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

Jan 17, 2016

$\text{20 moles}$

#### 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

$\textcolor{b l u e}{P V = n R T}$

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

$\frac{V}{n} = \frac{R T}{P}$

Now, Standard Temperature and Pressure conditions are defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$. 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"))))

$\frac{V}{n} = \text{22.7 L/mol}$

This of course implies that one mole of any ideal gas will occupy $\text{22.7 L}$.

In your case, the volume of the gas is said to be equal to $\text{500 L}$. 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

${n}_{H e} = \textcolor{g r e e n}{\text{20 moles}}$

SIDE NOTE 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 for pressure and temperature, one mole of any ideal gas occupies $\text{22.4 L}$. If these are the values for STP given to you by your instructor, make sure to redo the calculations using $\text{22.4 L}$ instead of $\text{22.7 L}$.