The reaction, M2O3(s) + C(s) → M(s) + CO2(g), is spontaneous at low temperatures but non-spontaneous at high temperatures. If we assume that, since the physical states do not change, the values of ΔHTo and ΔSTo are constant over a wide temperature range, including 25.0°C, we can deduce that, over this range

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The question deals with the temperature dependence of the Gibbs free energy, ΔG = ΔH − TΔS, for the reaction M2O3(s) + C(s) → M(s) + CO2(g). We are told the process is spontaneous at low temperatures but non-spontaneous at high temperatures, and that ΔH° and ΔS° are constants over a wide range including 25.0 °C. This means ΔG must be negative at low T and become positive at high T as T increases. Option a: ΔH < 0 and ΔS > 0. If ΔH is negative and ΔS is positive, then ΔG = ΔH − TΔS starts negative at low T (good), and as T increases the −TΔS term becomes more negative, making ΔG even more negative. The reaction would remain spontaneous at higher temperatures, which does not match the given behavior. Therefore, this option is inconsistent with the temperature-dependent spontaneity described. Option b: ΔH < 0 and ΔS < 0. With ΔH negative and ΔS negative, ΔG = ΔH − TΔS becomes ΔH + |ΔS|T. At low T, ΔG ≈ ΔH, which is negative, so the reaction is spontaneous as stated. As T increases, the +|ΔS|T term grows, making ΔG less negative and eventually positive, causing the reaction to become non-spontaneous at high T. This scenario aligns with the described temperature dependence. Option c: ΔH > 0 and ΔS < 0. Here ΔG at very low T would be positive (since ΔG ≈ ΔH > 0), meaning the reaction would not be spontaneous initially, contradicting the given condition that it is spontaneous at low temperatures. This option is inconsistent with the information provided. Option d: ΔH > 0 and ΔS > 0. With both positive, ΔG = ΔH − TΔS could become negative at sufficiently high T if TΔS exceeds ΔH, but at very low T, ΔG is positive (ΔG ≈ ΔH), so the reaction would not be spontaneous at low temperatures. This contradicts the requirement that the reaction is spontaneous at low T. In summary, only option b yields a ΔG that is negative at low temperature and becomes positive as temperature rises, matching the described behavior of the reaction being spontaneous at low temperatures and non-spontaneous at high temperatures.

CHM1051 MUM S2 2025 CHM1051 Practice Exam 2

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