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.


1 Answer 1


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 $\pu{159.8 g mol-1}$.

  • $\begingroup$ The question reads "at standard temperature and pressure (STP)"; therefore the pressure should be $p=100\,000\ Pa$ and not $p=101\,325\ Pa$; however, that's a common mistake in homework questions. Another mistake in this question is that bromine is a liquid at STP. $\endgroup$
    – Loong
    Commented Jun 5, 2021 at 14:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.