Question

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

Answer 1

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

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, $\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$.
We have been given the condition that the enthalpy and entropy, both $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ 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 $\mathrm{\Delta }G$ will have negative value. As given both $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are negative, means $\mathrm{\Delta }H$ is favorable, while $\mathrm{\Delta }S$ is non – favorable. So the process will be spontaneous, when enthalpy change will be greater than entropy change, which means $\mathrm{\Delta }H>T\mathrm{\Delta }S$, so the sign of the $\mathrm{\Delta }G$ 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 $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ being negative, the reaction will be spontaneous when $\mathrm{\Delta }H>T\mathrm{\Delta }S$.

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