Question

For a reaction both enthalpy change and entropy change are positive. Under what conditions the reaction will be spontaneous?

Answer 1

Gibbs free energy, also known as the Gibbs function, Gibbs energy, or free enthalpy, is a quantity that is used to measure the maximum amount of work done in a thermodynamic system when the temperature and pressure are kept constant. Gibbs free energy is a state function hence it doesn’t depend on the path. So change in Gibbs free energy is equal to the change in enthalpy minus the product of temperature and entropy change of the system. The equation is given below
$\Delta G = \Delta H-T\Delta S$,
$\Delta G=$ Change in Gibbs’ free energy
$\Delta H=$ Change in enthalpy
$T=$ Change in temperature
$\Delta S=$ Change in entropy

Complete step by step answer:
For a reaction to be spontaneous the value of $\Delta G$ should be negative. Here we have given that, in a reaction both enthalpy change and entropy changes are positive, i.e. $\Delta H$ and $\Delta G$are positive,
Let us consider that;
For a reaction to be spontaneous the value of $\Delta G$ should be negative($\Delta G<0$)
$\Delta G=+\Delta H-T(+\Delta S)$
$+\Delta H-T(+\Delta S)<0$
$\Delta H$<$(T\Delta S)$
Here, we have clear that for the reaction to be spontaneous the value of the product of $T\Delta S$(product of temperature and entropy change) should be greater than the value of entropy change($\Delta H$). Hene the value of $\Delta G$ will be negative. So the reaction will be spontaneous.

So, the reaction will be spontaneous.

Note: According to the second law of thermodynamics entropy of the universe always increases for a spontaneous process. The Gibbs free energy is important in biology research because it enables one to predict the direction of spontaneous change for a system under the constraints of constant temperature and pressure.