Combined Gas Law Calculator

Enter 5 of 6 variables and solve for the missing one. Temperature is automatically converted to Kelvin.

Initial State

Final State

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Result:

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Ideal Gas Law

PV = nRT
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Charles's Law

V₁/T₁ = V₂/T₂
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Boyle's Law

P₁V₁ = P₂V₂
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Gay-Lussac's Law

P₁/T₁ = P₂/T₂
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Dalton's Law

Pₜₒₜₐₗ = ΣPᵢ
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Avogadro's Law

V₁/n₁ = V₂/n₂
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Volume of Gas

V = nRT/P
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What is the Combined Gas Law?

The Combined Gas Law is an equation that merges three fundamental gas laws — Boyle's Law, Charles's Law, and Gay-Lussac's Law — into a single relationship. It describes how the pressure, volume, and temperature of a fixed amount of gas are related when the gas transitions from one state to another.

P₁V₁ / T₁ = P₂V₂ / T₂

Combined Gas Law Formula — All Rearranged Forms

P₂ = P₁V₁T₂ / (T₁V₂)
V₂ = P₁V₁T₂ / (T₁P₂)
T₂ = P₂V₂T₁ / (P₁V₁)

Step-by-Step Examples

Example 1: Solve for P₂

Given: P₁ = 2.0 atm, V₁ = 3.0 L, T₁ = 300 K, V₂ = 2.0 L, T₂ = 350 K. Find P₂.

1. Formula: P₂ = P₁V₁T₂ / (T₁V₂)
2. Substitute: P₂ = (2.0)(3.0)(350) / (300)(2.0)
3. Calculate: P₂ = 2100 / 600 = 3.5 atm

Example 2: Solve for V₂

Given: P₁ = 1.0 atm, V₁ = 5.0 L, T₁ = 273 K, P₂ = 2.0 atm, T₂ = 373 K. Find V₂.

1. Formula: V₂ = P₁V₁T₂ / (T₁P₂)
2. Substitute: V₂ = (1.0)(5.0)(373) / (273)(2.0)
3. Calculate: V₂ = 1865 / 546 = 3.416 L

Example 3: Solve for T₂

Given: P₁ = 1.5 atm, V₁ = 4.0 L, T₁ = 300 K, P₂ = 3.0 atm, V₂ = 3.0 L. Find T₂.

1. Formula: T₂ = P₂V₂T₁ / (P₁V₁)
2. Substitute: T₂ = (3.0)(3.0)(300) / (1.5)(4.0)
3. Calculate: T₂ = 2700 / 6.0 = 450 K

When to Use the Combined Gas Law

Use the Combined Gas Law when a gas changes from one set of conditions to another and all three variables (P, V, T) may change. The amount of gas (moles) must remain constant. If one variable stays constant, the equation simplifies to a simpler law.

Combined Gas Law vs Other Gas Laws

If Constant...Use...Formula
TemperatureBoyle's LawP₁V₁ = P₂V₂
PressureCharles's LawV₁/T₁ = V₂/T₂
VolumeGay-Lussac's LawP₁/T₁ = P₂/T₂
Nothing constantCombined Gas LawP₁V₁/T₁ = P₂V₂/T₂
Moles involvedIdeal Gas LawPV = nRT

Real-World Applications

  • Weather balloons: As a balloon rises, pressure decreases and temperature drops, causing the volume to change.
  • Scuba diving: Divers must account for changes in pressure and temperature as they descend and ascend.
  • Car engines: The combustion cycle involves rapid changes in all three variables as fuel ignites.

Frequently Asked Questions

  • The Combined Gas Law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation. It describes how pressure, volume, and temperature of a fixed amount of gas change together: P₁V₁/T₁ = P₂V₂/T₂.

  • The formula is P₁V₁/T₁ = P₂V₂/T₂, where subscript 1 is the initial state and subscript 2 is the final state. Temperature must always be in Kelvin.

  • Rearrange the formula: P₂ = P₁V₁T₂ / (T₁V₂). Plug in the known values for P₁, V₁, T₁, T₂, and V₂ (all temperatures in Kelvin), then calculate.

  • Always use Kelvin for temperature in gas law calculations. Convert from Celsius: K = °C + 273.15. Convert from Fahrenheit: K = (°F + 459.67) × 5/9.

  • The combined gas law (P₁V₁/T₁ = P₂V₂/T₂) compares two states of the same gas. The ideal gas law (PV = nRT) relates P, V, T, and moles at a single state. Use the combined law when moles are constant and you're comparing before/after.

  • Use the combined gas law when a gas changes from one set of conditions (P₁, V₁, T₁) to another (P₂, V₂, T₂) and the amount of gas stays the same. If one variable stays constant, the equation simplifies to Boyle's, Charles's, or Gay-Lussac's Law.