# What units should I use in the ideal gas law equation?

Jan 11, 2015

The ideal gas law equation allows for the use of a wide variety of units as long as you correlate these units with those that express the gas constant, $\text{R}$. The ideal gas law equation looks like this:

$P V = n R T$, where

$P$ - pressure - the most commonly used units used to express pressure are atm, mmHg, torr, Pa, kPa, bar;
$V$ - volume - commonly used units are L, ${\text{m}}^{3}$, ${\text{cm}}^{3}$, ${\text{dm}}^{3}$;
$n$ - the number of moles;
$T$ - temperature - commonly used units are $\text{^@"C}$, K, $\text{^@"F}$;
$R$ - the gas constant.

$\text{R}$ can be expressed in a multitude of units, depending on what is used for $P$, $V$, and $T$. Here's a list of the possible values and units used for $\text{R}$: http://www.cpp.edu/~lllee/gasconstant.pdf

All those units express the equation

$R = \frac{P V}{n T}$

There are however two widely used expressions for $\text{R}$

$R = 0.0821 \left(\text{L" * "atm")/("mol" * "K}\right)$

This value corresponds to a volume given in liters (L), a pressure given in atmospheres (atm), and a temperature given in Kelvin (atm).

This expression for $\text{R}$ can be used either when the three aforementioned paramaters are already expressed in these units, or when unit conversions are used to get to the units needed.

The other very common expression for the gas constant is

$R = 8.314 \left(\text{J")/("mol" * "K}\right)$

This time pressure and volume are given in Pa and ${\text{m}}^{3}$, respectively, which give Joules (J) when multiplied. Again, this value can be used if the appropiate units are given for temperature, pressure, and volume.

If you are given a particular expression for $\text{R}$ and asked to use it regardless of the units given for the three paramaters, then you must convert what is given to you to match the expression of the gas constant.