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

1 Answer
Feb 23, 2017

"22.4 L"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, 11 mole of any ideal gas occupies "22.4 L"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).