Gas Laws

Where These Laws Come From

Each of these laws is really just the ideal gas law, PV = nRT, with two of the four quantities held constant. Whatever varies traces out a simple relationship between the two remaining quantities.

Law	Relationship	Held Constant	What Varies
Boyle’s Law	P₁V₁ = P₂V₂	n, T	Pressure, Volume
Charles’s Law	V₁/T₁ = V₂/T₂	n, P	Volume, Temperature
Avogadro’s Law	V₁/n₁ = V₂/n₂	P, T	Volume, Moles
Gay-Lussac’s Law	P₁/T₁ = P₂/T₂	n, V	Pressure, Temperature

In every calculator below, enter any three of the four values and the last one is calculated automatically — there is no separate solve button, just start typing. Use Reset to clear a calculator and start over.

Boyle’s Law

Boyle’s Law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature: as volume decreases, pressure increases, and vice versa.

P_{1} V_{1} = P_{2} V_{2}

Starting from PV = nRT, if the amount of gas (n) and the temperature (T) don’t change, then nRT is a constant, so P₁V₁ and P₂V₂ must be equal to each other.

Example

A gas occupies 4.00 L at 1.20 atm. If the volume is compressed to 2.00 L at constant temperature, what is the new pressure?

P_{2} = \frac{P_{1} V_{1}}{V_{2}}

P₂ = (1.20 × 4.00) ÷ 2.00

P₂ ≈ 2.40 atm

Boyle’s Law Calculator

Enter any three values (using whichever units you like) and the fourth will be calculated for you.

P₁

V₁

P₂

V₂

The field with the green background is the one being calculated for you. Temperature and moles are assumed constant between state 1 and state 2.

Charles’s Law

Charles’s Law describes how volume and temperature vary together for a fixed amount of gas at constant pressure: heating a gas expands it, cooling it shrinks it.

\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}

Starting from PV = nRT, if the amount of gas (n) and the pressure (P) don’t change, then V/T is constant, so V₁/T₁ and V₂/T₂ must be equal. Temperature must always be in Kelvin for this relationship to hold.

Example

A balloon holds 2.50 L of gas at 300 K. If it is heated to 360 K at constant pressure, what is the new volume?

V_{2} = \frac{V_{1} T_{2}}{T_{1}}

V₂ = (2.50 × 360) ÷ 300

V₂ ≈ 3.00 L

Charles’s Law Calculator

Enter any three values (using whichever units you like) and the fourth will be calculated for you.

V₁

T₁

V₂

T₂

The field with the green background is the one being calculated for you. Pressure and moles are assumed constant between state 1 and state 2.

Avogadro’s Law

Avogadro’s Law describes how volume and the amount of gas vary together at constant pressure and temperature: adding more gas molecules increases the volume proportionally.

\frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}}

Starting from PV = nRT, if the pressure (P) and temperature (T) don’t change, then V/n is constant, so V₁/n₁ and V₂/n₂ must be equal.

Example

A 6.00 L container holds 0.500 mol of gas. If 0.250 more moles are added at constant pressure and temperature, what is the new volume?

V_{2} = \frac{V_{1} n_{2}}{n_{1}}

V₂ = (6.00 × 0.750) ÷ 0.500

V₂ ≈ 9.00 L

Avogadro’s Law Calculator

Enter any three values (using whichever units you like) and the fourth will be calculated for you.

V₁

n₁

V₂

n₂

The field with the green background is the one being calculated for you. Pressure and temperature are assumed constant between state 1 and state 2.

Gay-Lussac’s Law

Gay-Lussac’s Law describes how pressure and temperature vary together for a fixed amount of gas at constant volume: heating a sealed container raises the pressure inside it.

\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}

Starting from PV = nRT, if the amount of gas (n) and the volume (V) don’t change, then P/T is constant, so P₁/T₁ and P₂/T₂ must be equal. Temperature must always be in Kelvin for this relationship to hold.

Example

A sealed can of gas is at 1.00 atm and 290 K. If it is heated to 350 K at constant volume, what is the new pressure?

P_{2} = \frac{P_{1} T_{2}}{T_{1}}

P₂ = (1.00 × 350) ÷ 290

P₂ ≈ 1.21 atm

Gay-Lussac’s Law Calculator

Enter any three values (using whichever units you like) and the fourth will be calculated for you.

P₁

T₁

P₂

T₂

The field with the green background is the one being calculated for you. Volume and moles are assumed constant between state 1 and state 2.

Practice Problems

Problem 1 (Boyle’s Law)

A gas occupies 8.00 L at 1.00 atm. What volume will it occupy at 4.00 atm, assuming constant temperature?

Show Answer

V₂ = P₁V₁ ÷ P₂ = (1.00 × 8.00) ÷ 4.00 = 2.00 L

Problem 2 (Charles’s Law)

A gas sample has a volume of 4.00 L at 20°C. What is its volume at 80°C, assuming constant pressure? (Convert to Kelvin first.)

Show Answer

T₁ = 293.15 K, T₂ = 353.15 K
V₂ = V₁T₂ ÷ T₁ = (4.00 × 353.15) ÷ 293.15 ≈ 4.82 L

Problem 3 (Avogadro’s Law)

A 3.00 L container holds 0.200 mol of gas. How many moles are needed to fill a 9.00 L container at the same pressure and temperature?

Show Answer

n₂ = V₂n₁ ÷ V₁ = (9.00 × 0.200) ÷ 3.00 = 0.600 mol

Problem 4 (Gay-Lussac’s Law)

A rigid tank of gas is at 2.00 atm and 250 K. What is the pressure if the tank is cooled to 200 K?

Show Answer

P₂ = P₁T₂ ÷ T₁ = (2.00 × 200) ÷ 250 = 1.60 atm