ‚‚ = 100 + 273.15 = 373 K

Step 2: Rearrange for Pâ‚‚

P₂ = P₁V₁T₂ / (V₂T₁)

Step 3: Substitute values

Pâ‚‚ = (2.0 atm)(5.0 L)(373 K) / [(3.0 L)(298 K)]

Step 4: Calculate

Pâ‚‚ = 3730 / 894 = 4.17 atm

Answer: Pâ‚‚ = 4.2 atm

Pressure increased because: volume decreased (compression) AND temperature increased (heating).

Common Mistakes

❌ Using Celsius instead of Kelvin

Temperature MUST be in Kelvin! Using °C gives completely wrong answers. Always convert: K = °C + 273.15

❌ Mismatched pressure units

P₁ and P₂ must have the same units. Convert before calculating (e.g., all atm or all kPa).

❌ Mismatched volume units

V₁ and V₂ must have the same units. If one is mL and other is L, convert first!

❌ Assuming moles are constant when they're not

Combined gas law only works when amount of gas is FIXED. If gas leaks or is added, use ideal gas law instead.

Related Calculators

Combined Gas Law Calculator

Calculate P, V, or T changes

Ideal Gas Law

PV = nRT with moles

Boyle's Law

P-V relationship (T constant)

Charles's Law

V-T relationship (P constant)

Frequently Asked Questions

What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂. It relates pressure, volume, and temperature for a fixed amount of gas, combining three simpler gas laws.

When do I use combined gas law vs ideal gas law?

Use combined gas law when moles (n) are constant and you're comparing two states. Use ideal gas law when n varies or you need to find n.

Why must temperature be in Kelvin?

Gas laws assume absolute temperature scale. Celsius can be negative, which would give impossible negative volume/pressure ratios.

What happens if one variable stays constant?

The equation simplifies: constant T → Boyle's Law, constant P → Charles's Law, constant V → Gay-Lussac's Law.

Do pressure and volume units matter?

Units must be consistent (P₁ and P₂ same units, V₁ and V₂ same units), but they cancel out, so any units work if matched.

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