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# The Ideal Gas Law

This video and the notes below cover details about the ideal gas law, and the variables that make it up.

## Gas Laws

The ideal gas law is:

[pV=nRT]

Where the variables are:

symbol description
p pressure
V volume
n moles
R the universal gas constant
T temperature

The units of these variables will be discussed over the next steps, and are the key to applying this equation correctly.

### Empirical Gas Laws

The gas law leads to a number of relationships that can be empirically justified – the ideal gas law was historically assembled from these empirical laws. At constant temperature, pressure multiplied by volume is constant, so a change in pressure results in a predictable change in volume.

[p_1 V_1=p_2 V_2]

At constant pressure, a change in volume results in a predictable change in temperature and a change in temperature results in a predictable change in volume.

[frac{V_1}{T_1}=frac{V_2}{T_2}]

And at constant volume a change in pressure results in a predictable change in volume.

[frac{p_1}{T_1}=frac{p_2}{T_2}]

## What is Pressure?

Pressure comes from the force felt due to microscopic particles colliding with a container or the surrounding gases. Each particle carries momentum, and the momentum is felt as pressure after the collision.

It is quantified in two ways. First, as a force spread out over an area, and also the amount of energy divided by its volume (energy density). These concepts are related by how energy and force are related by distance.

### Pressure = Force over area

Equation: (P=frac{F}{A})

Justification of the units: (kg:m^{-1}s^{-2}=frac{kg:m:s^{-2}}{m^2})

### Pressure = Energy over volume

Equation: (P=frac{E}{V})

Justification of the units: (kg:m^{-1}s^{-2}=frac{kg:m^2:s^{-2}}{m^3})

### Force = energy over distance

Equation: (F=frac{E}{d})

Justification of the units: (kg:m:s^{-2}=frac{kg:m^2:s^{-2}}{m})

## What is Temperature?

Temperature is an SI base unit. It is measured in Kelvin. It is the manifestation of sub-microscopic kinetic energy of particles.

These particles do not all have the same kinetic energy, and so they don’t have the same speed. Temperature is a measure of the average amount of energy of the particles. Hotter gases have more particles that travel faster, cooler gases have more particles that travel slower.

## What is Volume?

Obviously, volume is a three-dimensional space. However, it’s worth bringing up because the ideal gas law has a two-dimensional analogue that relates to concepts in surface tension. So we can replace “V” with “A”, and pressure with “surface pressure”, which is related to surface tension measurements. This is useful in materials chemistry, should you study that later.

Ideal gas law Surface pressure
(pV=nRT) (pi A=nRT)