# Question eb368

Aug 22, 2015

You start from the idea lgas law equation and work your way from there.

#### Explanation:

The molar volume of a gas simply means the volume occupied by 1 mole of an ideal gas under certain conditions for temperature and pressure.

More often than not, the molar volume of a gas is given for a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$ - these values for pressure and temperature describe the Standard Temperature and Pressure conditions.

So, let's say that you want to determine what the molar volume of a gas at STP is. Start from the ideal gas law equation

$P V = n R T \text{ }$,where

$P$ - the pressure of the gas;
$V$ - the volume it occupies;
$n$ - the number of moles of gas;
$R$ - the universal gas constant, usually given as $0.082 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the temperature of the gas expressed in Kelvin.

Rearrange this equation to have $\frac{V}{n}$ on one side

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

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

Use the STP values to get - don't forget to convert the pressure from kPa to atm!

V/n = (0.082(color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(100/101.325color(red)(cancel(color(black)("atm"))))

$\frac{V}{n} = 22.7 \text{L"/"mol}$

To get the volume occupied by one mole, simple replace $n$ with $\text{1 mole}$

V/(1color(red)(cancel(color(black)("mole")))) = 22.7"L"/color(red)(cancel(color(black)("mole"))) = color(green)("22.7 L")

The molar volume of a gas at STP is equal to $\text{22.7 L}$.

You can calculate the molar volume of a gas at any pressure and temperature. For example, at a pressure of $\text{2 atm}$ and a temperature of ${100}^{\circ} \text{C}$, you get

V/n = (0.082(color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 100)color(red)(cancel(color(black)("K"))))/(2color(red)(cancel(color(black)("atm"))))

$\frac{V}{n} = 15.3 \text{L"/"mol}$

This means that under these conditions for pressure and temperature, the molar volume of a gas is

$V = \text{15.3 L}$

SIDE NOTE Many textbooks and online resources still give the molar volume of a gas as being equal to 22.4 L at STP.

That happens because the old definition of STP is being used, meaning that the condtions are ${0}^{\circ} \text{C}$ and $\text{1 atm}$.

If you use these values, you will indeed get

V/n = (0.082(color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(1color(red)(cancel(color(black)("atm"))))#

$V = \text{22.4 L}$