Final answer:
The volume of hydrogen gas produced from the reaction of 0.500 grams of zinc with excess HCl can be determined using the stoichiometry of the reaction and the ideal gas law. After converting to the appropriate units, the number of moles of zinc is calculated from its mass and molar mass, and these moles are then used in the ideal gas law equation to find the volume of hydrogen gas at the given temperature and pressure.
Step-by-step explanation:
The question asks about the volume of hydrogen gas produced when 0.500 grams of zinc reacts with excess hydrochloric acid at a temperature of 22.5 °C and a pressure of 762 mm Hg. To answer this question, we utilize the stoichiometry of the reaction and the ideal gas law. The balanced chemical equation for the reaction is:
Zn(s) + 2 HCl(aq) → ZnCl₂ (aq) + H₂(g)
From the equation, we see that one mole of zinc reacts to produce one mole of hydrogen gas. To find the number of moles of zinc, we use its molar mass:
Number of moles (Zn) = Mass (Zn) / Molar mass (Zn) = 0.500 g / 65.38 g/mol
Then, we calculate the volume of hydrogen produced using the ideal gas law PV = nRT, after converting all units to the correct SI units. We convert the temperature from degrees Celsius to Kelvin (Kelvin = Celsius + 273.15) and pressure from mm Hg to atmospheres (1 atm = 760 mm Hg).
Finally, we can solve for the volume (V) using the following rearranged equation:
V = nRT / P
By plugging all the known values into the ideal gas law, we can determine the volume of hydrogen gas formed by the reaction under the specified conditions.