Chemistry

Chemistry

Problem

An experiment measured a standard entropy change of ΔSexp∘=−174.0 J mol−1 K−1\Delta S^{\circ}_{\text{exp}} = -174.0\,\text{J mol}^{-1}\,\text{K}^{-1} for the complete combustion of liquid ethanol at 298 K298\,\text{K}: C2H5OH(l)+3 O2(g)→2 CO2(g)+3 H2O(l)\mathrm{C_2H_5OH(l)} + 3\,\mathrm{O_2(g)} \to 2\,\mathrm{CO_2(g)} + 3\,\mathrm{H_2O(l)} To evaluate this measurement, consider the following data, all at 298 K298\,\text{K}: Reaction 1: C(s,graphite)+O2(g)→CO2(g)ΔS1∘=+179.0 J mol−1 K−1\mathrm{C(s, graphite)} + \mathrm{O_2(g)} \to \mathrm{CO_2(g)} \quad \Delta S^{\circ}_{1} = +179.0\,\text{J mol}^{-1}\,\text{K}^{-1} Reaction 2: H2(g)+0.5 O2(g)→H2O(l)ΔS2∘=−163.5 J mol−1 K−1\mathrm{H_2(g)} + 0.5\,\mathrm{O_2(g)} \to \mathrm{H_2O(l)} \quad \Delta S^{\circ}_{2} = -163.5\,\text{J mol}^{-1}\,\text{K}^{-1} Reaction 3: 2 C(s,graphite)+3 H2(g)→C2H5OH(l)ΔS3∘=−174.1 J mol−1 K−12\,\mathrm{C(s, graphite)} + 3\,\mathrm{H_2(g)} \to \mathrm{C_2H_5OH(l)} \quad \Delta S^{\circ}_{3} = -174.1\,\text{J mol}^{-1}\,\text{K}^{-1} All species are in their standard states. (a) Using the reactions and data provided, calculate the theoretical standard entropy change ΔScalc∘\Delta S^{\circ}_{\text{calc}} for the combustion of ethanol at 298 K298\,\text{K}. (b) Determine whether ΔScalc∘\Delta S^{\circ}_{\text{calc}} agrees with the experimental value ΔSexp∘\Delta S^{\circ}_{\text{exp}} within ±5%\pm 5\%. Show your work. (c) If the values differ by more than this margin, propose two plausible experimental or methodological factors that could account for the discrepancy.

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