Question

the thermodynamics of ethanol
thermodynamic favorability
the thermodynamic data for the
combustion of ethanol is given below. use
the data to answer the question.
δs_comb = 217.9 j/mol k
δh_comb = -1,325 kj/mol c₂h₅oh
under what conditions will this reaction
be thermodynamically favorable?
the reaction will be favorable at all temperatures.
the reaction will be favorable at high
temperatures.
the reaction will be favorable at low temperatures.
the reaction will not be favorable at any
temperature.

Explanation:

To determine thermodynamic favorability, we use the Gibbs free energy equation: $\Delta G = \Delta H - T\Delta S$. For a reaction to be favorable, $\Delta G < 0$. Here, $\Delta H_{\text{comb}} = -1325\ \text{kJ/mol}$ (exothermic, negative) and $\Delta S_{\text{comb}} = 217.9\ \text{J/mol K} = 0.2179\ \text{kJ/mol K}$ (positive, since entropy increases). Substituting into $\Delta G$: $\Delta G = -1325 - T(0.2179)$. Since both $-1325$ (negative) and $-T(0.2179)$ (negative, because $T$ is positive and multiplied by a positive $\Delta S$ then negated) contribute to a negative $\Delta G$, $\Delta G$ will always be negative regardless of the temperature (as long as $T$ is a real, positive temperature, which it is in thermodynamic contexts). Thus, the reaction is favorable at all temperatures.

Answer:

The reaction will be favorable at all temperatures.