Question

For a chemical reaction,$\Delta H$ and $\Delta S$ are negative. State, giving reason, under what conditions this reaction is expected to occur spontaneously.

Answer 1

For a reaction, to occur spontaneously, the change in Gibbs free energy $\Delta G$ should be negative. The free energy is the criteria for spontaneity which depends on the values of enthalpy,$\Delta H$, and entropy, $\Delta S$. The relationship between these three entities is$\Delta G=\Delta H-T\Delta S$.

Complete answer:
There is a thermodynamic variable, called Gibbs energy, which is used to predict the spontaneity of a process, as enthalpy, and entropy cannot explain the spontaneity alone. Decrease in the free energy of a system is the sole criteria for determining the spontaneity of a reaction. The relationship between Gibbs energy, G, enthalpy, H and entropy, S is, G = H – TS.
This equation is also a state variable and can be written as, $\Delta G=\Delta H-T\Delta S$.
We have been given the condition that the enthalpy and entropy, both $\Delta H$ and $\Delta S$ are negative, for a chemical reaction. We have to find under what condition this reaction can occur spontaneously.
For a reaction to occur, the total Gibbs energy, G should be negative, the entropy, S should be positive, and enthalpy, H should be negative, then only, the $\Delta G$ will have negative value. As given both $\Delta H$ and $\Delta S$ are negative, means $\Delta H$ is favorable, while $\Delta S$ is non – favorable. So the process will be spontaneous, when enthalpy change will be greater than entropy change, which means $\Delta H > T\Delta S$, so the sign of the $\Delta G$ will be negative. This can happen at low temperature, when the reaction is exothermic, because exothermic reactions have a negative enthalpy value.
Hence, with both $\Delta H$ and $\Delta S$ being negative, the reaction will be spontaneous when $\Delta H>T\Delta S$.

Note:
When enthalpy change is positive, the reaction is endothermic, so it will be non – spontaneous. Also, when change in Gibbs energy $\Delta G$, is negative, the reaction is spontaneous, when $\Delta G$ is positive the reaction is nonspontaneous, while when $\Delta G$ is equal to 0, the reaction is at equilibrium.