# A 3.49*g mass of a gas occupies a volume of 4.48*dm^3 under standard conditions, what is the molar mass of the gas?

Jun 26, 2017

$\text{Molar mass} = 17.5 \cdot g \cdot m o {l}^{-} 1$
Depending on your syllabus, at $\text{STP}$ $1 \cdot m o l$ of Ideal Gas occupies $22.4 \cdot {\mathrm{dm}}^{3}$, i.e. $22.4 \cdot {\mathrm{dm}}^{3} \cdot m o {l}^{-} 1$.......and note that $1 \cdot {\mathrm{dm}}^{3} = 1 \times {\left({10}^{-} 1 \cdot m\right)}^{3} = \frac{1}{1000} \cdot {m}^{3} = 1 \cdot L$, cos' there are $1000 \cdot L$ in a $\text{cubic metre}$.
And thus the $\text{molar mass"="mass"/"molar quantity}$
$= \frac{3.49 \cdot g}{\frac{4.48 \cdot {\mathrm{dm}}^{3}}{22.4 \cdot {\mathrm{dm}}^{3} \cdot m o {l}^{-} 1}} = 17.5 \cdot g \cdot m o {l}^{-} 1$.......