# Real Gases

The Kinetic Molecular Theory describes the properties of ideal gases. Recall the tenets of the Kinetic Molecular Theory:

1. A gas consists of a collection of small particles that travel in straight-line motion and obey Newton’s Laws.

2. Gas particles occupy no volume.

3. Collisions between particles are perfectly elastic, meaning that no energy is gained or lost during the collision.

4. There are no attractive or repulsive forces between the particles.

The Kinetic Molecular Theory states that gas particles occupy no volume. But in reality, real gases DO occupy volume.

The Kinetic Molecular Theory says that collisions between particles are perfectly elastic, but real gases have inelastic collisions, which means that energy is lost when gas particles collide.

And finally, Kinetic Molecular Theory says that there are no attractive or repulsive forces between gas particles. Whereas, real gases DO attract and repel each other.

Let’s consider the volume of real gas particles.

## Real Gases DO Have Volume

Molecules of real gases DO take up space and have volume, which reduces the effective volume of their container. This volume is reduced by nb, where n represents the number of moles of gas, and b is an experimentally determined constant specific to that gas. Therefore, the effective volume of a real gas is less than that of an ideal gas, because the volume of the particles themselves is accounted for:

Where:

V = volume

n = moles of gas

b = an experimentally determined constant, specific to that gas.

The ideal gas law, taking into account this reduction in effective volume, can be rewritten as:

## Real Gases Exert Pressure

When the effective volume of the container is reduced, the pressure inside the container is INCREASED. This pressure is increased by $${\frac{{n^2a }}{{V^2 }}}$$,

where a is an experimentally determined constant specific to the gas.

Where:

P = pressure

V = volume

n = moles of gas

a = an experimentally determined constant, specific to that gas.

Combining the effect of pressure and volume on a gas, the ideal gas law becomes Van der Waal’s Equation.

## Van der Waal’s Equation

Where:

P = pressure

V = volume

n = moles of gas

R = 0.081 L-atm-K-1-mol-1

a and b are experimentally determined constants specific to the gas

## When does a Real Gas Behave Like an Ideal Gas?

A real gas behaves like an ideal gas when the gas particles stay as far away from each other as possible. This occurs at the conditions of low pressure and high temperature. Under low pressure and high temperature conditions, gas particles have little contact with each other thereby colliding less frequently and exerting minimal forces on each other.

Let’s look at a sample problem using Van der Waal’s equation:

Sample Problem

Using the Van der Waals equation, calculate the pressure in a 22.4 L vessel containing 1.00 mol of neon gas at 100 degrees Celsius (a = 0.211, b = 0.0171)

We are asked to find pressure, and we are given:

V = 22.4 L

n = 1.00 mol

T = 100 ºC

As with all gas problems we need to convert temperature into Kelvin:

Van der Waal’s equation is:

To solve for P, we first divide each side of the equation by V-nb:

Our equation becomes:

Then, we subtract n2a/V2 from each side:

Plugging in the given values, and solving for pressure, P: