# Ideal Gas Law Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jan 28, 2023

This ideal gas law calculator will help you establish the properties of an ideal gas subject to pressure, temperature, or volume changes. Read on to learn about the characteristics of an ideal gas, how to use the ideal gas law equation, and the definition of the ideal gas constant.

We also recommend checking out our combined gas law calculator for further understanding of the basic thermodynamic processes of ideal gases.

## What is an ideal gas

An ideal gas is a special case of any gas that fulfills the following conditions:

• The gas consists of a large number of molecules that move around randomly.
• All molecules are point particles (they don't take up any space).
• The molecules don't interact except for colliding.
• The particles obey Newton's laws of motion.

## Ideal gas law equation

The properties of an ideal gas are all summarized in one formula of the form:

$p \cdot V = n \cdot R \cdot T$

where:

• $p$ is the pressure of the gas, measured in Pa;
• $V$ is the volume of the gas, measured in m³;
• $n$ is the amount of substance, measured in moles;
• $R$ is the ideal gas constant; and
• $T$ is the temperature of the gas, measured in Kelvins.

To find any of these values, simply enter the other ones into the ideal gas law calculator.

For example, if you want to calculate the volume of 40 moles of a gas under a pressure of 1013 hPa and at a temperature of 250 K, the result will be equal to:

V = nRT/p = 40 * 8.31446261815324 * 250 / 101300 = 0.82 m³.

## Ideal gas constant

The gas constant (symbol R) is also called the molar or universal constant. It is used in many fundamental equations, such as the ideal gas law.

The value of this constant is 8.31446261815324 J/(mol·K).

The gas constant is often defined as the product of Boltzmann's constant k (which relates the kinetic energy and temperature of a gas) and Avogadro's number (the number of atoms in a mole of substance):

\scriptsize \begin{align*} R &= N_Ak \\ &= (6.02214076 \times 10^{23} \text{ /mol}) \cdot (1.38064852 \times 10^{-23} \text{ J/K})\\ &= 8.3144626 \text{ J/(mol} \cdot \text{K)} \end{align*}

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## FAQ

### When can I use the ideal gas law?

You can apply the ideal gas law for every gas at a *density low enough to prevent the emergence of strong intermolecular forces. In these conditions, every gas is more or less correctly modeled by the simple equation PV = nRT, which relates pressure, temperature, and volume.

### What is the formual of the ideal gas law?

The formula of the ideal gas law is:
P · V = n · R · T
where:

• P — The pressure, in pascal;
• V — The volume in cubic meters;
• n — The number of moles;
• T — The temperature in kelvin; and
• R — The ideal gas constant.

Remember to use consistent units! The value commonly used for R, 8.314... J · K/mol refers to the pressure measured exclusively in pascals.

### What is the pressure of 0.1 moles of a gas at 50 °C in a cubic meter?

268.7 Pa, or 0.00265 atm. To find this result:

1. Convert the temperature in kelvin: T [K] = 273.15 + 50 = 323.15 K.
2. Compute the product of temperature, the number of moles, and the gas constant: n · R · T = 0.1 mol · 323.15 K · 8.3145 J · K/mol = 268.7 J (that is, energy).
3. Divide by the volume. In this case, the volume is 1, hence:

P = 268.7 Pa.

### What are the three thermodynamics laws that can be identified in the ideal gas law?

The ideal gas law has four parameters. One of them is the number of moles which is a bit outside the scope of thermodynamics. The other three are pressure, temperature, and volume. We can identify three laws by fixing, in turn, each one of the three:

• Fixing the temperature, we find the isothermal transformation (or Boyle's law): PV = k.
• Fixing the volume, we find the isochoric transformation (Charles's law): P/T = k.
• Fixing the pressure, we have the isobaric transformation (Gay-Lussac's law): V/T = k.

## How do I calculate the temperature of a gas given moles, volume and pressure?

To calculate the temperature of a gas given the pressure and the volume, follow these simple steps:

1. Calculate the product of pressure and volumes. Be sure you're using consistent units: a good choice is pascals and cubic meters.
2. Calculate the product of the number of moles and the gas constant. If you used pascals and cubic meters, the constant is R = 8.3145 J · K/mol.
3. Divide the result of step 1 by the result of step 2: the result is the temperature (in kelvin):
T = P · V/n · R`
Bogna Szyk
Pressure (p)
Pa
Volume (V)
cu ft
Amount of substance (n)
mol
Temperature (T)
°F
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