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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?

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.

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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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