Which of the following statement is incorrect?

In K₃[Fe(CN)₆] the ligand has satisfied only the secondary valency of ferric ion

The correct answer is option 2. In \(K_3[Fe(CN)_6]\), the ligand has satisfied only the secondary valency of ferric ion.

Let us delve deeper into the concepts of primary and secondary valencies and analyze each statement regarding the given coordination compounds.

Primary and Secondary Valencies:

Primary Valency: This refers to the oxidation state of the metal ion in the coordination complex. It is the number of positive charges on the metal ion, which is satisfied by counterions or ligands carrying negative charges.

Secondary Valency: This refers to the coordination number of the metal ion, which is the number of ligand atoms directly bonded to the metal ion through coordinate covalent bonds.

Let us look at each of the given options:

1.In \( K_3[Fe(CN)_6] \), the ligand has satisfied both primary and secondary valencies of ferric ion

The given complex  is \( K_3[Fe(CN)_6] \). The central metal is \(Fe^{3+}\) (ferric ion)

Oxidation State (Primary Valency): +3

Coordination Number (Secondary Valency): 6 (from six cyanide \((CN^-)\) ligands)

The primary valency (oxidation state) of \(+3\) is satisfied by three potassium ions \((K^+)\), balancing the charge of the complex. The secondary valency is satisfied by six \(CN^-\) ligands coordinating to the \(Fe^{3+}\) ion. Thus, the cyanide ligands fulfill both primary (by charge balance) and secondary (by coordination) valencies. So, the option is correct.

2.In \( K_3[Fe(CN)_6] \), the ligand has satisfied only the secondary valency of ferric ion

The primary valency (charge balance) is satisfied by the potassium ions \((K^+)\), and the secondary valency (coordination) is satisfied by the cyanide ligands \((CN^-)\). Since the cyanide ligands contribute to both the primary (by forming part of the complex anion that needs charge balance) and secondary valencies, saying they only satisfy the secondary valency is incorrect. So, the statement is incorrect.

3. In \( K_4[Fe(CN)_6] \), the ligand has satisfied both primary and secondary valencies of ferrous ion

The given complex  is \( K_4[Fe(CN)_6] \). The central metal is \(Fe^{2+}\) (ferric ion)

Oxidation State (Primary Valency): +2

Coordination Number (Secondary Valency): 6 (from six cyanide \((CN^-)\) ligands)

The primary valency (oxidation state) of +2 is satisfied by four potassium ions \((K^+)\), balancing the charge of the complex. The secondary valency is satisfied by six \(CN^-\) ligands coordinating to the \(Fe^{2+}\) ion. Thus, the cyanide ligands fulfill both primary (by charge balance) and secondary (by coordination) valencies. So, the option is correct.

4. In \( [Cu(NH_3)_4]SO_4 \), the ligand has satisfied only the secondary valency of copper

The given complex  is \( [Cu(NH_3)_4]SO_4 \). The central metal is \(Cu^{2+}\) (ferric ion)

Oxidation State (Primary Valency): +2

Coordination Number (Secondary Valency): 4 (from four ammonia \((NH_3)\) ligands)

The primary valency (oxidation state) of +2 is satisfied by the sulfate ion \((SO_4^{2-})\), which balances the charge of the complex. The secondary valency is satisfied by four \(NH_3\) ligands coordinating to the \(Cu^{2+}\) ion. The ammonia ligands only satisfy the secondary valency through coordination bonds, while the primary valency is satisfied by the sulfate ion.
So, the option is correct.

Conclusion: The incorrect statement is: In \( K_3[Fe(CN)_6] \), the ligand has satisfied only the secondary valency of ferric ion. This statement is incorrect because the cyanide ligands in \( K_3[Fe(CN)_6] \) satisfy both the primary (through charge balance) and secondary (through coordination) valencies of the ferric ion.