Long free-response question

Getting copper from its ore

Units 4 and 9
10 points
About 23 minutes

You can use a calculator on this question, just like on exam day.

A multipart question, often built around a lab setup or a data table, that mixes several topics. You calculate, explain and justify your answers across many lettered parts. On the exam: 3 questions (Questions 1–3), part of the 1-hour-45-minute free-response section; calculator allowed.

The question and its sources

Copper can be obtained by heating copper(I) oxide, Cu₂O, with carbon. The copper produced is then purified by electrolysis.

Table 1. Thermodynamic data at 298 K

Substance	ΔH°f (kJ/mol)	ΔG°f (kJ/mol)	S° (J/(mol·K))
Cu₂O(s)	−168.6	−146.0	93.1
CO₂(g)	−393.5	−394.4	213.8
Cu(s)	0	0	33.2
C(s, graphite)	0	0	5.7
O₂(g)	0	0	205.2

Source: Standard thermodynamic values, rounded

Electrolytic refining

To purify the copper, a block of impure copper (containing small amounts of zinc and silver) and a thin sheet of pure copper are placed in a solution of CuSO₄(aq) and connected to an external power supply.

Copper atoms are oxidized at the impure block. Pure copper is deposited on the thin sheet.

Standard reduction potentials at 25 °C: Ag⁺(aq) + e⁻ → Ag(s), E° = +0.80 V; Cu²⁺(aq) + 2 e⁻ → Cu(s), E° = +0.34 V; Zn²⁺(aq) + 2 e⁻ → Zn(s), E° = −0.76 V.

Source: Standard reduction potentials, rounded

Suggested time: 23 minutes

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Part (a)

1 point

Calculate ΔG° at 298 K for reaction 1: 2 Cu₂O(s) → 4 Cu(s) + O₂(g).

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Part (b)

1 point

Reaction 1 is coupled with reaction 2: C(s) + O₂(g) → CO₂(g), ΔG° = −394.4 kJ/mol_rxn. Write the equation for the overall coupled reaction, calculate its ΔG° at 298 K, and state whether it is thermodynamically favorable.

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Part (c)

1 point

Without performing a calculation, predict the sign of ΔS° for the overall reaction 2 Cu₂O(s) + C(s) → 4 Cu(s) + CO₂(g). Justify your prediction.

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Part (d)

1 point

Calculate the value of the equilibrium constant, K, for the overall reaction at 298 K.

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Part (e)

1 point

A mixture of powdered Cu₂O and carbon shows no observable reaction at 298 K, even after many days. The mixture must be heated strongly before copper forms. Reconcile this observation with your answer to part (b).

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Part (f)

1 point

In the overall reaction 2 Cu₂O(s) + C(s) → 4 Cu(s) + CO₂(g), identify the element that is oxidized and the element that is reduced. Justify your answer using oxidation numbers.

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Part (g)

2 points

During electrolytic refining, the small amounts of zinc in the impure copper block are oxidized and go into solution as Zn²⁺(aq), but the silver is not oxidized and falls to the bottom of the cell as a solid. (i) Explain why zinc is oxidized. (ii) Explain why silver is not oxidized. Use the standard reduction potentials in your answers.

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Part (h)

1 point

The refining cell operates at a constant current of 2.50 A. Calculate the time, in hours, needed to deposit 25.0 g of pure copper on the thin sheet.

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Part (i)

1 point

Write the balanced half-reaction that occurs at the thin sheet of pure copper, and identify whether the sheet is the anode or the cathode.

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