For the electro chemical cell
M|M²⁺||X| X²⁻
If E_((M²⁺ / M))⁰=0.46 V and E_((x / x²⁻))⁰=0.34 V.
Which of the following is correct?

Solution

Chemistry ma’am · 3 steps

Write the reaction the cell stands for and check its sign. Negative means the reverse one runs.

1. Read the notation. The left electrode is the anode, where oxidation happens: M → M²⁺ + 2e⁻. The right electrode is the cathode, where reduction happens: X + 2e⁻ → X²⁻. So the cell as written stands for M + X → M²⁺ + X²⁻.

   E⁰_(cell) = E⁰_(cathode) - E⁰_(anode) = 0.34 - 0.46 = -0.12 V

2. Check the sign. Use Δ G⁰ = -nFE⁰_(cell). A negative E⁰_(cell) makes Δ G⁰ positive, so M + X → M²⁺ + X²⁻ is not spontaneous.
3. So. The reverse reaction, M²⁺ + X²⁻ → M + X, has E⁰ = +0.12 V and is spontaneous. The answer is (d).

The idea to keep. Both values are reduction potentials, so take cathode minus anode, never their sum. If the cell as written comes out negative, the reverse reaction is the spontaneous one.

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