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The standard reduction potential of zinc...

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?

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^+`

Text Solution

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The correct Answer is:
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.
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