Question #eb368

1 Answer
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 "100 kPa"100 kPa and a temperature of 0^@"C"0C - 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" "PV=nRT ,where

PP - the pressure of the gas;
VV - the volume it occupies;
nn - the number of moles of gas;
RR - the universal gas constant, usually given as 0.082("atm" * "L")/("mol" * "K")0.082atmLmolK
TT - the temperature of the gas expressed in Kelvin.

Rearrange this equation to have V/nVn on one side

V = (nRT)/PV=nRTP

V/n = (RT)/PVn=RTP

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"