Question

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:
M(s) | ${{M}^{+}}$(aq; 0.05 molar) || ${{M}^{+}}$(aq), 1 molar)|M(s)
For the above electrolytic cell the magnitude of the cell potential is ${{E}_{cell}}$=70mV
For the above cell:
(A) ${{E}_{cell}}$<0 ; $\Delta G$>0
(B) ${{E}_{cell}}$>0 ; $\Delta {{G}^{{}^\circ }}$<0
(C) ${{E}_{cell}}$<0 ; $\Delta {{G}^{{}^\circ }}$>0
(D) ${{E}_{cell}}$>0 ; $\Delta {{G}^{{}^\circ }}$>0

Answer 1

Hint: Nernst equation formulated by Walther Nernst can be used to calculate the EMF value of a given cell, provided the standard cell potential of the cell. If $\Delta {{G}^{{}^\circ }}$ is positive reaction is nonspontaneous, and if $\Delta {{G}^{{}^\circ }}$ is negative reaction is spontaneous.

Complete step by step answer:
The electromotive force of a cell or EMF of a cell is the maximum potential difference between two electrodes of a cell. It can also be defined as the net voltage between the oxidation and reduction half-reactions. The EMF of a cell is mainly used to determine whether an electrochemical cell is galvanic or not.
Normally, the cell voltage may be different from this ideal value, due to several factors like temperature difference, change in concentration, etc.
 The reaction given is as follows:
\[M(s)+M(aq)1{{M}^{+}}\to M(aq)0.05{{M}^{+}}+M(s)\]

According to Nernst equation,
\[\begin{align}
 & {{E}_{cell}}=0-\dfrac{2.303RT}{F}log\dfrac{{{M}_{0.05M}}^{+}}{{{M}_{1M}}^{+}} \\
 & {{E}_{cell}}=0-\dfrac{2.303RT}{F}log(5\times {{10}^{-2}})=positive \\
\end{align}\]
Hence, ${{E}_{cell}}$=0.70V and $\Delta G$<0 for the feasibility of the reaction.
So, the correct answer is “Option B”.

Note: 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.