Question

How do you calculate the ideal gas law constant?

Answer 1

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

`color(blue)(bar(ul(|color(white)(a/a)PV=nRTcolor(white)(a/a)|)))" "`

where `R` is the Universal Gas Constant.

We can rearrange this to get

`R = (PV)/(nT)`

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`.