Final answer:
To calculate the mass of the aluminum sample that reacted with hydrochloric acid, one must first account for water vapor pressure to find the pressure of hydrogen, convert the volume to liters, use the ideal gas law to find the moles of hydrogen, and apply the stoichiometry from the balanced chemical equation to calculate the mass of aluminum.
Step-by-step explanation:
The question involves calculating the mass of an aluminum sample when it reacts with hydrochloric acid to produce hydrogen gas. To find the mass of aluminum, we need to apply the concept of stoichiometry and the ideal gas law.
First, we need to adjust the pressure of the hydrogen gas to account for water vapor using the formula:
p₀(ᵢₒ₂) = p(total) - p₀(H₂O)
Where p₀(H₂O) is the vapor pressure of water at 25°C. Using tables, we find that p₀(H₂O) is approximately 23.8 mmHg, so:
p₀(ᵢₒ₂) = 736 mmHg - 23.8 mmHg = 712.2 mmHg
Now, we convert the pressure from mmHg to atm, the volume from mL to L, and use the ideal gas law:
PV = nRT
to calculate the moles of hydrogen gas produced. We then use the balanced chemical equation:
2 Al(s) + 6 HCl(aq) → 2 AlCl₃(aq) + 3 H₂(g)
To find the mole ratio and calculate the moles of aluminum from the moles of hydrogen. Finally, we multiply by the molar mass of aluminum to get the mass of the aluminum sample. By performing these steps, the student will be able to find the mass of the aluminum.
An exact calculation has not been performed here since the value for the vapor pressure of water at 25°C is not provided in the question, but this process outlines the steps the student would take to solve the problem.