Thermochemical data for the dehydration and decomposition of copper(II) sulfate…

CHEMISTRY · Multi-part · A Level · Chemistry · Energetics · Energetics

Problem

Thermochemical data for the dehydration and decomposition of copper(II) sulfate compounds at 298 K298\,\text{K} are provided below: (A) CuSO4⋅5H2O(s)→CuSO4(s)+5 H2O(g)ΔH∘=+314 kJ\mathrm{CuSO_4\cdot 5H_2O(s)} \to \mathrm{CuSO_4(s)} + 5\,\mathrm{H_2O(g)} \quad \Delta H^\circ = +314\,\text{kJ} (B) CuSO4(s)→CuO(s)+SO3(g)ΔH∘=+272 kJ\mathrm{CuSO_4(s)} \to \mathrm{CuO(s)} + \mathrm{SO_3(g)} \quad \Delta H^\circ = +272\,\text{kJ} Standard molar enthalpies of formation (298 K298\,\text{K}) for selected species are: • CuO(s):−601.6 kJ mol−1\mathrm{CuO(s)}: -601.6\,\text{kJ}\,\text{mol}^{-1} • SO3(g):−396.0 kJ mol−1\mathrm{SO_3(g)}: -396.0\,\text{kJ}\,\text{mol}^{-1} • H2O(g):−241.8 kJ mol−1\mathrm{H_2O(g)}: -241.8\,\text{kJ}\,\text{mol}^{-1} • CuSO4(s):  ?\mathrm{CuSO_4(s)}: \; ? • CuSO4⋅5H2O(s):  ?\mathrm{CuSO_4\cdot 5H_2O(s)}: \; ? Use the information to answer the following. (1) Part 1: Formulate an algebraic relationship that connects the unknown ΔHx∘(CuSO4⋅5H2O)\Delta H^\circ_x(\mathrm{CuSO_4\cdot 5H_2O}) to ΔHx∘(CuSO4)\Delta H^\circ_x(\mathrm{CuSO_4}) using reaction (A) and the tabulated data. (2) Part 2: Formulate a separate algebraic relationship linking ΔHx∘(CuSO4)\Delta H^\circ_x(\mathrm{CuSO_4}) to known quantities using reaction (B). (3) Part 3: Solve the two equations simultaneously to obtain numerical values for ΔHx∘(CuSO4)\Delta H^\circ_x(\mathrm{CuSO_4}) and ΔHx∘(CuSO4⋅5H2O)\Delta H^\circ_x(\mathrm{CuSO_4\cdot 5H_2O}). Show every algebraic step, carry units throughout, and express answers to three significant figures. (4) Part 4: Based on your results, evaluate which solid---anhydrous CuSO4\mathrm{CuSO_4} or its pentahydrate---is thermodynamically more stable under standard conditions. Support your claim with quantitative evidence from the calculated enthalpies.

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