# Question 73fe8

Nov 26, 2015

The volume of the gas at STP is 7.58 L.

#### Explanation:

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

Convert molecules to moles by dividing by $\left(6.022 \times {10}^{23} \text{molecules")/(1"mol}\right)$.

$2.01 \times {10}^{23} \text{molecules"xx(1"mol")/(6.022xx10^23"molecules")="0.33378 mol}$

(I am keeping a couple of guard digits to reduce rounding errors.)

$\text{STP}$ is $\text{273.15 K}$ and $\text{100 kPa}$.

Given/Known
$P = \text{100 kPa}$
$n = \text{0.33378 mol}$
$R = \text{8.3144598 L kPa K"^(-1) "mol"^(-1)}$
https://en.m.wikipedia.org/wiki/Gas_constant
$T = \text{273.15 K}$

Unknown
$V$

Equation
$P V = n R T$

Solution
Rearrange the equation so that $V$ is isolated and solve.

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

V=(0.33378cancel"mol"xx8.3144598 "L" cancel"kPa" cancel("K"^(-1)) cancel("mol"^(-1))xx273.15cancel"K")/(100 cancel"kPa")="7.58 L"#