The Gas Constant

In order to apply these equations, it’s vital to get the dimensions and units correct. This will then let us introduce the gas constant, what it means, and applying the ideal gas law.

Units of Pressure

The units of pressure are complicated due to the way it has been historically measured. Often, it’s measured by a manometer, where a column of liquid is pushed up by pressure pushing down on it elsewhere. This means that pressure has sometimes measured as a distance, such as in mmHg (millimetres of mercury) or mmH₂O (millimetres of water). Mercury is more useful than water, here, because its high density means you get a wider range of pressures from a shorter column.

Pressure is also measured in atm (atmospheres), which is a convenient unit because 1 atm is approximately the pressure at sea level. The weather and climate vary slightly day to day, so 1 atm is defined as 101,325 Pa.

The Pascal (Pa) is the SI standard unit. 1 Pa is 1 kg m s^-2 or 1 N m^-2. This is compatible with anything else measured in SI units.

Units of Temperature

Temperature is measured in K (Kelvin). No other units exist as far as we are concerned!

Units of the Gas Constant

To keep the ideal gas law correct and compatible, the units of the gas constant must match the other values you use in the equation.

The value most people use is 8.314 J K^-1 mol^-1. This is a standard SI unit.

In order to use this exact value you must:

• Use temperature in K
• Use pressure in Pa
• Use volume in m³

Alternative Values

The requirement to use SI units is slightly unfortunate. It’s convenient to state pressure in atm, which relates to atmospheric pressure – we can easily get a feel for what “1 atm” pressure is, as we live in that pressure. And it’s also convenient to state volume in litres (L), as chemistry doesn’t usually deal with volumes as large as cubic meters.

If we change the units of the variables, the value of the gas constant must change.

Note: this does not mean that the gas constant itself is changing. Only the units we use to measure it have changed. This is much the same way as to how a car going at 113 kilometres per hour is not traveling faster than a car going at 70 miles per hour.

So, another value of the gas constant that is useful is 0.082 L atm K^-1 mol^-1.

Using this for R allows you to use litres (dm³) and atm directly in the ideal gas law. Note that “L atm” is “volume × pressure”, which you should know equals energy. 1 L × 1 atm = 101.3 J, however, there is not a standard unit of energy for this. Also notice that 8.314 ÷ 101.3 = 0.082! The two values of the gas constant are related.