Question

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

Answer 1

`"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)`.