Question

When enthalpy is positive and entropy is negative:
A.Free energy is negative
B.\[\Delta {\text{G}}\] is negative at high temperature
C.\[\Delta {\text{G}}\] is negative at low temperature
D.Free energy is never negative

Answer 1

Hint:\[\Delta {\text{G}} = \Delta {\text{H}} - {\text{T}}\Delta {\text{S}}\] is the relation used to determine change in Gibbs free energy, change in enthalpy, change in entropy in single equation. If change of Gibbs free energy is positive, reaction is non spontaneous and negative change corresponds to spontaneous reaction.

Complete step by step answer:
\[\Delta {\text{H}}\] means change in enthalpy. When \[\Delta {\text{H}}\] is positive it means final enthalpy is greater than initial enthalpy which means for a reaction having positive \[\Delta {\text{H}}\] corresponds to the products in the reaction have more energy compared to the reactant, so the reaction has gained energy or we can say it is an endothermic reaction. On the other hand, when \[\Delta {\text{H}}\] is negative it means final enthalpy is less than initial enthalpy which means for a reaction having negative \[\Delta {\text{H}}\] corresponds to the reactants in the reaction have more energy as compared to the product, so the reaction has evolved energy or we can say it is an exothermic reaction.
Entropy is qualitatively defined as a measure of how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system. For a reversible process the entropy generation is zero and the entropy change of a system is equal to net entropy transfer. The entropy balance is analogous to energy balance relation.
Gibbs free energy is the energy associated with a chemical reaction that can be used to do work, and is the sum of its absolute enthalpy and the absolute entropy of the system. If change in Gibbs free energy is positive then the reaction is non spontaneous and if it is negative, then reaction is spontaneous.
Change in Gibbs free energy, change in enthalpy, change in entropy and temperature are related as: \[\Delta {\text{G}} = \Delta {\text{H}} - {\text{T}}\Delta {\text{S}}\] . According to the question, if enthalpy is positive and negative then free energy is never negative because if entropy is negative then the product of entropy with temperature becomes negative and the subtraction of negative value from the given positive value of enthalpy can never result in negative Gibbs free energy.

Thus, the correct option is D.

Note:
 A spontaneous reaction does not require any external energy input and on the other hand, a non-spontaneous reaction requires an input of external energy for the reaction to proceed.