The ideal gas equation is a single equation that connects pressure, volume, temperature, and moles for a gas:

The symbolic form is short, but each symbol must be interpreted with care.

In this equation:

• p = pressure in pascals, Pa
• V = volume in cubic metres, m^3
• n = amount of gas in moles, mol
• R = gas constant
• T = temperature in kelvin, K

One useful boundary to remember is that you do not need to memorise the value of R. If a calculation needs it, the value will be given.

This equation is especially useful because it gives a good model for many gases, especially at ordinary temperatures and pressures, provided you use the correct units and substitute carefully. It is still an idealised model, so you should not treat it as exact for every gas under all conditions.

Most mistakes with the ideal gas equation happen before the calculation even begins. The algebra may be right, but if the values are not in SI units, the final answer will be wrong.

The three conversions you need most often are:

• pressure: kPa to Pa by multiplying by 1000
• volume: dm^3 to m^3 by dividing by 1000
• volume: cm^3 to m^3 by multiplying by 1.0 x 10^-6
• temperature: degrees C to K by adding 273

These unit choices are not arbitrary. R is usually given in J K^-1 mol^-1, and 1 J = 1 Pa m^3, so using Pa, m^3, mol, and K keeps the units on both sides of pV = nRT consistent.

Worked example:

A gas has pressure 95.0 kPa, volume 250 cm^3, and temperature 27 degrees C.

• p = 95.0 kPa = 95 000 Pa
• V = 250 cm^3 = 250 x 10^-6 m^3 = 2.50 x 10^-4 m^3
• T = 27 degrees C = 300 K

The diagram below summarises the unit conversions you should check before substituting values into pV = nRT.

[DIAGRAM: asset_name: 1.2.3 - The Ideal Gas Equation - Diagram 1; asset_slug: 1.2.3 - The Ideal Gas Equation - Diagram 1; recommended_method: retained_png; description: A 16:9 landscape SI-unit conversion checklist for pV = nRT with a centred header box Use SI units in pV = nRT above three evenly spaced vertical panels labelled pressure, volume, and temperature. In the pressure panel show kPa x 1000 -> Pa and the example 95.0 kPa -> 95 000 Pa. In the volume panel show dm^3 / 1000 -> m^3, cm^3 x 1.0 x 10^-6 -> m^3, and the example 250 cm^3 -> 2.50 x 10^-4 m^3. In the temperature panel show degrees C + 273 -> K and the example 27 degrees C -> 300 K. Add a footer note Check units before rearranging or substituting. Use white background, thin grey lines, light sans-serif labels, and a clean uncluttered revision-card layout.]

The best habit is to rewrite every value in SI units before rearranging the equation or reaching for a calculator.

A very common use of the equation is to calculate the amount of gas present. To do that, rearrange the equation so that n is the subject:

This is a good place to work methodically:

1. convert all values into SI units
2. write the rearranged equation
3. substitute with units
4. give the answer to a sensible number of significant figures

Worked example:

Calculate the number of moles of gas in 500 cm^3 at 100 000 Pa and 25 degrees C.

First convert the units:

• V = 500 cm^3 = 5.00 x 10^-4 m^3
• T = 25 degrees C = 298 K

Now substitute into the equation:

The step students most often miss is the volume conversion. 500 cm^3 is not 0.500 m^3; it is 5.00 x 10^-4 m^3.

This reflection matters because the chemistry is usually simple here, but one careless unit slip changes the whole answer.

The same equation can be rearranged for other quantities. For example:

and

This means the ideal gas equation can be used to find:

• the volume occupied by a known amount of gas
• the pressure exerted by a known amount of gas
• the number of moles present in a measured sample

If the pressure stays the same, increasing temperature increases volume. If the volume stays the same, increasing temperature increases pressure. The equation helps you calculate those changes rather than just describing them.

Worked example:

Find the volume of 0.250 mol of gas at 300 K and 1.00 x 10^5 Pa.

So the gas occupies 6.23 x 10^-3 m^3, which is 6.23 dm^3.

If pressure is the unknown, rearrange to p = nRT/V and check the volume is in m^3 before substituting.

Worked example:

Find the pressure of 0.200 mol of gas at 300 K in 5.00 dm^3.

First convert the volume:

• V = 5.00 dm^3 = 5.00 x 10^-3 m^3

Now substitute into the equation:

So the pressure is 9.97 x 10^4 Pa, which is about 1.00 x 10^5 Pa.

You can treat that as a checklist to run through before pressing =.

These calculations are usually short, but they reward disciplined method. If you choose the correct rearrangement and keep the units visible throughout, the result is usually very dependable.