# How do you calculate the ideal gas law constant?

Jan 1, 2014

You do an experiment in which you measure the values of $P , V , n$, and $T$, and then you insert these values into the Ideal Gas Law.

#### Explanation:

The Ideal Gas Law is

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where $R$ is the Universal Gas Constant.

We can rearrange this to get

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

The units of $R$ depend on the units you use for $P$ and $V$.

For example, repeated experiments show that at standard temperature and pressure (STP) — 273.15 K and 1 bar — 1 mol of gas occupies 22.711 L.

You can use this information to evaluate $R$.

R = (PV)/(nT) = ("1 bar ×22.711 L")/("1 mol × 273.15 K") = "0.083 14 bar·L·K"^"-1""mol"^"-1"

If the pressure is measured in kilopascals (1 bar = 100 kPa), you calculate

R = (PV)/(nT) = ("100 kPa × 22.711 L")/("1 mol × 273.15 K") = "8.314 kPa·L·K"^"-1""mol"^"-1"

If you use strictly SI units, then pressure is measured in pascals and volume is measured in cubic metres.

R = (PV)/(nT) = (100 × 10^3 color(white)(l)"Pa" × 22.711 × 10^"-3" color(white)(l)"m"^3)/("1 mol × 273.15 K") = "8.314 Pa·m"^3"K"^"-1""mol"^"-1"

Always use the value of $R$ that corresponds to the units that you are using for $P$ and $V$.