# How do you find the number of moles for a gas from temperature and pressure?

Jun 21, 2017

You use the Ideal Gas Law.

#### Explanation:

You also need the volume.

Then, you insert the pressure, volume, and temperature into the expression and calculate the number of moles.

The Ideal Gas Law is

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this formula to get the number of moles, $n$.

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

EXAMPLE

A 3.00 L container is filled with neon gas at 770 mmHg and 27 °C. How many moles of neon are present?

Solution

Step 1. List the information given, making conversions as necessary.

p = 770 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "1.013 atm"
$V = \text{3.00 L}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(30 + 273.15) K = 303.15 K}$

Step 2. Calculate the number of moles.

n = (1.013 color(red)(cancel(color(black)("atm"))) × 3.00 color(red)(cancel(color(black)("L"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 300.15 color(red)(cancel(color(black)("K")))) = "0.123 mol"

There are 0.123 mol of neon in the container.