`DeltaG` is the available energy (energy produced) during the electochemical reaction in galvanic cell which can be converted into useful work. In the light of second law of thermodynamics, in the cell, the change in electrode potential with temperature will be equal to:

Options

A. `(triangleS)/(nF)`
B. `(nF)/(triangleS)`
C. `-2.303RTlogK_(C)`
D. `(-2.303)/(nF)`

Answer

To solve the problem regarding the change in electrode potential with temperature in a galvanic cell, we can follow these steps:

### Step 1: Understand the relationship between Gibbs free energy and electrode potential
In electrochemistry, the Gibbs free energy change (ΔG) is related to the electrode potential (E) of a galvanic cell by the equation:

\[ \Delta G = -nFE \]

where:
- \( \Delta G \) is the change in Gibbs free energy,
- \( n \) is the number of moles of electrons transferred,
- \( F \) is Faraday's constant (approximately 96485 C/mol),
- \( E \) is the electrode potential.

### Step 2: Apply the second law of thermodynamics
According to the second law of thermodynamics, the change in entropy (ΔS) is related to the change in Gibbs free energy and temperature (T) by the equation:

\[ \Delta G = \Delta H - T\Delta S \]

For a spontaneous process in a galvanic cell, ΔG is negative, and we can express the change in Gibbs free energy in terms of temperature and entropy.

### Step 3: Differentiate the Gibbs free energy equation with respect to temperature
To find the change in electrode potential with temperature, we differentiate the equation for ΔG with respect to temperature (T):

\[ \frac{d(\Delta G)}{dT} = -nF\frac{dE}{dT} \]

### Step 4: Relate the change in Gibbs free energy to entropy
From the thermodynamic identity, we know that:

\[ \Delta S = -\frac{d(\Delta G)}{dT} \]

Substituting this into our differentiated equation gives:

\[ -nF\frac{dE}{dT} = -\Delta S \]

### Step 5: Solve for the change in electrode potential with temperature
Rearranging the equation to solve for \(\frac{dE}{dT}\):

\[ \frac{dE}{dT} = \frac{\Delta S}{nF} \]

### Final Answer
Thus, the change in electrode potential with temperature in a galvanic cell is given by:

\[ \frac{dE}{dT} = \frac{\Delta S}{nF} \]