Final answer:
To find the density of hydrogen gas at STP, the molar mass of aluminum is used to determine the amount of hydrogen produced from a given amount of aluminum reacting with hydrochloric acid. The stoichiometry provides the amount of hydrogen produced at STP, and the density is then calculated as the molar mass of hydrogen divided by the molar volume at STP.
Step-by-step explanation:
The question revolves around the chemical reaction of aluminum with hydrochloric acid, which produces hydrogen gas. To determine the density of hydrogen gas at Standard Temperature and Pressure (STP), we can use the molar mass of aluminum and the stoichiometry of the reaction. The balanced chemical equation is:
2 Al(s) + 6 HCl(aq) → 2 AlCl₃(aq) + 3 H₂(g)
Firstly, we calculate the number of moles of aluminum that reacts:
- Moles of aluminum = mass / molar mass = 27.0 g / 26.98 g/mol ≈ 1.00 mol
From the stoichiometry of the reaction:
- 2 moles of Al produce 3 moles of H₂
- Therefore, 1 mole of Al will produce 1.5 moles of H₂
At STP (0°C and 1 atm), 1 mole of any gas occupies 22.4 L. Hence, the volume of hydrogen gas produced is:
- Volume of H₂ = 1.5 moles × 22.4 L/mol = 33.6 L
Finally, the density (ρ) is mass over volume.
- For hydrogen gas, ρ = molar mass / molar volume at STP
- ρ = 2.016 g/mol / 22.4 L/mol ≈ 0.09 g/L