The standard potentials at `25^@C` for the following half reactions are given against them
` Zn^(2+) +2e^(-) rarr Zn, E^0 =-0 . 762 V `
`Mg^(2+) +2e^(-) rarr Mg, =- 2.37 V`.
When zinc dust is added to a solution of magnesium chloride .`

Options

A. No reaction will take place
B. Zinc chloride is formed
C. Zinc dissolve in solution
D. Magnesium is preciptiated

Explanation

To solve the problem, we need to analyze the half-reactions and their standard electrode potentials to determine if a reaction will occur when zinc dust is added to a magnesium chloride solution.

### Step-by-Step Solution:

1. **Identify the Half-Reactions**:
- The half-reaction for zinc is:
\[ \text{Zn}^{2+} + 2e^{-} \rightarrow \text{Zn}, \quad E^{\circ} = -0.762 \, \text{V} \]
- The half-reaction for magnesium is:
\[ \text{Mg}^{2+} + 2e^{-} \rightarrow \text{Mg}, \quad E^{\circ} = -2.37 \, \text{V} \]

2. **Determine the Oxidation and Reduction**:
- When zinc is added to magnesium chloride, zinc will potentially oxidize (lose electrons) and magnesium ions will potentially reduce (gain electrons).
- The oxidation reaction can be written as:
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^{-} \]
- The reduction reaction can be written as:
\[ \text{Mg}^{2+} + 2e^{-} \rightarrow \text{Mg} \]

3. **Calculate the Standard Cell Potential (E°cell)**:
- The standard cell potential can be calculated using the formula:
\[ E^{\circ}_{\text{cell}} = E^{\circ}_{\text{reduction}} - E^{\circ}_{\text{oxidation}} \]
- Here, the reduction potential for magnesium is -2.37 V and the oxidation potential for zinc is +0.762 V (note that we take the negative of the oxidation potential).
- Therefore:
\[ E^{\circ}_{\text{cell}} = (-2.37) - (-0.762) = -2.37 + 0.762 = -1.608 \, \text{V} \]

4. **Analyze the Result**:
- A negative cell potential indicates that the reaction is not spontaneous. This means that zinc cannot oxidize in the presence of magnesium ions.

5. **Conclusion**:
- Since the cell potential is negative, no reaction occurs when zinc dust is added to a solution of magnesium chloride.

### Final Answer:
No reaction will take place when zinc dust is added to a solution of magnesium chloride because magnesium has a higher tendency to oxidize than zinc.