Question
A reaction occurs spontaneously if
A.
$$T\Delta S < \Delta H$$ and both $$\Delta H$$ and $$\Delta S$$ are $$ + ve$$
B.
$$T\Delta S > \Delta H$$ and both $$\Delta H$$ and $$\Delta S$$ are $$ + ve$$
C.
$$T\Delta S = \Delta H$$ and both $$\Delta H$$ and $$\Delta S$$ are $$ + ve$$
D.
$$T\Delta S > \Delta H$$ and $$\Delta H$$ is $$ + ve$$ and $$\Delta S$$ is $$ - ve$$
Answer :
$$T\Delta S > \Delta H$$ and both $$\Delta H$$ and $$\Delta S$$ are $$ + ve$$
Solution :
The spontaneity of a reaction is based upon the negative value of $$\Delta G$$ and $$\Delta G$$ is based upon $$T,\Delta S$$ and $$\Delta H$$ according to following equation ( Gibbs-Helmholtz equation )
$$\Delta G = \Delta H - T\Delta S$$
If the magnitude of $$\Delta H - T\Delta S$$ is negative, then the reaction is spontaneous.
when $$T\Delta S > \Delta H$$ or we can say that $$\Delta H$$ and $$\Delta S$$ are positive, then $$\Delta G$$ is negative.