Question

Cell reaction is spontaneous, when:
a.G is negative
b.E is negative
c.G is positive
d.E is positive

Answer 1

The free energy is calculated differently depending on the nature of the operation. When examining processes that occur under constant pressure and temperature circumstances, for example, the Gibbs free energy change is employed, but the Helmholtz free energy change is utilized when analyzing processes that occur under constant volume and temperature conditions. Temperature, pressure, and volume can affect the value and even the sign of both free energy changes.

Complete answer:
A spontaneous process in thermodynamics is one that happens without any external input to the system. The time evolution of a system in which it releases free energy and goes to a lower, more thermodynamically stable energy state is a more technical definition (closer to thermodynamic equilibrium). The sign convention for free energy change is the same as for thermodynamic measurements, with a release of free energy from the system resulting in a negative change in the system's free energy and a positive change in the free energy of the surroundings.
$\Delta G=-nF{{E}^{o}}_{cell}$
If $\Delta G<0$, then cell reaction becomes spontaneous. Also, the ${{E}^{o}}_{cell}$​ of the cell should be positive.
Because a spontaneous reaction yields free energy, the sign of G must be negative. There are four distinct potential combinations since both H and S can be positive or negative depending on the parameters of the reaction. In the table below, the results for G based on the signs of H and S are listed. Remember that H denotes an exothermic reaction and a +H implies an endothermic reaction. When it comes to entropy, a value of +S indicates that the entropy is growing and the system is getting more chaotic. Entropy is dropping, and the system is getting less chaotic, as shown by an S. (more ordered).

Hence option a is correct.

Note:
Free energy is energy that can be used to perform tasks. As they progress, spontaneous reactions generate free energy. Remember that the enthalpy and entropy changes that occur in the system determine the spontaneity of a reaction. A reaction's free energy change is a mathematical mixture of enthalpy and entropy changes.