Final answer:
Using the ideal gas law and the given conditions, the corrected pressure of hydrogen gas allows the calculation of moles of hydrogen and thus zinc consumed. With 0.0061 moles of Zn reacted, approximately 0.3989 g of Zn has been consumed to produce the given volume of hydrogen gas.
Step-by-step explanation:
To calculate the mass of zinc consumed when hydrogen gas is produced, we need to consider the reaction: Zn(s) + H2SO4(aq) → ZnSO4(aq) + H2(g). Given the conditions (24°C and a total pressure of 738 torr), we first adjust the pressure of hydrogen gas by subtracting the water vapor pressure at 24°C (22.38 torr) from the total pressure. Using ideal gas law PV = nRT and the corrected pressure, we can calculate the number of moles of hydrogen gas produced. As the molar ratio of Zn to H2 in the reaction is 1:1, the moles of zinc consumed will be the same as the moles of hydrogen gas produced.
Converting torr to atm (1 atm = 760 torr) and using R = 0.0821 L atm mol−1 K−1, we can perform the calculation as follows:
P(H2) = total pressure - vapor pressure of water = 738 torr - 22.38 torr = 715.62 torr ≈ 0.9421 atm
V(H2) = 159 mL = 0.159 L
T = 24°C = 297.15 K
n = PV / (RT) = (0.9421 atm × 0.159 L) / (0.0821 L atm mol−1 K−1 × 297.15 K)
n ≈ 0.0061 moles of H2 (and thus 0.0061 moles of Zn)
Finally, using the molar mass of zinc (65.38 g/mol), we calculate the mass of zinc consumed:
mass Zn = moles Zn × molar mass of Zn = 0.0061 mol × 65.38 g/mol
mass Zn ≈ 0.3989 g of Zn consumed