Gas Stoichiometry

Question

On December 1, 1783, Jacque Charles became the first human to pilot a non-tethered hydrogen balloon. He flew the balloon for fifteen miles and stayed in the air for a total flight time of 45 minutes. The balloon was made of silk coated with a  thin layer of natural rubber and had a diameter of 27 feet. He generated the hydrogen gas needed to lift the balloon by mixing a large amount of iron with aqueous sulfuric acid. If he used 1 x 10^3 lbs. of iron and excess sulfuric acid, how many liters of hydrogen gas were made?

 

 

Answer 1

Hi Bridget! This is a great stoichiometry problem. The trick is to ignore the extra history details and focus on the chemistry: iron reacting with sulfuric acid to make hydrogen gas. Here are the steps that I would take:

1. Write the balanced equation.

Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g)

Notice the 1:1 ratio between iron and hydrogen gas. Every mole of iron that reacts produces one mole of H₂.

1. Convert pounds of iron to grams.

Stoichiometry works in moles, so first we need grams:

1.0 x 10³ lb ⋅ (453.6 g/1 lb) = 4.536 x 10⁵ g Fe

1. Convert grams of iron to moles.

Use the molar mass of iron, 55.85 g/mol:

4.536 x 10⁵ g ⋅ (1 mol/55.85 g) = 8.12 ⋅ 10³ mol Fe

1. Use the mole ratio to find moles of H₂.

8.12 ⋅ 10³ mol Fe ⋅ (1 mol H₂/1 mol Fe) = 8.12 ⋅ 10³ mol H₂

1. Convert moles of H₂ to liters.

The problem doesn't give a temperature or pressure, so we'll assume STP, where 1 mole of any gas takes up 22.4 L:

8.12 ⋅ 10³ mol ⋅ 22.4 L/mol ≈ 1.8 ⋅ 10⁵ L of H₂

_{Quick tip: Almost every gas stoichiometry problem follows the same path: mass → moles → mole ratio → moles → volume. If your class uses conditions other than STP, use PV = nRT in the last step rather than 22.4 L/ mol.}

Hope this helps, and feel free to ask if any step is unclear!