Question

For a particular reversible reaction at temperature T, $\Delta H$and $\Delta S$ were found to be both positive. If ${{T}_{e}}$ is the temperature at equilibrium, the reaction would be spontaneous when:
A. ${{T}_{e}}>T$
B. $T>{{T}_{e}}$
C. ${{T}_{e}}$is 5 times T
D. $T={{T}_{e}}$

Answer 1

Spontaneous reactions are those types of reactions which approves the formation of a product at the conditions below which the reaction takes place. Spontaneous processes are identified by a decrease in the system's free energy so they do not need any energy from outside.

Complete Step by step solution: A spontaneous process is one of the processes of thermodynamics in which it releases free energy and moves to a lower thermodynamically stable energy state to more thermodynamically stable energy state. The sign customized for free energy change follows the general custom for thermodynamic calculations in which a loss of free energy from the system relates to a negative change in the free energy of the system and a positive change in the free energy of the surroundings.
Free energy can be determined differently depending on the nature of the processes. For example, the Gibbs free energy change is used when the reactions occur under the conditions of constant temperature and pressure on the other hand Helmholtz free energy change is used when the reactions occur under the conditions of constant volume and temperature. The value and sign of both free energy changes can depend upon the temperature and pressure or volume.
For a process that occurs at constant temperature and pressure their spontaneity can be determined using the change in Gibbs free energy, which is given by:
$\Delta G=\Delta H-T\Delta S$
Now we known that at equilibrium
$\Delta G=0$
$\Delta H-T\Delta S=0$
For a reaction to be spontaneous $\Delta G$ should be negative so that the temperature should be greater than the equilibrium temperature.

Thus the option$T>{{T}_{e}}$, B is correct.

In cases where $\Delta G$ is negative the process is spontaneous and may proceed in the forward direction and if it is positive the process is non-spontaneous but it may proceed spontaneously in the reverse direction if zero the process is at equilibrium with no change taking place over time.

Note: Spontaneity not only depend upon the $\Delta G$value, it also depends on the signs of $\Delta H$and $\Delta S$and other than these factors entropy is one of the best chosen method for the reaction to decide whether it is spontaneous or nonspontaneous in nature.