# If 49.5 moles of an ideal gas occupies 37.5 liters at 479 K, what is the pressure of the gas?

Apr 17, 2016

The pressure of the gas is 51.9 atm.

#### Explanation:

This looks like a good time to apply the Ideal Gas Law:

color(blue)(|bar(ul(PV = nRT)|),

where

• $P$ is the pressure
• $V$ is the volume
• $n$ is the number of moles
• $R$ is the gas constant
• $T$ is the temperature

We can rearrange the Ideal Gas Law to get

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

$n = \text{49.5 mol}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{479 K}$
$V = \text{37.5 L}$

P = (nRT)/V = (49.5 color(red)(cancel(color(black)("mol"))) × "0.082 06" color(red)(cancel(color(black)("L")))"·atm·"color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 479 color(red)(cancel(color(black)("K"))))/(37.5 color(red)(cancel(color(black)("L")))) = "51.9 atm"