# What is the volume, in liters, occupied by 0.723 mol of a gas at 32.0°C if the pressure is 852 mm Hg?

Jun 10, 2016

the volume will be $V = 16.2 L$

#### Explanation:

To solve for the volume we can use the Ideal Gas Law equation

$P V = n R T$

$P =$ Pressure in $a t m$
$V =$ Volume in $L$
$n =$ moles
$R =$ the Gas Law Constant $0.0821 \frac{a t m \cdot L}{m o l \cdot K}$
$T =$ Temperature in $K$

When using the Ideal Gas Law Constant we must convert the Pressure to $a t m$
$P = 852 m m H g \cdot \frac{1 a t m}{760 m m H g} = 1.12 a t m$

V=?

$n = 0.723 m o l$

$R = 0.0821 \frac{a t m \cdot L}{m o l \cdot K}$

When using the Ideal Gas Law Constant we must convert the Temperature to $K$
$T = {32.0}^{o} C + 273 = 305 K$

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

$V = \frac{\left(0.723 \cancel{m o l}\right) \left(0.0821 \frac{\cancel{a t m} \cdot L}{\cancel{m o l} \cdot \cancel{K}}\right) \left(305 \cancel{K}\right)}{1.12 \cancel{a t m}}$

$V = 16.2 L$