## Core Concepts

This tutorial will teach you about the gas laws, the derivation of the ideal gas law equation, and how to use it. You will also learn what defines an ideal gas, what the ideal gas constant is, ideal gas law units, and what assumptions we make to call a gas ideal – the ideal gas properties.

## Topics Covered in Other Articles

- What is Pressure
- Measuring Gas Pressure
- Dalton’s Law of Partial Pressure
- Charles’ Law
- Avogadro’s Law
- Boyle’s Law
- Van der Waal’s Equation
- Kinetic Gas Theory
- Gay Lussac’s Law
- Combined Gas Law
- Henry’s Law
- Graham’s Law of Effusion

## What are the Gas Laws?

The **gas laws** are a set of laws that describe the behavior of gases under different conditions of temperature, pressure, and finally, volume. These laws were developed by scientists such as Robert Boyle, Charles’s Law, and Gay-Lussac’s Law, and they are based on the idea that the particles in a gas are in constant motion and interact with each other only through collisions. The gas laws describe how the pressure, volume, and temperature of a gas relate to one another, and chemists use them to predict the behavior of gases under different conditions.

## What is the Ideal Gas Law?

For example, the ideal gas law states that the pressure, volume, and temperature of a gas are directly proportional to each other, as long as the number of particles and the mass of the gas remain constant. This law can be used to calculate the properties of a gas, such as its density or molar mass, given certain information about its pressure, volume, and temperature. The gas laws are an important concept in chemistry, and chemists use them to explain many of the properties and behavior of gases.

The ideal gas law is an equation of state that describes basically ideal gases and their behaviour. This equation of state relates a gas’s pressure, volume, temperature, and mass, and is very useful for describing how gases will behave in ideal conditions. This is the most common equation of state for gases.

Additionally, there are a few other gas laws that are worth noting. For instance, the Van der Waal’s and the Virial equation of state are two laws that describe the state of gases in non-ideal states. If you are interested in learning more about Van der Waal’s Equation, check out our article on it besides this one.

The **ideal gas equation** was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. Clapeyton was a French engineer, and one of the founders of thermodynamics.

## What are the Ideal Gas Properties?

Gases consist of a large number of particles constantly colliding with each other randomly. In order to model and predict the behavior of gases, the concept of an ideal gas was thus created. If a gas is ideal, then a few assumptions need to be made. These can also be viewed as the **ideal gas properties**.

- Firstly , we assume that the volume of the gas particles is negligible. This means that the volume of the container is much larger than the volume of the gas particles.
- Secondly, we assume that the gas particles have equal size, and do not have intermolecular forces with other gas particles.
- Thirdly, we assume that the gas particles move randomly according to Newton’s Laws of Motion.
- Lastly, we assume that all collisions are perfectly elastic and have no energy loss. This means that the collisions between gas particles and the walls don’t lose energy, and exert constant pressure.

Although no gas is perfectly ideal most gases are close enough at room temperature and are nearly ideal.

## Combining the Gas Laws into the Ideal Gas Law Equation

When we take into account the three basic gas laws – Charles’ Law, Avogadro’s Law, and Boyle’s Law – we can establish relationships between a gas’s pressure, volume, temperature, and quantity of moles. By combining each equation, we can derive the ideal gas law equation.

Because this proportionality takes into account all changes of state of gases, it will be constant for an ideal gas. This constant is generally known as the **Ideal Gas Constant**, or Universal Gas Constant, and has a value of . We can plug this constant, labeled , into the equation to derive the ideal gas law, .

## Ideal Gas Law Units

When using SI units (international system of units), the ideal gas law equation employs the following units.

- equals pressure measured in Pascals, .
- equals the volume measured in cubic meters,
- equals the number of moles.
- represents the universal gas constant measured in , or alternatively
- equals the temperature measured in Kelvin.

If you are using liters and atmospheres of pressure, instead of Pascals and cubic meters, then you have the following:

- equals pressure measured in atmospheres
- equals the volume measured in liters
- equals the number of moles.
- represents the universal gas constant measured in
- equals the temperature measured in Kelvin.

## For More Help, Watch our Interactive Video Explaining the Ideal Gas Law!

## Ideal Gas Law Practice Problems

**Problem 1**

Ethanol and methanol combust according to the following chemical equations:

A mixture of ethanol and methanol combusts in oxygen to produce of CO_{2} and of H_{2}O. They perform complete combustion and measure the volumes of both products at and . What is the molar ratio, ethanol to methanol, in the mixture?

**Problem 2**

Given that the sample of gas in a vessel has a pressure of at and there is a known amount of of gas present, the task at hand is to determine the gas’s identity. (Hint: To accomplish this, you will need to calculate the molar mass of the gas before.)