Question

For a process to be spontaneous at constant T and P :
A. $(\Delta G)_(system) must be negative$
B. $(\Delta G)_(system) must be positive$
C. $(\Delta S)_(system) must be positive$
D. $(\Delta S)_(system) must be negative$

Answer 1

For a process to be spontaneous, at constant temperature and pressure, there must be decrease in free energy in the direction of process, that is $\Delta G$< 0 for spontaneous and, $\Delta G$> 0 corresponding situation to non-spontaneity.

Complete step by step answer: Gibb’s Helmholtz equation relates the free energy change ($\Delta G$) to the enthalpy ($\Delta H$) and the entropy change ($\Delta S$) of the process. The equation is:
$\Delta G = \Delta H - T\Delta S$ -------- (1)
We know that the magnitude of $\Delta H$ does not change much with the change in temperature but the $T\Delta S$ changes appreciably. Thus, spontaneity of a process depends very much on temperature.
For the endothermic process, both $\Delta H$ and $\Delta S$ are positive. So the first factor(favourable) $T\Delta S$ will be small and maybe less than $\Delta H$, $\Delta G$ will have positive value indicating the non-spontaneity of the process. On raising the temperature, the factor $T\Delta S$ increases appreciably and when it exceeds $\Delta H$, $\Delta G$would become negative and the process would be spontaneous.
For an exothermic process both $\Delta H$ and $\Delta S$ would be negative. In this case, the first factor of equation (1) favours the spontaneity and whereas the second factor opposes it. At high temperature, when $T\Delta S$> $\Delta H$, $\Delta G$will have positive value, showing thereby the non-spontaneity of the process. However on decreasing the temperature factor $T\Delta S$ < $\Delta H$, $\Delta G$ becomes negative and the process occurs spontaneously.
Thus, an exothermic reaction may be spontaneous at low temperature and non-spontaneous at high temperature.
Thus, taking in view, endothermic and exothermic conditions, we concluded that $\Delta G$ of the system must be negative.

So, the correct answer is “Option A”.

Note: Delta G ($\Delta G$) is the symbol for spontaneity and there are two factors affecting it, these are enthalpy and entropy. When $\Delta G$> 0 , it is a non spontaneous reaction, and, $\Delta G$< 0, it is a spontaneous reaction, when $\Delta G$ = 0, it is considered to be equilibrium.