# Ideal Gas Law Calculator

Created by Gabriela Diaz
Last updated: Jun 24, 2022

If you're studying ideal gases, the ideal gas law calculator may be helpful. Are you wondering how to find the pressure of a gas? With this tool, you'll be able to quickly determine this and other properties such as the volume, mass, or temperature of an ideal gas.

• What is an ideal gas;
• The ideal law gas equation;
• The universal gas constant; and
• A numerical example of how to calculate the pressure of a gas.

## What is an ideal gas?

An ideal gas is a theoretical model of a gas that allows simplifying the study of real gases through the ideal gas law equation (PV = nRT). At very low densities all gases behave very similarly to an ideal gas. This low-density condition corresponds to gases at higher temperatures and lower pressures.

Given the simplicity of the state equation, it results convenient to approximate real gases to an ideal gas. Many gases, including nitrogen, oxygen, hydrogen, argon, helium, and even heavier gases like carbon dioxide, and mixtures like air, can be treated as ideal gases by employing the ideal gas law with a small margin of error.

The above explains why we use the ideal gas approximation. Let's now take a look at what the main characteristics of an ideal gas are:

• The gas consists of a large number of molecules that are randomly moving at high speeds;
• When compared to the volume occupied by the gas, the volume of these molecules is considerably small (particles);
• The distances between the molecules are relatively large (low density);
• Because the gas particles are widely spaced and moving at high speeds, they only interact via elastic collisions; and
• Potential energy is considered insignificant compared to the kinetic energy of molecules.

Why not take a look at to find out how to calculate the density of different substances.

## Ideal gas law equation

A state equation is any equation that relates pressure, temperature, and specific volume. The ideal gas law is one of the simplest state equations used in thermodynamics. It's used to calculate and predict gases' properties such as pressure (p), temperature (T), or volume (V).

The ideal gas law is a result of empirical research that showed that the volume of a gas, under specific pressure and temperature conditions, is inversely proportional to its pressure and directly proportional to its temperature:

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

where:

• $p$ - Absolute pressure of the gas usually in kPa or psia;
• $V$ - Volume occupied by of the ideal gas in m3 or ft3;
• $n$ - Number of moles in mol or kmol;
• $R$ - Ideal gas constant; and
• $T$ - Absolute temperature of the gas in Kelvin K or Rankine R.

To find any of these values, simply enter the other ones into the ideal gas law calculator. For example, if you'd like to determine the volume $V$ of gas, you'd need to input the values of $p$, $n$, and $T$.

The universal gas constant or ideal gas constant $R$ has been measured for various gases under ideal conditions of high temperatures and low pressures. It has been found to have the same value for all substances: 8.3144626 J/(mol·K).

The ideal gas equation can also be expressed in the following ways:

\begin{aligned} p \, v &= R_s \, T \\ p \, V &= m \, R_s \, T \\ P \, \overline{v} &= R \, T \end{aligned}

where:

• $R_s$ - Specific gas constant in J/(kg·K) or BTU/(lb·R);
• $m$ - Mass in kg or lb;
• $v$ - Specific volume in m3/kg or ft3/lb; and
• $\overline{v}$ - Specific molar volume in m3/mol or ft3/kmol.

From the ideal gas law, other gas laws are derived. That is the case of the Boyle's law, Charles's law, and Gay-Lussac's law.

💡 When a gas is close to its condensation point, it does not satisfy the ideal gas equation. This would be the case of a vapor.

## How to find the pressure of a gas with the ideal gas law calculator

Imagine that we are interested in determining the pressure of 140.5 kg of air that occupies a volume of 120 m3, at 25 °C. Let's see how to calculate the pressure of the gas using the ideal gas law calculator:

1. On the Volume (V) row, enter the volume of the gas. By clicking on the unit's dropdown menu, you can choose between different volume units.
2. Next, we are going to input the mass of air. Click on the Advanced mode button, and the Total mass of the gas (m) field will appear. Here input the value of the mass, 140 kg.
3. Proceed to enter the value of the substance's Molar mass (M). For air, this value corresponds to 28.9647 g/mol or 0.0289647 kg/mol.*
4. Finally, in the Temperature (T) field, enter the temperature, 25 ° C.
5. Once these are entered, the calculator will display the value of Pressure (P), 100.2063 kPa,

🙋 Use the Advanced mode of the calculator to input or get the values of the total mass of gas, molar mass, and ideal gas constant.

Gabriela Diaz
Pressure (p)
Pa
Volume (V)
cu ft
Amount of substance (n)
mol
Temperature (T)
°F
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