Final answer:
To find the volume of hydrogen gas produced when 49.1 g of iron reacts completely, divide the given mass by the molar mass of iron to determine the number of moles. Use the balanced chemical equation to determine the moles of hydrogen gas produced (1:4 ratio with iron).
Step-by-step explanation:
To find the volume of hydrogen gas produced when 49.1 g of iron reacts completely, we need to use stoichiometry and the ideal gas law. First, we determine the number of moles of iron by dividing the given mass by the molar mass of iron. Then, we use the balanced chemical equation to determine the moles of hydrogen gas produced, which is a 1:4 mole ratio with iron. Finally, we can use the ideal gas law PV = nRT to calculate the volume of hydrogen gas, with P being the pressure (1 atm), T being the temperature in Kelvin (25 + 273 = 298 K), and n being the number of moles of hydrogen gas.
Using the given information, we can calculate:
Number of moles of iron (Fe):
n(Fe) = mass of Fe / molar mass of Fe
n(Fe) = 49.1 g / 55.85 g/mol = 0.878 mol
Moles of hydrogen (H₂) using the mole ratio:
n(H₂) = 4 * n(Fe) = 4 * 0.878 mol = 3.51 mol
Volume of hydrogen gas using the ideal gas law:
V(H₂) = (n(H₂) * R * T) / P
Substituting the values:
V(H₂) = (3.51 * 0.0821 * 298) / 1 = 89.8 L