Question

Question #eb368

Answer 1

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 `"100 kPa"` and a temperature of `0^@"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

`PV = nRT" "`,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("atm" * "L")/("mol" * "K")`
`T` - the temperature of the gas expressed in Kelvin.

Rearrange this equation to have `V/n` on one side

`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 `n` with `"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 `"22.7 L"`.

You can calculate the molar volume of a gas at any pressure and temperature. For example, at a pressure of `"2 atm"` and a temperature of `100^@"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"))))`

`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 `0^@"C"` and `"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 = "22.4 L"`