Skip main navigation

Revision — all equations so far

This is a short summary article of what we have already covered.
Header image for revision

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.

This article is from the free online

Introduction to Thermodynamics

Created by
FutureLearn - Learning For Life

Our purpose is to transform access to education.

We offer a diverse selection of courses from leading universities and cultural institutions from around the world. These are delivered one step at a time, and are accessible on mobile, tablet and desktop, so you can fit learning around your life.

We believe learning should be an enjoyable, social experience, so our courses offer the opportunity to discuss what you’re learning with others as you go, helping you make fresh discoveries and form new ideas.
You can unlock new opportunities with unlimited access to hundreds of online short courses for a year by subscribing to our Unlimited package. Build your knowledge with top universities and organisations.

Learn more about how FutureLearn is transforming access to education