The **key difference** between ideal gas law and real gas law is that **ideal gas law describes the behaviour of a theoretical gas, whereas real gas law describes the behaviour of actually occurring gases in the universe**.

An ideal gas is a theoretical gas whose randomly moving gas particles have completely elastic collisions and no other interactions between them. According to this definition, we can understand that these ideal gases cannot occur in nature because there are essentially interactions between gas particles for any gas we know. In fact, the gases we know are real gases.

### CONTENTS

1. Overview and Key Difference

2. What is Ideal Gas Law

3. What is Real Gas Law

4. Side by Side Comparison – Ideal Gas Law vs Real Gas Law in Tabular Form

5. Summary

## What is the Ideal Gas Law?

Ideal gas law is an equation that describes the behaviour of an ideal gas. Ideal gases are hypothetical, and these gases occur only in theories. Therefore, using the ideal gas law, we can understand and estimate the behaviour of many real gases we know. However, it has several limitations. Also, this law is a combination of several other laws:

- Boyle’s law
- Charles’s law
- Avogadro’s law
- Gay-Lussac’s law

### Calculation

Basically, we can give the ideal gas law as follows;

**PV = nRT**

Where, P is pressure, V is volume and T is the temperature of the ideal gas. Here, “n” is the number of moles of the ideal gas and “R” is a constant – we call it **ideal gas constant**. It has a universal value; the value of R is the same for any gas, and it is 8.314 J/(K·mol).

Moreover, we can obtain different derivatives from this law; molar form, combined form, etc. For example, since “n” is the number of moles, we can give it using the molecular weight of the gas. The derivation is as follows.

**n = m/M**

where, n is the number of moles of gas, m is the mass of the gas and M is the molecular weight of the gas. By using the above equation,

**PV = nRT**

**PV = (m/M)RT**

If we want to get the density of the gas, we can use the above equation as follows;

**P = (m/VM) RT**

**P = ρRT/M**

Moreover, if we want to get the combined gas law from the ideal gas law, we can derive it as follows; for two gases “1” and “2”, the pressure, volume and temperature are P_{1},V_{1},T_{1} and P_{2}, V_{2} and T_{2}. Then for the two gases, we can write two equations as;

P_{1}V_{1} = nRT_{1} ……………..(1)

P_{2}V_{2} = nRT_{2 }……………..(2)

By dividing equation (1) from equation (2), we get,

(P_{1}V_{1})/(P_{2}V_{2}) = T_{1}/ T_{2}

We can rearrange this equation as follows;

P_{1}V_{1}/ T_{1} = P_{2}V_{2}/ T_{2}

## What is Real Gas Law?

Real gas law, also called **Van der Waals law**, is derived from the ideal gas law to describe the behaviour of real gases. Since real gases cannot behave ideally, the real gas law has made changes to the pressure and volume components in the ideal gas law. Thus, we can obtain the volume and pressure as follows:

Volume** of real gas = (V _{m} – b)**

**Pressure of real gas = (P + a{n ^{2}/V^{2}})**

Then, we can get the real gas law by applying these modified components to the ideal gas law as follows:

**(P + a{n ^{2}/V^{2}})(**V

_{m}– b) = nRTWhere, V_{m} is the molar volume of gas, R is universal gas constant, T is the temperature of real gas, P is the pressure.

## What is the Difference Between Ideal Gas Law and Real Gas Law?

Ideal gas law is an equation that describes the behaviour of an ideal gas. Real gas law is derived from the ideal gas law to suit the behaviour of real gases. So, the key difference between ideal gas law and real gas law is that ideal gas law describes the behaviour of a theoretical gas, whereas real gas law describes the behaviour of actually occurring gases in the universe.

Moreover, we can derive the ideal gas law from the equation PV=nRT, and the real gas law from the equation (P + a{n^{2}/V^{2}})(V_{m} – b) = nRT.

## Summary – Ideal Gas Law vs Real Gas Law

In brief, an ideal gas is a hypothetical substance which has completely elastic collisions between gas particles, a property which most real gases we know don’t show. The key difference between ideal gas law and real gas law is that ideal gas law describes the behaviour of a theoretical gas, whereas real gas law describes the behaviour of actually occurring gases in the universe.

##### Reference:

1. Ideal Gas Law, Hyperphysics. Georgia State University, Available here.

##### Image Courtesy:

1. “Ideal gas law relationships” By Cmglee – Own work (CC BY-SA 4.0) via Commons Wikimedia

2. “Ideal Gas Law” By BlyumJ – Own work (CC BY-SA 4.0) via Commons Wikimedia

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