# 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?

Mar 26, 2016

$\text{0.123 moles}$

#### Explanation:

The idea here is that an ideal gas kept under Standard Temperature and Pressure (STP) conditions has a molar volume equal to $\text{22.7 L}$.

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

So, if your sample of water vapor occupies $\text{2.80 L}$ 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 $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

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