Coupled Reactions And Thermodynamic Feasibility

Spontaneity is governed by (\Delta G = \Delta H - T\Delta S). To find where the reaction ceases to be spontaneous, we set (\Delta G = 0): (T = \Delta H / \Delta S). However, this crossover analysis applies when (\Delta H) and (\Delta S) have opposite signs — in that case a crossover temperature exists. Here (\Delta H = -28.5) kJ/mol (negative, exothermic) and (\Delta S = +52.0) J/mol·K (positive, entropy increases). When both (\Delta H < 0) and (\Delta S > 0), the Gibbs free energy (\Delta G = \Delta H - T\Delta S) is negative for ALL values of (T > 0): the negative (\Delta H) already drives (\Delta G < 0), and the positive (T\Delta S) term makes (\Delta G) even more negative at higher temperatures. Therefore the reaction is spontaneous at all temperatures. Option B (above 548 K non-spontaneous) would only apply if both terms had the same sign. Option C (above 1235 K) uses the wrong formula application. Option D contradicts the clearly negative (\Delta G) at all temperatures. This is a discriminating JEE Advanced question that tests whether students correctly identify the regime where no crossover exists. Plausibility check: the reduction of iron oxide by CO is the basis of blast furnace ironmaking, which operates at hundreds to over a thousand Kelvin — confirming spontaneity across a wide temperature range.