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Ideal Gas Law Calculator

Enter the required inputs into the calculator and find unknown gas properties such as pressure, volume, temperature, and quantity of substance.

To Calculate::

m³ ▾

mol ▾

°C ▾

Gas constant (R):

J⋅K⁻¹⋅mol⁻¹

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The ideal gas law calculator helps calculate the unknown property in the ideal gas law equation (PV = nRT) when three of the variables are known. This tool simplifies calculations of pressure, volume, temperature, or the number of moles of a gas.

What Is An Ideal Gas?

An ideal gas is a theoretical concept. It is considered to consist of many randomly moving particles that interact only through elastic collisions. These interactions follow a predictable law described by the ideal gas equation. Real gases approximate this behavior under high temperature and low pressure conditions.

Ideal Gas Law Formula:

The behavior of an ideal gas is described by the ideal gas law equation:

PV = nRT

This equation can be rearranged to calculate the unknown variable:

Pressure: \( P = \dfrac{nRT}{V} \)
Volume: \( V = \dfrac{nRT}{P} \)
Moles: \( n = \dfrac{PV}{RT} \)
Temperature: \( T = \dfrac{PV}{nR} \)

Where:

n = Number of moles of gas
R = Ideal gas constant = 8.3145 J/mol·K
T = Temperature in Kelvin
P = Pressure in Pascals
V = Volume of the gas

The Gas Constant (R)

The gas constant, R, also called the universal gas constant, is fundamental in many physics and chemistry equations. Its value is 8.3144626 J·K⁻¹·mol⁻¹, derived from the combination of constants in Boyle’s Law, Charles’s Law, Avogadro’s Law, and Gay-Lussac’s Law.

Gas Laws Combined in the Ideal Gas Equation

The ideal gas law combines the following gas laws:

Boyle’s Law: At constant temperature, the product of pressure and volume is constant.
\( P_1 V_1 = P_2 V_2 \)

Charles’s Law: At constant pressure, the ratio of volume to temperature is constant.
\( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)

Gay-Lussac’s Law: At constant volume, the ratio of pressure to temperature is constant.
\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)

Avogadro’s Law: At constant temperature and pressure, the ratio of volume to number of moles is constant.
\( \frac{V_1}{n_1} = \frac{V_2}{n_2} \)

How to Calculate Using the Ideal Gas Law

Identify the known variables: P, V, T, and n.
Convert units to ensure consistency (e.g., P in Pascals, T in Kelvin).
Substitute the known values into PV = nRT to solve for the unknown.

Examples

Case 1: Calculate the volume of a gas:

P = 200 kPa
T = 300 K
n = 0.250 mol

Solution:

\( V = \dfrac{nRT}{P} = \dfrac{0.250 \times 8.314 \times 300}{200 \times 10^3} \)

V ≈ 3.12 × 10⁻³ m³ = 3.12 L

Case 2: Calculate the temperature of a gas:

P = 153 kPa
V = 0.250 L
n = 0.50 mol

Solution:

\( T = \dfrac{PV}{nR} = \dfrac{153000 \times 0.00025}{0.50 \times 8.314} \)

T ≈ 9.2 K

FAQ

When Can I Use the Ideal Gas Law?

The ideal gas law is applicable under these conditions:

High temperature
Low pressure
Sufficient volume
Non-reacting gases

References:

Wikipedia: Ideal Gas Law

Chemguide: Ideal Gases

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