Which equation gives relation between concentration of ions in solution , electrode potential (E) and standard electrode potential `(E^@?)`

Options

A. Faraday's equation
B. Nernst's equation
C. Ohm's equation
D. Kohlrausch's equation

Answer

To find the relationship between the concentration of ions in solution, electrode potential (E), and standard electrode potential (E°), we can use the Nernst equation. Here’s a step-by-step solution:

### Step 1: Understand the Nernst Equation
The Nernst equation relates the electrode potential of a half-cell to the standard electrode potential and the concentration of the ions involved in the reaction. The general form of the Nernst equation is:

\[ E = E° - \frac{RT}{nF} \ln Q \]

Where:
- \( E \) = Electrode potential
- \( E° \) = Standard electrode potential
- \( R \) = Universal gas constant (8.314 J/mol·K)
- \( T \) = Temperature in Kelvin
- \( n \) = Number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (96485 C/mol)
- \( Q \) = Reaction quotient, which is the ratio of the concentrations of products to reactants.

### Step 2: Define the Reaction Quotient (Q)
For a general redox reaction, the reaction quotient \( Q \) can be defined as:

\[ Q = \frac{[\text{Products}]}{[\text{Reactants}]} \]

For example, in the reaction:

\[ \text{Zn}^{2+} + 2 \text{e}^- \rightleftharpoons \text{Zn (s)} \]

The reaction quotient \( Q \) would be:

\[ Q = \frac{1}{[\text{Zn}^{2+}]} \]

### Step 3: Substitute Q into the Nernst Equation
Now, substituting \( Q \) into the Nernst equation gives us:

\[ E = E° - \frac{RT}{nF} \ln \left( \frac{[\text{Products}]}{[\text{Reactants}]} \right) \]

### Step 4: Simplify for Standard Conditions
At standard conditions (298 K), the equation can be simplified using the fact that \( \frac{RT}{F} \) at 298 K is approximately 0.059 V for \( n = 1 \):

\[ E = E° - \frac{0.059}{n} \log Q \]

### Step 5: Final Formulation
Thus, the final relationship between the concentration of ions, electrode potential, and standard electrode potential can be summarized as:

\[ E = E° - \frac{0.059}{n} \log \left( \frac{[\text{Products}]}{[\text{Reactants}]} \right) \]