What is the volume occupied by one mole of helium at 0 C and 1 atm pressure?

1 Answer
Feb 23, 2017

Answer:

#"22.4 L"#

Explanation:

The conditions for temperature and pressure provided to you actually correspond to the old definition of STP (Standard Pressure and Temperature).

Under these specific conditions, #1# mole of any ideal gas occupies #"22.4 L"#. This value is known as the molar volume of a gas.

You can show that this is the case by using the ideal gas law equation, which looks like this

#color(blue)(ul(color(black)(PV = nRT)))#

Here

  • #P# is the pressure of the gas
  • #V# is the volume it occupies
  • #n# is the number of moles of gas present in the sample
  • #R# is the universal gas constant, equal to #0.0821("atm L")/("mol K")#
  • #T# is the absolute temperature of the gas

Rearrange the ideal gas law equation to

#PV = nRT implies V/n = (RT)/P#

Plug in your values to find -- do not forget to convert the temperature from degrees Celsius to Kelvin

#V/n = (0.0821 (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/n = "22.4 L mol"^(-1)#

This means that under these conditions for pressure and temperature, you get #"22.4 L"# for every mole of an ideal gas present in a sample.

SIDE NOTE STP conditions are currently defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#.

Under these specific conditions, the molar volume of a gas is equal to #"22.7 L mol"^(-1)#.