# Revision — all equations so far

This is a short summary article of what we have already covered.
So far, we’ve come a long way, and worked on a number of problems. This article summarises the equations we’ve come across.

### Ideal gas law

First, the ideal gas law, an equation burned into the eyelids of most physical chemists:

[pV = nRT]

This implies that for a set volume and temperature, one mole of gas will always be at the same pressure. And that for a set volume and pressure, one mole of gas will always be at the same temperature. And also for a set temperature and pressure, one mole of gas will occupy the same volume.

Can you calculate that for ambient temperature and pressure?.

### Mole fractions and partial pressures

A mole fraction of a mixture of gases is:

[x_1 = frac{n_1}{n_1 + n_2 + …}]

A partial pressure is the total pressure multiplied by this mole fraction:

[p_1 = x_1 times p_tot]

## Real gases

### Compressibility

The compressibility(Z) of a gas comes from rearranging the ideal gas law. When it’s close to ideal, Z = 1.

[frac{pV}{nRT} = Z]

### van der Waals equation

The van der Waals equation modifies the ideal gas law to take into account gas interactions:

[left(p+frac{n^2a}{V^2}right)left(V-nbright)=nRT]

Parameter a adjusts pressure by taking into account molecular interactions. Parameter b adjust volume by accounting for molecular size.