Final answer:
To find the mass of zinc consumed in the reaction with hydrochloric acid to produce hydrogen gas, apply the ideal gas law and stoichiometry using the pressure of dry hydrogen, temperature, and molar mass of zinc.
Step-by-step explanation:
The subject of this question is Chemistry, specifically involving a reaction between zinc metal and hydrochloric acid to produce hydrogen gas. This is a stoichiometry problem that requires using the ideal gas law and the concept of molar ratios to find the mass of zinc consumed. To solve this problem:
- Use the balanced chemical equation Zn(s) + 2 HCl(aq) → ZnCl₂(aq) + H₂(g) which indicates that one mole of Zn reacts with two moles of HCl to produce one mole of H₂.
- Find the number of moles of H₂ using the ideal gas law (PV = nRT) and correct the pressure by subtracting the water vapor pressure from the atmospheric pressure to find the pressure of dry hydrogen gas.
- Convert the given volumes and pressures to appropriate units (liters and atm respectively), temperature to Kelvin, and use the molar mass of zinc to determine the mass of zinc that reacted.
Given the atmospheric pressure (0.963 atm) and the water vapor pressure (32 torr, which is 32/760 atm), the pressure exerted by the dry hydrogen gas can be found. Then, by applying the ideal gas law and the stoichiometric relationship that one mole of zinc produces one mole of hydrogen gas, we calculate the molar amount of hydrogen gas. Using the molar mass of zinc, we finally determine the mass of the consumed zinc.