How to calculate molar mass using the ideal gas law?


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> It is found that 250 ml of a diatomic gas at standard temperature and pressure (STP) has a mass of 1.78 g. What is the diatomic gas?
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How can this question be solved? I know that I am supposed to use the ideal gas law


$$pV = nRT,$$


but am not sure how to apply it to this question.




You can first use the ideal gas law to calculate $n$:
\begin{align}
pV &= nRT\\
(\pu{101325 Pa})(\pu{0.250 l}) &= n(\pu{8.314 J K-1 mol-1})(\pu{273 K})\\
\end{align}


Solving for "$n$" gives $n = \pu{0.0111577 mol}$.


Now we use the connection between mass $m$, amount of substance $n$, and molar mass mass $M$:


\begin{align}
 M &=\frac{m}{n}\\
 n &=\frac{m}{M}\\
 \pu{0.0111577 mol} &= \frac{\pu{1.78 g}}{M},
\end{align}


which gives a molar mass of $M = \pu{159.53 g mol-1}$.


Looking at the Periodic Table, we can identify the diatomic gas as being bromine gas ($\ce{Br2}$), which has a molar mass of $\pu{159.8 g mol-1}$.


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