# How to claculate value of universal gas constant?

Jan 8, 2017

You must do an experiment in which you measure the values of $P , V , n$, and $T$.

#### 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

$P$ = the pressure
$V$ = the volume
$n$ = the number of moles
$R$ = the Universal Gas Constant
$T$ = the temperature

We can rearrange the Ideal Gas Law to get

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

If you do an experiment in which you measure the values of $P , V , n$, and $T$, you can insert these values into the equation and calculate $R$.

For example, repeated experiments show that at standard temperature and pressure (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") = "0.083 145 L·atm·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) = (1.013 25 × 10^5 color(white)(l)"Pa" × 22.414× 10^"-3"color(white)(l) "m"^3)/"1 mol × 273.15 K" = "8.3145 Pa·m"^3"K"^"-1""mol"^"-1"

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