Hydrate Mass Error in a Copper Displacement Lab
Students react 2.00 g of copper(II) sulfate pentahydrate with 0.50 g of iron nails in 50 mL of water. After the blue color fades, they filter, wash, and dry the copper and recover 0.45 g. One student calculates the theoretical yield using 159.6 g/mol for CuSO4, obtains 0.796 g Cu, and reports a 56.5% yield. The student explains the low yield by saying 'iron was the limiting reactant, so some copper sulfate was left unreacted.' The teacher checks the hydrate formula, CuSO4·5H2O (molar mass 249.7 g/mol), and the reaction Fe(s) + CuSO4(aq) → FeSO4(aq) + Cu(s). The nails were not weighed after the reaction. The class has a balance that reads to 0.01 g and a drying oven at 105 °C.
1. Evaluate the student's theoretical yield and limiting-reactant claim. Show the mole reasoning.
Read the worked answer
The theoretical yield is too high because the molar mass used is for anhydrous CuSO4, but the solid weighed was the pentahydrate. Moles of CuSO4·5H2O = 2.00 g / 249.7 g/mol = 0.00801 mol. Moles of Fe = 0.50 g / 55.85 g/mol = 0.00895 mol. The reaction is 1:1, so CuSO4 is limiting (0.00801 < 0.00895), not iron. Theoretical Cu = 0.00801 mol × 63.55 g/mol = 0.509 g. The student's 0.796 g is larger by the ratio 249.7/159.6 ≈ 1.56, which is the hydrate-mass error.
2. Calculate the corrected percent yield and propose two plausible sources of the difference between recovered and theoretical copper.
Read the worked answer
Corrected percent yield = 0.45 g / 0.509 g × 100 = 88.4%, not 56.5%. The remaining 0.059 g (about 12%) is plausibly transfer and filtration loss of fine copper, copper retained on the nails or in the flask, incomplete reaction if the blue color was judged too early, and small oxidation or drying effects. Because iron was in excess, unreacted copper sulfate is not a good explanation unless the reaction was stopped prematurely. The student should weigh the dried nails to see whether they gained mass.
3. What question would you ask the student to help them catch the hydrate error without telling them the answer?
Read the worked answer
Ask: 'What is the formula mass of the exact solid you weighed, including the water of hydration?' and 'How many moles of Cu are in one mole of that solid?' Have the student calculate the moles of water separately and compare the mole ratio. This prompt targets the representation of the hydrate without supplying the correction, so the student must reconcile the formula with the mass.