# Question 963da

Aug 17, 2017

The molar mass of the element is approximately 100 g/mol.

#### Explanation:

We can use the Ideal Gas Law to solve this problem:.

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Since $n = \frac{m}{M}$, we can rearrange this equation to get

$p V = \left(\frac{m}{M}\right) R T$

And we can solve this equation to get

$M = \frac{m R T}{p V}$

$m = \text{40 mg" = "0.040 g}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{300 K}$
$p = \text{1 atm}$
$V = \text{4.92 mL" = "0.004 92 L}$

M = ("0.040 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 300 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("atm"))) × "0.004 92" color(red)(cancel(color(black)("L")))) = "200 g/mol"#

However, the gas is diatomic, with molecular formula ${\text{X}}_{2}$.

∴ The molar mass of $\text{X}$ is 100 g/mol.