# Question #eb368

##### 1 Answer

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 **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

#PV = nRT" "# ,where

*universal gas constant*, usually given as

Rearrange this equation to have

#V = (nRT)/P#

#V/n = (RT)/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"))))#

#V/n = 22.7"L"/"mol"#

To get the volume occupied by **one mole**, simple replace

#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

You can calculate the molar volume of a gas at any pressure and temperature. For example, at a pressure of

#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"))))#

#V/n = 15.3 "L"/"mol"#

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

#V = "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* *and*

*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 = "22.4 L"#