# How would you find the volume of 7 moles of CH4 at standard temperature and pressure?

Nov 13, 2015

The volume of 7 moles of $\text{CH"_4}$ at STP is approximately $\text{200 L}$.

#### Explanation:

STP is 273.15 K and 100 kPa.

Use the ideal gas law, $P V = n R T$, where $P$ is pressure, $V$ is volume, $n$ is moles, $R$ is the gas constant, and $T$ is temperature.

$P = \text{100 kPa}$
V= ???
$n = \text{7 mol CH"_4}$
$R = \text{8.3144598 L kPa K"^(−1) "mol"^(−1)}$
$T = \text{273.15 K}$

Equation
$P V = n R T$

Solution
Rearrange the equation to isolate volume and solve.

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

V=(7 cancel(mol) * 8.3144598"L" cancel"kPa" cancel"K"^(−1)""cancel"mol"^(−1) * 273.15cancel"K")/(100cancel"kPa")="159 L"="200 L CH"_4"(rounded to one significant figure)