Combined Gas Law Calculator

The combined gas law merges Boyle's, Charles's, and Gay-Lussac's laws into one equation. Use when pressure, volume, AND temperature all change simultaneously. Temperature must be in Kelvin.

💨 Gas Laws📐 P₁V₁/T₁ = P₂V₂/T₂⚗️ Ideal Gas

P₁

V₁

T₁ (K)

V₂

T₂ (K)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Combined Gas Law	—	P₁V₁/T₁ = P₂V₂/T₂	—
Find P₂	P₂	P₁V₁T₂/(T₁V₂)	atm
Find V₂	V₂	P₁V₁T₂/(T₁P₂)	L
Find T₂	T₂	T₁P₂V₂/(P₁V₁)	K

Step-by-Step Examples

Example 1

Full Three-Variable Change

Gas at 2.00 atm, 4.00 L, 300 K is compressed to 2.00 L and heated to 400 K. Find P₂.

P₂ = P₁V₁T₂/(T₁V₂) = 2.00×4.00×400/(300×2.00)
P₂ = 3200/600 = 5.33 atm

✓ 5.33 atm

Example 2

Volume Change

Gas at 3.00 atm, 5.00 L, 250 K changes to 1.00 atm, 350 K. Find V₂.

V₂ = 3.00×5.00×350/(250×1.00) = 21.0 L

✓ 21.0 L

Example 3

STP to Lab Conditions

Convert gas from STP (1 atm, 273 K) to lab conditions (0.90 atm, 298 K). V₁=22.4 L.

V₂ = 1.00×22.4×298/(273×0.90) = 27.2 L

✓ 27.2 L at lab conditions

Real-World Applications

✈️

Aviation

Gas volume changes with altitude as both P and T change simultaneously.

🔬

Gas Collection

Gases collected over water must be corrected for pressure and temperature changes.

🧪

Lab Calculations

Converting gas volumes between different conditions uses combined gas law.

⚽

Sports Equipment

Ball pressure changes with both temperature and altitude require combined law.

Common Mistakes to Avoid

⚠️

Temperature MUST be in Kelvin

The most common error. -10°C = 263 K. Always add 273.15 to convert °C to K.

⚠️

Keep amount of gas constant

Combined gas law assumes n (moles) is constant. If gas escapes or is added, use PV=nRT instead.

⚠️

Same units throughout

P₁ and P₂ must be the same units; V₁ and V₂ the same units; T₁ and T₂ both in Kelvin.

Frequently Asked Questions

What happened to Avogadro in this law? ▾

Combined gas law holds n constant. Include n (moles) by using the full ideal gas law: PV = nRT.

When should I use combined vs ideal gas law? ▾

Combined gas law: two states of same gas (no change in n). Ideal gas law: absolute values when n is known or needed.

How do I convert to STP? ▾

STP = 0°C (273.15 K), 1 atm (101.325 kPa). Use combined law to adjust any volume to STP conditions.

What is SATP? ▾

Standard Ambient Temperature and Pressure: 25°C (298.15 K) and 1 bar (100 kPa). Some references use SATP instead of STP.

Can I use this for partial pressures? ▾

Yes, for a single component. For mixtures, add partial pressures (Dalton's Law) first, then apply combined gas law.

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Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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