The potential associated with each electrode is known as electrode potential. If the concentration of each species taking part in the electrode reaction is unity (if any appears in the electrode reaction, it is confined to 1 atmospheric pressure) and further the reaction is carried out at 298 K, then the potential of each electrode is said to the standard electrode potential. By convention, the standard electrode potential of hydrogen electrode is 0.0 volt. The electrode potential value for each electrode process is a measure of relative tendency of the active species in the process to remain in the oxidised/reduced form. A negative `E^(@)` means that the redox couple is a stronger reducing agent than the `H^(+)//H_(2)` couple. A positive `E^(@)` means that the redox couple is a weaker reducing agent than the `H^(+)//H_(2)` couple. The metal with greater positive value of standard reduction potential forms the oxide of greater thermal stability.
Which of the following couples will have highest value of emf ?

Options

A. `Mg|Mg^(2+)||Ag^(+)//Ag`
B. `Zn|Zn^(2+)||Cu^(2+)||Cu`
C. `Zn|Zn^(2+)||Ag^(+)//Ag`
D. `Cu|Cu^(2+)||Ag^(+)|Ag`

Answer

To determine which redox couple will have the highest value of electromotive force (emf), we need to calculate the emf for each couple based on their standard reduction potentials. Here’s how we can solve the problem step by step:

### Step 1: Identify the Electrode Couples
We need to identify the electrode couples provided in the question. For this example, let's assume the following couples are given:
1. Magnesium (Mg) and Silver (Ag⁺)
2. Zinc (Zn) and Copper (Cu²⁺)
3. Zinc (Zn) and Silver (Ag⁺)
4. Copper (Cu) and Silver (Ag⁺)

### Step 2: Write Down the Standard Reduction Potentials
Next, we need to write down the standard reduction potentials for each half-reaction:
- \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \) : \( E^\circ = +0.80 \, \text{V} \)
- \( \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \) : \( E^\circ = -2.37 \, \text{V} \)
- \( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \) : \( E^\circ = -0.76 \, \text{V} \)
- \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) : \( E^\circ = +0.34 \, \text{V} \)

### Step 3: Calculate the EMF for Each Couple
Using the formula for cell potential:
\[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \]

#### Couple 1: Mg and Ag⁺
- Anode: Mg (oxidation, \( E^\circ = -2.37 \, \text{V} \))
- Cathode: Ag⁺ (reduction, \( E^\circ = +0.80 \, \text{V} \))
\[ E_{\text{cell}} = 0.80 - (-2.37) = 0.80 + 2.37 = 3.17 \, \text{V} \]

#### Couple 2: Zn and Cu²⁺
- Anode: Zn (oxidation, \( E^\circ = -0.76 \, \text{V} \))
- Cathode: Cu²⁺ (reduction, \( E^\circ = +0.34 \, \text{V} \))
\[ E_{\text{cell}} = 0.34 - (-0.76) = 0.34 + 0.76 = 1.10 \, \text{V} \]

#### Couple 3: Zn and Ag⁺
- Anode: Zn (oxidation, \( E^\circ = -0.76 \, \text{V} \))
- Cathode: Ag⁺ (reduction, \( E^\circ = +0.80 \, \text{V} \))
\[ E_{\text{cell}} = 0.80 - (-0.76) = 0.80 + 0.76 = 1.56 \, \text{V} \]

#### Couple 4: Cu and Ag⁺
- Anode: Cu (oxidation, \( E^\circ = +0.34 \, \text{V} \))
- Cathode: Ag⁺ (reduction, \( E^\circ = +0.80 \, \text{V} \))
\[ E_{\text{cell}} = 0.80 - 0.34 = 0.46 \, \text{V} \]

### Step 4: Compare the EMF Values
Now we can compare the calculated emf values:
1. Mg/Ag⁺: 3.17 V
2. Zn/Cu²⁺: 1.10 V
3. Zn/Ag⁺: 1.56 V
4. Cu/Ag⁺: 0.46 V

### Step 5: Conclusion
The couple with the highest emf is **Mg/Ag⁺** with an emf of **3.17 V**.