Which of the following represents the potential of silver wire dipped into 0.1 M AgNO3 solution at 25°C?A. E°redB.(E°red + 0.059)C. (E°ox - 0.059)D. (E°red - 0.059).**Please Give detailed explanation.

To determine the potential of a silver wire dipped into a 0.1 M AgNO3 solution at 25°C, we need to consider the electrochemical principles involved, particularly the Nernst equation. The options provided relate to the standard reduction potential and how it can be adjusted based on concentration. Let’s break this down step by step.

Understanding Standard Reduction Potential

The standard reduction potential (E°) for the silver ion reduction reaction is given by:

• Ag⁺ + e^- → Ag (s) with E° = +0.80 V

This value indicates the tendency of silver ions to gain electrons and be reduced to solid silver. A higher E° value means a greater tendency for reduction.

Applying the Nernst Equation

The Nernst equation allows us to calculate the actual cell potential (E) under non-standard conditions, which in this case involves the concentration of Ag⁺ ions in the solution:

E = E° - (RT/nF) * ln(Q)

Where:

• E = cell potential
• E° = standard reduction potential
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (25°C = 298 K)
• n = number of moles of electrons transferred (1 for silver)
• F = Faraday's constant (96485 C/mol)
• Q = reaction quotient, which for our case is [Ag⁺]

Calculating the Potential

At 25°C, the Nernst equation simplifies to:

E = E° - (0.059/n) * log(Q)

For our reaction, since n = 1 and Q = [Ag⁺] = 0.1 M, we can substitute these values into the equation:

E = E° - 0.059 * log(0.1)

Calculating log(0.1) gives us -1, so:

E = E° - 0.059 * (-1) = E° + 0.059

Choosing the Correct Option

From our calculation, we see that the potential of the silver wire in the 0.1 M AgNO3 solution is represented by:

E = E° + 0.059

Thus, the correct answer is:

B. (E°red + 0.059)

Conclusion

This analysis shows how the concentration of ions in solution affects the electrochemical potential of a metal in contact with its ions. By using the Nernst equation, we can adjust the standard potential to find the actual potential under specific conditions. This understanding is crucial in electrochemistry and applications such as batteries and electroplating.