Final answer:
To find the mass of iron that reacted, calculate the moles of hydrogen gas using the Ideal Gas Law, then use the stoichiometry of the reaction to find moles of iron, and finally, convert this to mass with iron's molar mass.
Step-by-step explanation:
To determine the mass of iron that reacted to produce 10.679 L of hydrogen gas, we first need to calculate the moles of hydrogen gas produced. We'll use the Ideal Gas Law for this purpose: PV = nRT.
Step 1: Calculate the moles of hydrogen gas (n)
At 25°C (298 K) and 752 torr (1 atm = 760 torr), we can convert the pressure to atmospheres:
P = 752 torr × (1 atm / 760 torr) = 0.99 atm
V = 10.679 L (Volume of H₂ gas)
R = 0.0821 L·atm/K·mol (Ideal Gas Constant)
T = 25°C + 273 = 298 K (Temperature in Kelvin)
Using PV = nRT: n = PV / RT = (0.99 atm × 10.679 L) / (0.0821 L·atm/K·mol × 298 K)
The calculated value of n gives the moles of H₂ gas produced.
Step 2: Determine moles of iron reacted
From the given balanced chemical equation 2 Fe + 3 H₂SO₄ → Fe₂(SO₄)₃ + 3 H₂, we see that 2 moles of Fe produce 3 moles of H₂. Thus, we use the stoichiometry to find the moles of Fe.
Step 3: Determine the mass of iron that reacted
Once we have the moles of Fe, we convert this to mass using the molar mass of iron (55.85 g/mol).
Mass of Fe = moles of Fe × molar mass of Fe