Chemistry

Chemistry

Problem

A student wants to calculate ΔG∘\Delta G^\circ for the decomposition reaction CaCO3(s)→CaO(s)+CO2(g)\mathrm{CaCO_3(s)\rightarrow CaO(s)+CO_2(g)} Which set of terms must be included in the summation when using tabulated ΔGf∘\Delta G_f^\circ values at 298 K? a) ΔGf∘(CaCO3(s))−[ΔGf∘(CaO(s))+ΔGf∘(CO2(g))]\Delta G_f^\circ(\mathrm{CaCO_3(s)})-\big[\Delta G_f^\circ(\mathrm{CaO(s)})+\Delta G_f^\circ(\mathrm{CO_2(g)})\big] b) Only ΔGf∘(CO2(g))\Delta G_f^\circ(\mathrm{CO_2(g)}) c) [ΔGf∘(CaO(s))+ΔGf∘(CO2(g))]−ΔGf∘(CaCO3(s))\big[\Delta G_f^\circ(\mathrm{CaO(s)})+\Delta G_f^\circ(\mathrm{CO_2(g)})\big]-\Delta G_f^\circ(\mathrm{CaCO_3(s)}) d) ΔGf∘(CaO(s))−ΔGf∘(CaCO3(s))\Delta G_f^\circ(\mathrm{CaO(s)})-\Delta G_f^\circ(\mathrm{CaCO_3(s)})
Intuitive explanation

The key is remembering that ΔGrxn∘\Delta G^\circ_{\text{rxn}} always equals the sum of products minus reactants using standard formation free energies. You need ΔGf∘\Delta G_f^\circ values for all three substances—calcium carbonate, calcium oxide, and carbon dioxide—then apply the formula: ΔGrxn∘=∑ΔGf∘(products)−∑ΔGf∘(reactants)\Delta G^\circ_{\text{rxn}} = \sum \Delta G_f^\circ(\text{products}) - \sum \Delta G_f^\circ(\text{reactants}). Formation free energies are already tabulated at 298 K, so you can use them directly without needing temperature corrections.

Intuitive explanation

The key is remembering that ΔGrxn∘\Delta G^\circ_{\text{rxn}} always equals the sum of products minus reactants using standard formation free energies. You need ΔGf∘\Delta G_f^\circ values for all three substances—calcium carbonate, calcium oxide, and carbon dioxide—then apply the formula: ΔGrxn∘=∑ΔGf∘(products)−∑ΔGf∘(reactants)\Delta G^\circ_{\text{rxn}} = \sum \Delta G_f^\circ(\text{products}) - \sum \Delta G_f^\circ(\text{reactants}). Formation free energies are already tabulated at 298 K, so you can use them directly without needing temperature corrections.

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