Question

At standard temperature and pressure, a given sample of water vapor occupies a volume of 2.8 0 L. How many moles of water vapor are present?

Answer 1

`"0.123 moles"`

Explanation:

The idea here is that an ideal gas kept under Standard Temperature and Pressure (STP) conditions has a molar volume equal to `"22.7 L"`.

In other words, when pressure is set to `"100 kPa"` and temperature to `0^@"C"`, one mole of any ideal gas occupies `"22.7 L"` - this is known as the molar volume of a gas at STP.

So, if your sample of water vapor occupies `"2.80 L"` at STP, it follows that it must contain

`2.80 color(red)(cancel(color(black)("L"))) * overbrace("1 mole"/(22.7color(red)(cancel(color(black)("L")))))^(color(purple)("molar volume of a gas at STP")) = "0.12335 moles"`

of water vapor. You need to round this off to three sig figs, the number of sig figs you have for the volume of water vapor

`"no. of moles of water vapor" = color(green)(|bar(ul(color(white)(a/a)"0.123 moles"color(white)(a/a)|)))`

It's worth noting that many textbooks and online sources still list STP conditions as a pressure of `"1 atm"` and a temperature of `0^@"C"`.

Under these conditions, one mole of any ideal gas occupies `"22.4 L"`. If this is the value given to you for the molar volume of a gas at STP, simply redo the calculation using `"22.4 L"` instead of `"22.7 L"`.