# What is the molecular mass (in amu) of a gaseous element if 8.79 g occupies 4.54 L at 447.77 torr and 37.6 °C?

Jul 2, 2016

The molecular mass is 83.8 u.

#### 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 $n = \text{mass"/"molar mass} = \frac{m}{M}$, we can write the Ideal Gas Law as

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

We can rearrange this to get

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

$m = \text{8.79 g}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(37.6 + 273.15) K" = "310.75 K}$
P = 447.77 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.589 17 atm"
$V = \text{4.54 L}$

M = ("8.79 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 310.75 color(red)(cancel(color(black)("K"))))/("0.589 17" color(red)(cancel(color(black)("atm"))) × 4.54 color(red)(cancel(color(black)("L")))) = "83.8 g/mol"

∴ The molecular mass is 83.8 u.