For a Mg | Mg²⁺ (aq) || Ag⁺ (aq) | Ag the correct Nernst Equation is :

Solution

Chemistry ma’am · 3 steps

Balance the cell reaction first; the square on [Ag⁺] and the plus sign both come from there.

1. Write the reaction. Mg on the left is the anode and is oxidised; Ag⁺ on the right is reduced. Each Mg gives 2 electrons and each Ag⁺ takes 1, so you need 2 silver ions: Mg + 2Ag⁺ → Mg²⁺ + 2Ag, with n = 2.
2. Build Q. Solid Mg and Ag do not appear in Q. Products go on top and reactants go below, each raised to its coefficient, so Q = [Mg²⁺]/[Ag⁺]².

   E_(cell) = E°_(cell) - RT/2F ln[Mg²⁺]/[Ag⁺]² = E°_(cell) + RT/2F ln[Ag⁺]²/[Mg²⁺]

3. So. Turning the fraction upside down flips the sign of the log, since ln 1/Q = -ln Q. That is option (d).

The idea to keep. Always balance the cell reaction before writing Nernst: n and the powers in Q come from it. Flipping the fraction inside ln flips the sign in front.

Answer from the NTA final answer key. Solution by PrepWiser.