# If the density of an unknown gas Z 4.50 g/L at STP, what is the molar mass of gas Z?

May 17, 2016

$P . M M = d . R . T$

#### Explanation:

Use the ideal gas equation

$P . V = n . R . T$

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

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

$P . M M = d . R . T$

$P \text{ is the pressure of the gas (" atm")}$
$M M \text{ is the molar mass ("g.mol^-1")}$
$d \text{ is the density of the gas ("g.L^-1")}$
$R \text{ is the universal gas constant ("0.0821*L.\atm.mol^-1.K^-1")}$

Solve for $M M$

$M M = \frac{d . R . T}{P}$

$M M = \frac{4.50 \cdot g \cdot {L}^{-} 1 \cdot 0.0821 \cdot L \cdot a t m \cdot m o {l}^{-} 1 \cdot {K}^{-} 1 \cdot 273 \cdot K}{1.00 \cdot \setminus a t m}$

$M M \cong 101 \text{ } g . m o {l}^{-} 1$