pV = nRT: the ideal gas equation

By the end of this lesson

By the end you can state the ideal gas equation, convert every quantity into the right unit, and use it to find $p$ , $V$ , $n$ or $T$ .

Definition

The ideal gas equation

$pV = nRT$

$p$ = pressure, in pascals ( $\text{Pa}$ ) — or kilopascals ( $\text{kPa}$ ), if you keep the units consistent (see below)
$V$ = volume, in cubic metres ( $\text{m}^3$ ) or cubic decimetres ( $\text{dm}^3$ )
$n$ = amount of gas, in moles ( $\text{mol}$ )
$R$ = the molar gas constant, $8.31\ \text{J K}^{-1}\text{mol}^{-1}$
$T$ = thermodynamic temperature, in kelvin ( $\text{K}$ )

Why kelvin, and what is R?

Kelvin is the absolute temperature scale: $0\ \text{K}$ is the coldest anything can possibly be, and gas volume and pressure scale nicely from it. The conversion is simple:

$T(\text{K}) = T(^\circ\text{C}) + 273$

$R$ is a fixed constant that sets the scale between "how much gas" and "what $p$ and $V$ do". Its units look odd now; they make the two sides of $pV = nRT$ balance in joules.

Two unit recipes that both work

The most common lost mark in gas calculations is a unit mismatch. There are two safe recipes:

recipe	pressure	volume	then $pV$ comes out in
SI	$\text{Pa}$	$\text{m}^3$	$\text{J}$
chemist's	$\text{kPa}$	$\text{dm}^3$	$\text{J}$

Both work because $1\ \text{Pa m}^3 = 1\ \text{J}$ and $1\ \text{kPa dm}^3 = 1\ \text{J}$ .

Conversions you will need constantly:

$1\ \text{dm}^3 = 1000\ \text{cm}^3 = 0.001\ \text{m}^3$
$1\ \text{m}^3 = 10^{6}\ \text{cm}^3$
$1\ \text{kPa} = 1000\ \text{Pa}$

Pick one recipe per question and convert everything to it before you calculate.

Units and symbols

Fill in the blanksQuestion 1 · Recall

CalculateQuestion 2 · Recall

Answer the 2 questions above to continue.