Final answer:
Without knowledge of the entropy change (AS°) for the reaction, we cannot determine the exact temperature range for spontaneity. If the reaction is similar to other examples of reactions with positive AH° and AS°, it may become spontaneous at high temperatures. So, the correct option is C.
Step-by-step explanation:
The given reaction 2H2(g) + CO(g) → CH3OH(g) has an enthalpy change (AH°) of 90 kJ, which indicates the amount of heat absorbed or released during the reaction at standard conditions. To determine the spontaneity of the reaction at different temperatures, we need to consider both the enthalpy change and the entropy change (AS°). The free energy change (AG°) is calculated using the equation AG° = AH° - TAS°, where T is the temperature in Kelvin. If AG° is less than zero, the reaction is spontaneous; if AG° is greater than zero, the reaction is nonspontaneous. Without knowing the entropy change (AS°) for the reaction, we cannot conclusively determine the temperature range over which the reaction is spontaneous. If we assume that the entropy change is negative (AS° < 0), then based on the provided enthalpy value being positive (AH° > 0), the reaction would not be spontaneous at any temperature, option (a). However, if we assume that the entropy change is positive (AS° > 0), then we would find that the reaction may become spontaneous at higher temperatures, option (e), since the negative TΔS° term would become more significant. With the given information, it is not possible to conclude definitively without knowing the value of AS°. However, if we follow the trend from similar examples provided, we can infer that if AS° is sufficiently large and positive, the reaction could become spontaneous at high temperatures due to the entropy term overcoming the positive enthalpy term in the free energy equation.