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

The \(E_{cell}\) for \(Ni + Mg^{2+} \rightarrow products\) should be positive

The correct answer is option (4) → The \(E_{cell}\) for \(Ni + Mg^{2+} \rightarrow products\) should be positive

1. Forward Reaction Spontaneity:

The question states that $E^{0}_{\text{cell}}$ for the forward reaction ($\text{Mg} + \text{Ni}^{2+} \rightarrow \text{Mg}^{2+} + \text{Ni}$) is positive.

• Since $\Delta G^{0} = -nFE^{0}_{\text{cell}}$, a positive $E^{0}_{\text{cell}}$ means $\Delta G^{0} < 0$. This confirms the forward reaction is spontaneous.

2. Reverse Reaction Non-Spontaneity:

If a forward reaction is spontaneous, its exact reverse reaction ($\text{Ni} + \text{Mg}^{2+} \rightarrow \text{products}$) must be non-spontaneous. The potential for this reverse reaction will have an opposite sign, making it negative ($-E^{0}_{\text{cell}}$).

Evaluating the Options

• Option 1: "When a strip of magnesium is placed in a nickel salt solution, a rapid reaction will occur spontaneously" $\rightarrow$ True (Forward reaction is spontaneous).
• Option 2: "Nickel atoms will not spontaneously give electrons to magnesium ions" $\rightarrow$ True (The reverse reaction is non-spontaneous, so nickel will not react spontaneously).
• Option 3: "Magnesium is more electropositive than Ni" $\rightarrow$ True ($\text{Mg}$ readily oxidizes and loses electrons to $\text{Ni}^{2+}$, making it the more reactive/electropositive metal).
• Option 4: "The $E_{\text{cell}} \text{ for } \text{Ni} + \text{Mg}^{2+} \rightarrow$ products should be positive" $\rightarrow$ FALSE (As established above, the reverse reaction's potential must be negative).

Conclusion

• Statement to Mark: Option 4 is the false statement.