# Is this calculation of the amount of required hydrogen gas correct?

I was a bit hesitant to post this question for it may appear like a "homework help" type of question. But upon rethinking it felt like a genuine question. I was studying stoichiometry with my son (from the OpenStax Chemistry 2e book) and suddenly I had an idea to use these calculations in a real chemistry experiment that I am going to perform at home (of course, I truly believe in a "safety first" approach). I wrote it all up here on GitHub, but reposting here to keep it all at one place:

A practical problem: It was decided to inflate a common latex balloon to 5cm radius by the hydrogen gas produced during a single-displacement reaction: $$\ce{2HCl(aq) + Zn(s) -> ZnCl2(s) + H2(g)}$$ that uses an N/10 i.e. 0.1M HCl solution (available in many drugstores, typically in $$\pu{200ml}$$ bottles). How much reactants are needed?

Solution: We need to inflate the balloon to about $$\pu{5cm}$$ radius. Assuming the balloon to be a sphere gives us the volume of balloon, $$V_b$$, as: $$V_b = \frac{4}{3}\cdot \pi r^3 = \pu{523.599cm^3}$$.

Assuming the density of hydrogen at STP as 0.0000899 $$\pu{g/cm^3}$$, the mass of hydrogen is $$\pu{523.599 \times \space 0.0000899 g} = \pu{0.0471 g}$$. Since 1 mol $$\ce{H_2(g)}$$ has a mass of $$\pu{2 \times \space 1.008 g} = \pu{2.016 g}$$, we need $$\pu{\frac{0.0471}{2.016} mol} = \pu{0.0233 mol}$$ $$\ce{H_2(g)}$$.

Balancing the reaction, we see that to produce 1mol $$\ce{H_2(g)}$$ we need 2 mol HCl(aq) and 1 mol Zn(s).

This means that to produce 0.0233 mol $$\ce{H_2(g)}$$ we need $$2 \times 0.0233 = \pu{0.0466 mol}\ \ce{HCl(aq)}$$. We have a 0.1M HCl (aqueous) solution which means that $$\frac{\text{mol of solute}}{\text{litres of solution}} = 0.1$$. Clearly, we need $$\frac{0.0466}{0.1} = \pu{0.466 L}$$ or $$\pu{466 ml}$$ HCl.

The amount of zinc needed = $$0.0233 \times \text{molar mass of zinc} = 0.0233 \times 65.38 = \pu{1.523 g}$$.

• Looks good to me. I would have calculated 523.6/22400= 0.023375 mole H2 for simplicity, but you got it right. Nov 7, 2020 at 15:06
• editing tip: use \pu{} for physical units and \ce{} for chemical formulae/equations. Nov 7, 2020 at 16:06
• @Kedar do not apologize to anyone or feel guilty about posting a genuine question. You are trying to help your son and this should be enough to convince anyone interested in science. Nov 8, 2020 at 3:36

Kedar's calculation may be right. But it must be realized that the reaction will be rather slow. Even with a $$1 M$$ solution, the reaction is slow. The reaction of $$1.5$$ $$\pu{g}$$ metallic zinc with such a diluted $$\ce{HCl}$$ solution ($$0.1 M$$) will last more than one hour. Anyway, in order to inflate such a balloon a higher pressure than the atmospheric pressure must be applied. If not, the balloon will keep its original dimension. How to increase the pressure of $$\ce{H2}$$ in such a balloon for inflating it, if the hydrogen is produced by the reaction of zinc on $$\ce{HCl}$$ ?