Question

What is the number of moles in 500 L of `He` gas at STP?

Answer 1

`"20 moles"`

Explanation:

The important thing to realize here is that you're working under STP conditions, which implies that you can use the molar volume of a gas at STP to find how many moles of helium will occupy that volume.

Now, the molar volume of a gas represents the volume occupied by one mole of a gas under some specific conditions for pressure and temperature.

Starting from the ideal gas law equation

`color(blue)(PV = nRT)`

you can say that the molar volume of gas at a pressure `P` and a temperature `T` will be equal to

`V/n = (RT)/P`

Now, Standard Temperature and Pressure conditions are defined as a pressure of `"100 kPa"` and a temperature of `0^@"C"`. Under these specific conditions, the molar volume of a gas will be equal to

`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"))))/(100/101.325color(red)(cancel(color(black)("atm"))))`

`V/n = "22.7 L/mol"`

This of course implies that one mole of any ideal gas will occupy `"22.7 L"`.

In your case, the volume of the gas is said to be equal to `"500 L"`. This means that you will have

`500 color(red)(cancel(color(black)("L"))) * "1 mole He"/(22.7color(red)(cancel(color(black)("L")))) = "22.026 moles He"`

Rounded to one sig fig, the number of sig figs you have for the volume of the gas, the answer will be

`n_(He) = color(green)("20 moles")`

SIDE NOTE Many textbooks and online sources still list STP conditions as a pressure of `"1 atm"` and a temperature of `0^@"C"`.

Under these conditions for pressure and temperature, one mole of any ideal gas occupies `"22.4 L"`. If these are the values for STP given to you by your instructor, make sure to redo the calculations using `"22.4 L"` instead of `"22.7 L"`.