Consider the following relations for `emf` of a electrochemical cell
(i) emf of cell = (Oxidation potential of anode)-(Reduction potential of cathode)
(ii) emf of cell = (Oxidation potential of anode)+(Reduction potential of cathode)
(iii) emf of cell = (Reduction potential of anode)+(Reduction potential of cathode)
(iv) emf of cell = (Oxidation potential of anode)-(Oxidation potential of cathode)
Which of the above realtions are correct?

Options

A. (a) and (b)
B. (c ) and (d)
C. (b) and (d)
D. (c ) and (a)

Answer

To determine which of the given relations for the EMF (Electromotive Force) of an electrochemical cell are correct, we need to analyze each option based on the principles of electrochemistry.

### Step-by-Step Solution:

1. **Understanding EMF of an Electrochemical Cell:**
The EMF of an electrochemical cell can be calculated using the standard reduction potentials of the electrodes involved. The general formula for the EMF of the cell is:
\[ \text{EMF} = E_{\text{cathode}} - E_{\text{anode}} \]
where \(E_{\text{cathode}}\) is the reduction potential of the cathode and \(E_{\text{anode}}\) is the reduction potential of the anode.

2. **Identifying Oxidation and Reduction Potentials:**
- At the anode, oxidation occurs, and we can express the oxidation potential as the negative of the reduction potential:
\[ E_{\text{oxidation, anode}} = -E_{\text{reduction, anode}} \]
- At the cathode, reduction occurs, so the reduction potential remains as is.

3. **Analyzing Each Option:**
- **Option (i):** EMF of cell = (Oxidation potential of anode) - (Reduction potential of cathode)
- This can be rewritten using the relation of oxidation and reduction potentials:
\[ \text{EMF} = -E_{\text{reduction, anode}} - E_{\text{reduction, cathode}} \quad \text{(Incorrect)} \]
- **Option (ii):** EMF of cell = (Oxidation potential of anode) + (Reduction potential of cathode)
- This can be rewritten as:
\[ \text{EMF} = -E_{\text{reduction, anode}} + E_{\text{reduction, cathode}} \quad \text{(Correct)} \]
- **Option (iii):** EMF of cell = (Reduction potential of anode) + (Reduction potential of cathode)
- This is:
\[ \text{EMF} = E_{\text{reduction, anode}} + E_{\text{reduction, cathode}} \quad \text{(Incorrect)} \]
- **Option (iv):** EMF of cell = (Oxidation potential of anode) - (Oxidation potential of cathode)
- This can be rewritten as:
\[ \text{EMF} = -E_{\text{reduction, anode}} - (-E_{\text{reduction, cathode}}) = -E_{\text{reduction, anode}} + E_{\text{reduction, cathode}} \quad \text{(Correct)} \]

4. **Conclusion:**
From the analysis, we find that the correct relations for the EMF of an electrochemical cell are:
- Option (ii) and Option (iv) are correct.

### Final Answer:
The correct relations for the EMF of an electrochemical cell are:
- Option (ii) and Option (iv).