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( R=$8\,J{{K}^{-1}}mo{{l}^{-1}}$, F=$96500\,C\,mo{{l}^{-1}}$)

A. ${{e}^{160}}$

B. ${{e}^{320}}$

C. ${{e}^{-160}}$

D. ${{e}^{-80}}$

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Gibbs free energy, denoted $\vartriangle G$, combines enthalpy and entropy into one value. The change in free energy commonly called $\vartriangle G$, is up to the sum of the enthalpy plus the merchandise of the temperature and entropy of the system. $\Delta G$ can predict the direction of the chemical process under two conditions:

1. constant temperature and

2. constant pressure.

If $\vartriangle G$ is positive, then the reaction is nonspontaneous (i.e., the input of external energy is critical for the reaction to occur) and if it's negative, then it's spontaneous (occurs without external energy input).

Spontaneous - could be a reaction that's fancy to be natural because it's a reaction that happens by itself with none external action towards it. Non spontaneous - needs constant external energy applied to that so as for the method to continue and once you stop the external action the method will cease. When solving for the equation, if change of G is negative, then we say that the reaction is spontaneous. If the change of G is positive, then it is non spontaneous. The symbol that's commonly used at no cost ENERGY is G. is more properly considered as "standard free energy change". Now, we have two equations for $\vartriangle G$:

$\vartriangle G=-nF{{E}^{0}}_{cell}$ and $\vartriangle G=-RT\ln {{K}_{c}}$

Where F= Faraday, R=universal gas constant, T=temperature, ${{K}_{c}}$=equilibrium constant, n=number of moles

Equating both, we get

$nF{{E}^{0}}_{cell}=RT\ln K$

Also, we have $Zn->Z{{n}^{2+}}+2{{e}^{-}}$. Since there is an exchange of 2 electrons, we have n=2. By putting the values from the question, we have

$\ln K=\dfrac{2\times 96500\times 2}{300\times 8}$, which is approximately equal to 160.