Nernst equation is useful in determining

Options

A. EMF of a cell
B. Equilibrium constant
C. Spontaneity of a cll reaction
D. All of these

Answer

To determine the usefulness of the Nernst equation, we can break down its applications step by step:

### Step 1: Understanding the Nernst Equation
The Nernst equation is expressed as:
\[ E = E^\circ - \frac{RT}{nF} \ln Q \]
Where:
- \( E \) = EMF of the cell
- \( E^\circ \) = standard EMF of the cell
- \( R \) = universal gas constant (8.314 J/(mol·K))
- \( T \) = temperature in Kelvin
- \( n \) = number of moles of electrons exchanged
- \( F \) = Faraday's constant (96485 C/mol)
- \( Q \) = reaction quotient

### Step 2: Determining the EMF of the Cell
The Nernst equation allows us to calculate the electromotive force (EMF) of an electrochemical cell under non-standard conditions. By knowing the concentrations of the reactants and products, we can find the current potential of the cell.

### Step 3: Relating to Equilibrium Constant
At equilibrium, the cell potential \( E \) becomes zero, and the Nernst equation can be rearranged to find the equilibrium constant \( K \):
\[ 0 = E^\circ - \frac{RT}{nF} \ln K \]
This implies:
\[ E^\circ = \frac{RT}{nF} \ln K \]
Thus, the Nernst equation helps in determining the equilibrium constant for the reaction.

### Step 4: Assessing Spontaneity of the Reaction
The spontaneity of a reaction can be assessed using the relationship between Gibbs free energy (\( \Delta G \)) and EMF. According to thermodynamics:
\[ \Delta G = -nFE \]
From the Nernst equation, we can derive \( \Delta G \) under non-standard conditions, which helps in determining whether the reaction is spontaneous or not.

### Conclusion
The Nernst equation is useful in determining:
1. The EMF of the cell.
2. The equilibrium constant of the reaction.
3. The spontaneity of the cell reaction.

Thus, the answer to the question is "all of these" (option D).

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