# Question b1da4

##### 1 Answer
May 7, 2017

Element $\text{X}$ is chlorine.

#### 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

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

In your problem,

$m = \text{283.3 g}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(27 + 273.15) K" = "300.15 K}$
$p = \text{3.2 atm}$
$V = \text{30 L}$

M = ("283.3 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 300.15 color(red)(cancel(color(black)("K"))))/(3.2 color(red)(cancel(color(black)("atm"))) ×30 color(red)(cancel(color(black)("L")))) = "72.7 g/mol"#

The molecular mass of ${\text{X}}_{2}$ is 72.7u.

The atomic mass of $\text{X}$ is 36.3 u.

The atomic mass of $\text{Cl}$ is 35.45 u, and the atomic mass of $\text{Ar}$ is 39.95 u.

The atomic mass of $\text{X}$ is closer to that of $\text{Cl}$, and $\text{Cl}$ also forms diatomic ${\text{Cl}}_{2}$ molecules.

Element $\text{X}$ is chlorine.