Question

The occurrence of a reaction is impossible if
A. \[\Delta H\] is +ve; \[\Delta S\] is also +ve but \[\Delta H < T\Delta S\]
B. \[\Delta H\] is -ve; \[\Delta S\] is also -ve but \[\Delta H > T\Delta S\]
C. \[\Delta H\] is -ve; \[\Delta S\] is +ve
D. \[\Delta H\] is +ve; \[\Delta S\] is -ve

Answer 1

Hint: The spontaneity of a reaction is decided by the change in Gibbs free energy (\[\Delta G\] ) associated with it. A negative value of the change in Gibbs free energy indicates that the reaction is spontaneous, and a positive value indicates that the reaction is non-spontaneous. Recollect the mathematical relation between Gibbs free energy change (\[\Delta G\]) and the enthalpy (\[\Delta H\] ) and entropy change (\[\Delta S\] ) associated with a reaction to answer this question.

Formula used:
\[\Delta G = \Delta H - T\Delta S\] … (1)
\[\Delta G\] = change in Gibbs free energy (SI unit = Joule (J))
\[\Delta H\] = change in enthalpy (SI unit = Joule (J) or Joule per mole (\[Jmo{l^{ - 1}}\] ))
 T = temperature (assumed to be constant) (SI unit = Kelvin (K))
\[\Delta S\] = change in entropy (SI unit = Joules per Kelvin (\[J{K^{ - 1}}\] ))

Complete step-by-step answer:
The enthalpy of a system (H) is a thermodynamic parameter that is, in essence, a measure of the energy content of the system. During a chemical reaction, as reactants convert into products, the enthalpy associated with the reaction changes. This change in the enthalpy (\[\Delta H\]) is given by the difference in the enthalpies of the products and the reactants.
\[\Delta H = {H_{products}} - {H_{reactants}}\]
The entropy of a system (S) is a measure of how much the energy of the atoms and molecules of the system becomes spread out over the course of a reaction. It is also commonly described as a measure of the chaos and disorder within the system.
The spontaneity of a reaction can be predicted from the value of the change in Gibbs free energy (\[\Delta G\]) associated with the reaction. The relation between\[\Delta G\],\[\Delta H\] and\[\Delta S\] is given in equation (1). The change in Gibbs free energy for a reaction decides its spontaneity.
If \[\Delta G < 0\], the reaction is spontaneous.
If \[\Delta G > 0\], the reaction is non-spontaneous.
If \[\Delta G = 0\], the reaction is at equilibrium.
In the question, we are asked in which conditions a reaction will be “impossible” by which we mean “non-spontaneous”.
The condition is \[\Delta G > 0\]
\[ \Rightarrow \Delta H - T\Delta S > 0\] … (2)
The above inequality can be satisfied only when \[\Delta H > 0\] and\[\Delta S < 0\] since T can never be negative.

Thus, option D is correct.
Note:Students might be inclined to write the following step after arriving at equation (2):
\[ \Rightarrow \Delta H - T\Delta S > 0\]
\[ \Rightarrow \Delta H > T\Delta S\] … (3)
Doing this may lead to some confusion in this scenario. Instead, what students should do is after arriving at equation (2) they should substitute some positive and negative values for \[\Delta H\] and\[\Delta S\], and see which combination of values satisfies equation (2). That combination would be the correct answer.