The \(E^0_{cell}\) for the reaction \(Mg + Ni^{2+} \rightarrow Mg^{2+} + Ni\) is positive, then which of the following is false?

Nickel atoms will not spontaneously give electrons to magnesium ions

The correct answer is option 2. Nickel atoms will not spontaneously give electrons to magnesium ions.

The given cell reaction is:

\(\text{Mg} + \text{Ni}^{2+} \rightarrow \text{Mg}^{2+} + \text{Ni} \)

The standard cell potential (\( E^\circ_{\text{cell}} \)) for this reaction is positive, indicating that the reaction proceeds spontaneously in the forward direction under standard conditions. This means that magnesium atoms spontaneously donate electrons to nickel ions, resulting in the formation of magnesium ions and metallic nickel.

Let is analyze the statements:

1. When a strip of magnesium is placed in a nickel salt solution, a rapid reaction will occur spontaneously.

The statement is true. This statement aligns with the spontaneous nature of the given reaction. The positive standard cell potential indicates that the forward reaction occurs spontaneously without requiring an external source of energy.

2. Nickel atoms will not spontaneously give electrons to magnesium ions.

The statement is false. This statement contradicts the spontaneous nature of the reaction implied by the positive standard cell potential. In reality, nickel atoms will spontaneously accept electrons from magnesium ions, as indicated by the forward reaction.

3. Magnesium is more electropositive than nickel.

The statement is true. The fact that magnesium atoms donate electrons to nickel ions in the forward reaction supports the notion that magnesium is more electropositive (or less electronegative) than nickel.

4. The \( E^\circ_{\text{cell}} \) for \( \text{Ni} + \text{Mg}^{2+} \rightarrow \text{products} \) should be positive.

This statement is true because the given reaction is the reverse of the spontaneous forward reaction. Reversing a spontaneous reaction changes the sign of the cell potential. Since the forward reaction has a positive \( E^\circ_{\text{cell}} \), the reverse reaction will have a negative \( E^\circ_{\text{cell}} \), indicating that it does not occur spontaneously under standard conditions.

In summary, the false statement is that "Nickel atoms will not spontaneously give electrons to magnesium ions." This statement is incorrect because the positive standard cell potential indicates that nickel atoms do indeed spontaneously accept electrons from magnesium ions in the forward reaction.