Question

A reaction at one bar is non-spontaneous at low temperatures but becomes spontaneous at high temperatures. Identify the correct statement about the reaction among the following:
A. Both ${{\Delta H}}$ and ${{\Delta S}}$ are negative
B. Both ${{\Delta H}}$ and ${{\Delta S}}$ are positive
C. ${{\Delta H}}$ is positive while ${{\Delta S}}$ is negative
D. ${{\Delta S}}$ is positive while ${{\Delta H}}$ is negative

Answer 1

Hint: A non-spontaneous reaction is a reaction that does not proceed in a forward direction or does not favor the formation of products under the given set of conditions. For a reaction to be non-spontaneous it must be endothermic, accompanied by a decrease in entropy.

Complete step by step answer:
${{\Delta H}}$ represents the change in standard enthalpy of a reaction. A negative ${{\Delta H}}$ represents an exothermic reaction while a positive ${{\Delta H}}$ represents an endothermic reaction.
${{\Delta S}}$ represents the change in entropy. Ideally, during a reaction entropy should always increase. Entropy is the degree of randomness of a system.
The question says that the reaction is nonspontaneous at low temperatures but becomes spontaneous at high temperatures. And we need to predict the nature of ${{\Delta H}}$ and ${{\Delta S}}$.
The relation between temperature, change in standard enthalpy, and change in entropy is given by the equation:
\[{{\Delta G = \Delta H - T\Delta S}}\], where ${{\Delta G}}$ represents the change in Gibbs Free, ${{\Delta H}}$ is the change in standard enthalpy, ${{\Delta S}}$ is the change in entropy and T is the temperature.
For a spontaneous reaction, change in entropy should be negative that means the Gibbs free should increase.
At low temperature, the reaction is spontaneous, thus change in Gibbs free energy is positive (${{T\Delta S < \Delta H}}$) and at high temperature, the change in Gibbs free energy is negative (non-spontaneous reaction) therefore, ${{T\Delta S > \Delta H}}$. The only condition that satisfies both the conditions is that both ${{\Delta H}}$ and ${{\Delta S}}$ are positive.

Hence, the correct answer is option B .

Note:
According to thermodynamics there are two types of chemical reactions spontaneous and non-spontaneous.
Gibbs free energy is defined as a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure.