How can we get the pure mass of an unclean metal?

So I'm facing a small chemistry problem that I can't find a way to solve. I'm not looking for answers, I'm just looking for how can I approach this problem.

The problem is as follows :

We put 5 g of non-pure zinc (with some impurities) into a 200 ml solution containing hydronium ions. At the end, we get some gases and we are left with 0.05 mol of hydronium ions in the solution.

Find the pure mass of zinc in that non-pure 5 g of zinc.

I really don't have any idea how to approach this problem. I have written and balanced the chemical equation:

$$\ce{Zn + 2H^+ = Zn^{2+} + H2}$$

I've arrived at the above equation from redox half-reactions. From here I don't know where to go.

Generally I would use the degree of purity formula:

$$P = \frac{C\cdot M}{10\cdot d}$$

where $P$ is degree of purity, $C$ is concentration, $M$ is the molar mass, and $d$ is the density, but this one is used for gases and liquids only. Besides, we've never studied how to compute the density of a metal.

• There is not enough information to solve the problem as you have described it. From the nature of the problem it seems that some amount of acid was used to dissolve the zinc. So two moles of acid dissolved one mole of zinc. Your problem statement does indicate how much acid was left, but not how much you started with. It would also seem that whatever the impurities were, that they did not dissolve in acid. – MaxW Sep 24 '16 at 19:16
• The only info I have about the initial state of the acid is it's volume : 200ml, and that at the end we have 0.05 moles of that acid . – Anis Souames Sep 24 '16 at 19:28
• Again, there is not enough information to solve the problem as you have described it. It could just be a bad problem, or you might not have translated it properly. I don't know which. – MaxW Sep 24 '16 at 19:33
• Okay, it might be the problem that is bad or missing some info, but let's say I have the molar quantity of the acid at initial state how can I proceed in this case ? (please write an answer with this assumption so that I can mark it as solved if it helped me) . – Anis Souames Sep 24 '16 at 20:24
• It depends on the "impurities": if they were alkali metals (e.g. Na or K) or other metal more reactive than zinc, you have no way of knowing the proportions of impurity to Zn. – DrMoishe Pippik Sep 25 '16 at 2:53