The standard reduction potential of zinc and silver at 298 K are `E_((Zn^(2+)) /(Zn))^0 = -0.76 V`, `E_((Ag^(+))/(Ag))^0= 0.80V` Which of the following reactions actually takes place in a cell reaction?

Options

A. `Zn^(2+)(aq) + 2Ag^(+)(aq) rarr Zn(s) + 2Ag(s)`
B. `Zn(s) + 2Ag^+(aq)rarr Zn^(2+)(aq) + 2Ag(s)`
C. `Zn^(2+)(aq) + 2Ag(s) rarr 2Ag^+(aq) + Zn(s)`
D. `Zn(s) + 2Ag(s) rarr Zn^(2+)(aq) + 2Ag^+`

Answer

To determine which reaction takes place in a cell reaction involving zinc and silver, we need to analyze the standard reduction potentials provided and identify the oxidation and reduction processes.

### Step-by-Step Solution:

1. **Identify the Standard Reduction Potentials:**
- For Zinc:
\[ E^\circ_{(Zn^{2+}/Zn)} = -0.76 \, V \]
- For Silver:
\[ E^\circ_{(Ag^+/Ag)} = 0.80 \, V \]

2. **Determine Which Species Will Be Reduced and Oxidized:**
- The species with a higher standard reduction potential will be reduced, while the species with a lower standard reduction potential will be oxidized.
- Since \(E^\circ_{Ag^+/Ag} (0.80 \, V) > E^\circ_{(Zn^{2+}/Zn)} (-0.76 \, V)\), silver ions (\(Ag^+\)) will be reduced, and zinc (\(Zn\)) will be oxidized.

3. **Write the Half-Reactions:**
- **Oxidation (Anode):** Zinc is oxidized:
\[ Zn (s) \rightarrow Zn^{2+} (aq) + 2e^- \]
- **Reduction (Cathode):** Silver ions are reduced:
\[ Ag^+ (aq) + e^- \rightarrow Ag (s) \]

4. **Balance the Half-Reactions:**
- The oxidation reaction produces 2 electrons, while the reduction reaction consumes only 1 electron. To balance the electrons, we multiply the reduction half-reaction by 2:
\[ 2Ag^+ (aq) + 2e^- \rightarrow 2Ag (s) \]

5. **Combine the Balanced Half-Reactions:**
- Now, we can add the two half-reactions together:
\[ Zn (s) + 2Ag^+ (aq) \rightarrow Zn^{2+} (aq) + 2Ag (s) \]

6. **Final Cell Reaction:**
- The overall cell reaction is:
\[ Zn (s) + 2Ag^+ (aq) \rightarrow Zn^{2+} (aq) + 2Ag (s) \]

7. **Identify the Correct Option:**
- From the options provided, we check which one matches the final cell reaction. The correct option is the one that represents this reaction.