Mark the incorrect relationship from the following:

Options

A. Equilibrium constant is related to emf as log `K="nFE"/"2.303RT"`
B. EMF of a cell `Zn|Zn_((a_1))^(2+)"| |"Cu_((a_2))^(2+)|Cu` is `E=E^@-"0.591"/n"log " ([a_2])/([a_1])`
C. Nernst equations is `E_"cell"=E_"cell"^@-0.0591/n"log""[Products]"/"[Reactants]"`
D. For the electrode `M^(n+)//M` at 273 K `E=E^@+ 0.591/n "log"[M^(n+)]`

Explanation

To solve the problem of identifying the incorrect relationship among the given statements related to electrochemistry, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Evaluate the First Statement:**
- The first statement claims that the equilibrium constant \( K \) is related to the electromotive force (emf) as:
\[ \log K = \frac{nFE}{2.303RT} \]
- We know from thermodynamics that:
\[ \Delta G = -RT \ln K \quad \text{and} \quad \Delta G = -nFE \]
- Equating these two expressions gives:
\[ -RT \ln K = -nFE \implies \ln K = \frac{nFE}{RT} \]
- Converting natural logarithm to base 10 logarithm:
\[ \ln K = 2.303 \log K \implies \log K = \frac{nFE}{2.303RT} \]
- Thus, the first statement is **correct**.

2. **Evaluate the Second Statement:**
- The second statement describes an electrochemical cell where zinc is the anode and copper is the cathode. It states:
\[ E_{\text{cell}} = E^\circ - \frac{0.591}{n} \log \left(\frac{A_1}{A_2}\right) \]
- In a standard electrochemical cell, the equation should be:
\[ E_{\text{cell}} = E^\circ - \frac{0.0591}{n} \log \left(\frac{[\text{products}]}{[\text{reactants}]}\right) \]
- Here, \( A_1 \) should represent the concentration of the cathode and \( A_2 \) the concentration of the anode. The statement incorrectly places them, making it **incorrect**.

3. **Evaluate the Third Statement:**
- The third statement asserts:
\[ E_{\text{cell}} = E^\circ - \frac{0.0591}{n} \log \left(\frac{\text{products}}{\text{reactants}}\right) \]
- This is consistent with the Nernst equation, which is correctly formulated. Thus, this statement is **correct**.

4. **Evaluate the Fourth Statement:**
- The fourth statement involves the electrode reaction:
\[ E = E^\circ + 0.0591 \log [M^{n+}] \]
- The correct form for a reduction reaction is:
\[ E = E^\circ - \frac{0.0591}{n} \log \left[\frac{1}{[M^{n+}]}\right] \]
- This can be rearranged to:
\[ E = E^\circ - \frac{0.0591}{n} \log [M^{n+}] \]
- Therefore, this statement is also **correct**.

### Conclusion:
The incorrect relationship among the statements is the **second statement**, which misrepresents the concentrations of the anode and cathode in the Nernst equation.