# Question 1c1be

Jun 4, 2015

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

For example, the molar volume of a gas at STP represents the volume 1 mole of any ideal gas occupies at a pressure of 100 kPa and a temperature of 273.15 K.

In other words, if those conditions for pressure and temperature are met, 1 mole of any gas will occupy a volume of 22.7 L.

You can determine the molar volume of a gas under any conditions of pressure and temperature by using the ideal gas law equation.

$P V = n R T$, where

$P$ - the pressure of the gas;
$V$ - its volume;
$n$ - the number of moles of gas;
$T$ - its temperature.

You can rearrange this equation to get

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

If the pressure is equal to 1 atm and the temperature to 273.15 K, you'll get

V/n = (0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * 273.15cancel("K"))/(1cancel("atm")) = "22.4 L/mol"

If you want to see what volume 1 mole would occupy, simply replace $n$ with 1

V/(1cancel("mol")) = 22.4"L"/cancel("mol") => V = "22.4 L"

SIDE NOTE This is the actually the old definition of the molar volume of a gas at STP.

If you have a pressure of 2 atm and a temperature of 355 K, you would get

V/n = (0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * 355.15cancel("K"))/(3cancel("atm")) = "9.71 L"#

So, under these specific conditions for pressure and temperature, 1 mole occupies 9.71 L. You would have

• 2 moles $\to$ $9.71 \cdot 2 = \text{19.4 L}$
• 4.5 moles $\to$ $9.71 \cdot 4.5 = \text{43.7 L}$
• 0.05 moles $\to$ $9.71 \cdot 0.05 = \text{0.486 L}$

and so on.

As a conclusion, the molar volume of a gas represents the volume occupied by 1 mole of any ideal gas under specific conditions for temperature and pressure.

If pressure and/or temperature change, the molar volume changes as well.