Question

The electrochemical cell shown below is a concentration cell. $\text{M }\!\!|\!\!\text{ }{{\text{M}}^{\text{2+}}}$ (saturated solution of a sparingly soluble salt, $\text{M}{{\text{X}}_{\text{2}}}$) || ${{\text{M}}^{\text{2+}}}\left( \text{0}\text{.001 mol/ d}{{\text{m}}^{-\text{3}}} \right)\text{ }|\text{ M}$. The emf of the cell depends on the difference in concentrations of ${{\text{M}}^{\text{2+}}}$ ions at the two electrodes.
The emf of the cell at 298 is 0.059 V. The value of delta G ($~\text{kJ mo}{{\text{1}}^{-1}}$) for the given cell is: [take $\text{1F = 96500 C mo}{{\text{l}}^{-1}}$]
A. - 5.7
B. 5.7
C. 11.4
D. -11.4

Answer 1

Hint: The delta G that is measured in the question, is known as the Gibbs Energy. We need to know the formula of Gibbs energy, in relation to the concentration of the electrolytic cell.

Complete step-by-step answer:
In a galvanic cell, the Gibbs free energy is related to the potential as:

$\begin{align}
  & \because \,\Delta \text{G = }-\text{nFE} \\
 & \text{M }-\text{ 2}{{\text{e}}^{-}}\text{ }\xrightarrow{{}}\text{ }{{\text{M}}^{\text{2}}}^{\text{+}} \\
 & \therefore \text{ n = 2} \\
 & \Delta \text{ G = }-2\text{ }\times \text{ 0}\text{.059 }\times \text{ 96500 = }-11387\text{ J mo}{{\text{l}}^{-1}} \\
 & =\text{ }-\text{11}\text{.4 kJ mo}{{\text{l}}^{-1}} \\
\end{align}$
So the correct answer to the above mentioned question is Option D.
If the $\text{E}{}^\circ \text{ cell > 0}$ then the process is known as spontaneous. This happens in a galvanic cell.
If the $\text{E}{}^\circ \text{ cell < 0}$ then the process is non spontaneous. This happens in an electrolytic cell.

Additional Information:
Enthalpy is defined as the heat content of a system at constant pressure. Chemists routinely measure changes in enthalpy of chemical systems. As reactants are converted into products the heat is absorbed or released by a reaction at constant pressure is the same as that of the enthalpy change.

Entropy measures the level of disorder in a thermodynamics system. The entropy of a substance can be obtained by measuring the heat which is required to raise the temperature to a given amount using a reversible process.

Note: In thermodynamics, Gibbs free energy is defined as a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamics system at a constant temperature and pressure.
Gibbs free energy can also be defined in a way where it is represented as a difference between the enthalpy of a system and the product of its entropy and absolute temperature.