Gas Laws: The Ideal Gas Law

Core Concepts

In this tutorial, you will learn how the ideal gas law was derived and how to use it. You will also learn what defines an ideal gas, and what assumptions we make to call a gas ideal.

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The ideal gas law is an equation of state that describes ideal gases. 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.

A few notable other ones are the Van der Waal’s and the Virial equation of state, which both describe the state of gases in non-ideal states. See our article on Van der Waal’s Equation of State to learn more about this.

What is an Ideal Gas?

For a gas to be ideal, a few assumptions need to be made.

For one, we assume that the volume of the gas particles are negligible. This means that the volume of the container is much larger than the volume of the gas particles.

The second assumption we make is that the gas particles are equally sized, and do not have intermolecular forces with other gas particles.

Third, 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 a constant pressure.

Combining the Gas Laws

If we consider the three basic gas laws, Charles’ Law, Avogadro’s Law, and Boyle’s Law, we can make relations between a gas’s pressure, volume, temperature, and quantity of moles. By taking each equation and combining them, we can derive the ideal gas law.

     \begin{align*} P&\propto\frac{1}{V}\\ V&\propto T\\ n&\propto V\\ \implies PV&\propto nT\\ \implies \frac{PV}{nT}&=c \end{align*}

Because this proportionality takes into account all changes of state of gases, it will be constant for an ideal gas. This constant is known as the Universal Gas Constant, and has a value of 0.0082057\frac{\text{atm L}}{\text{mol K}}. We can plug this constant, labeled R, into the equation to derive the ideal gas law, \boxed{PV=nRT}.

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