# A sample that contains 3.66 mol of a gas at 265 K has a pressure of 1.09 atm. What is the volume?

Mar 11, 2016

The volume of the gas is 73.1 L.

#### Explanation:

This question requires the ideal gas law. The equation for the ideal gas law is $P V = n R T$, where $P$ is pressure, $V$ is volume, $n$ is moles, $R$ is the gas constant, and $T$ is the temperature in Kelvins.

Given/Known
$P = \text{1.09 atm}$
$n = \text{3.66 moles gas}$
$R = 0.082057338 \left(\text{L·atm")/("K·mol}\right)$
https://en.m.wikipedia.org/wiki/Gas_constant
$T = \text{265 K}$

Unknown
$V$

Solution
Rearrange the equation to isolate volume. Substitute the known values into the equation and solve.

$P V = n R T$

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

V=(3.66cancel"mol"·0.082057338("L"·cancel("atm"))/(cancel("K")·cancel("mol"))·265cancel"K")/(1.09cancel"atm")="73.1 L of gas" rounded to three significant figures