The standard oxidation potentials of Ze and Ag in water at `25^@C` are
`Zn(s) rarr Zn^(2+) + 2e" "[E^@= 0. 76 V]`
`Ag(s) rarr Ag^+ +e" " [E^@=- 0. 80 V]`
Which of the following reactions actually takes place ?

Explanation

To determine which of the given reactions actually takes place, we need to analyze the standard oxidation potentials of zinc (Zn) and silver (Ag) and use them to calculate the cell potential for each reaction.

### Step-by-Step Solution:

1. **Identify Standard Oxidation Potentials:**
- For Zinc:
\[ \text{Zn(s)} \rightarrow \text{Zn}^{2+} + 2e^- \quad [E^0 = +0.76 \, \text{V}] \]
- For Silver:
\[ \text{Ag(s)} \rightarrow \text{Ag}^+ + e^- \quad [E^0 = -0.80 \, \text{V}] \]

2. **Determine the Reactions:**
- We will analyze each of the proposed reactions to see if they involve oxidation and reduction.

3. **Reaction A:**
\[ \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]
- **Oxidation:** Zn → Zn²⁺ + 2e⁻ (E° = +0.76 V)
- **Reduction:** 2Ag⁺ + 2e⁻ → 2Ag (E° = -0.80 V)
- **Calculate E°cell:**
\[ E°_{\text{cell}} = E°_{\text{reduction}} - E°_{\text{oxidation}} = (-0.80) - (+0.76) = 1.56 \, \text{V} \]
- Since E°cell is positive, this reaction will occur.

4. **Reaction B:**
\[ \text{Zn}^{2+} + 2\text{Ag} \rightarrow \text{Zn} + 2\text{Ag}^+ \]
- **Reduction:** Zn²⁺ + 2e⁻ → Zn (E° = -0.76 V)
- **Oxidation:** 2Ag → 2Ag⁺ + 2e⁻ (E° = +0.80 V)
- **Calculate E°cell:**
\[ E°_{\text{cell}} = E°_{\text{reduction}} - E°_{\text{oxidation}} = (-0.76) - (+0.80) = -1.56 \, \text{V} \]
- Since E°cell is negative, this reaction will not occur.

5. **Reaction C:**
\[ \text{Zn} + 2\text{Ag} \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]
- This is the same as Reaction A, so it will also have a positive E°cell and will occur.

6. **Reaction D:**
\[ \text{Zn}^{2+} + \text{Ag} \rightarrow \text{Zn} + \text{Ag}^+ \]
- **Reduction:** Zn²⁺ + 2e⁻ → Zn (E° = -0.76 V)
- **Oxidation:** Ag → Ag⁺ + e⁻ (E° = +0.80 V)
- **Calculate E°cell:**
\[ E°_{\text{cell}} = E°_{\text{reduction}} - E°_{\text{oxidation}} = (-0.76) - (+0.80) = -1.56 \, \text{V} \]
- Since E°cell is negative, this reaction will not occur.

### Conclusion:
The only reaction that actually takes place is **Reaction A**.