Ideal Gas Law Calculator (PV = nRT)

About the Ideal Gas Law Calculator (PV = nRT)

The ideal gas law relates the pressure, volume, amount and temperature of a gas. Provide any three quantities and the calculator solves for the fourth using PV = nRT.

Use SI units: pressure in pascals (Pa), volume in cubic metres (m³), amount in moles (mol) and temperature in kelvin (K). R = 8.314 J/(mol·K). Leave exactly one field blank.

How to use this calculator

1. Enter the three known values for pressure \(P\), volume \(V\), moles \(n\), and temperature \(T\).
2. Choose which variable you want to solve for, pressure, volume, moles, or temperature.
3. Make sure your units match the gas constant \(R\) you are using, because the calculator depends on consistent units.
4. Click calculate to get the missing value and check the worked steps for the rearranged formula.

The formula explained

The formula \(PV = nRT\) computes the relationship between a gas's pressure, volume, amount in moles, and absolute temperature. You rearrange it to solve for the missing variable, for example \(P = \frac{nRT}{V}\) or \(T = \frac{PV}{nR}\).

• P = pressure of the gas
• V = volume of the gas
• n = amount of gas in moles
• R = ideal gas constant
• T = absolute temperature in kelvin

Step by step method

1. Start with \(PV = nRT\).
2. Move the known factors to one side to isolate the unknown, for example divide by \(V\) to solve for \(P\).
3. Substitute the values and compute using consistent units.
4. Check that temperature is in kelvin and that your pressure and volume units match the value of \(R\).

Worked example

Problem. A gas has volume \(V = 10.0\,\text{L}\), amount \(n = 0.50\,\text{mol}\), and temperature \(T = 300\,\text{K}\). Find the pressure \(P\) using \(R = 0.0821\,\text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})\).

1. Use \(P = \frac{nRT}{V}\).
2. Substitute the values, \(P = \frac{(0.50)(0.0821)(300)}{10.0}\).
3. Compute \(P = 1.23\,\text{atm}\).

Tips and common mistakes

• Use kelvin for temperature, not Celsius, because the ideal gas law requires absolute temperature.
• Choose a gas constant \(R\) that matches your units, for example \(0.0821\,\text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})\) or \(8.314\,\text{J}/(\text{mol}\cdot\text{K})\).

Frequently asked questions