Number if ions produced on electrolysis of \([Co(NH_3)_6]Cl_3\) which gives 3 moles of \(AgCl\) on reacting with \(AgNO_3\), are:

4

The correct answer is option 4. 4.

In this problem, we are to determine the number of ions produced upon electrolysis of \([Co(NH_3)_6]Cl_3\), a coordination complex.

Understanding the Compound:

\([Co(NH_3)_6]Cl_3\) is a coordination complex made up of:  A central metal ion \(Co^{3+}\), surrounded by six ammonia ligands \((NH_3)\). These ammonia molecules are neutral ligands and are bound directly to the cobalt ion within the coordination sphere, forming the complex ion \([Co(NH_3)_6]^{3+}\). Three chloride ions \((Cl^-)\) are present outside the coordination sphere. These are not part of the complex but are ionically bound to neutralize the charge of the complex.

Dissociation in Solution:

When \([Co(NH_3)_6]Cl_3\) is dissolved in water, it dissociates into its ions as follows:

\([Co(NH_3)_6]Cl_3 \longrightarrow [Co(NH_3)_6]^{3+} + 3Cl^-\)

One cation: \([Co(NH_3)_6]^{3+}\), which is the complex ion.

Three anions: \(Cl^-\), which are chloride ions.

So, in total, 4 ions are produced when the compound dissociates in solution:

1. The single complex ion \([Co(NH_3)_6]^{3+}\) contributes 1 ion.

2. The three chloride ions \((Cl^-)\) contribute 3 ions.

Reaction with \(AgNO_3\):

When this solution is treated with silver nitrate \((AgNO_3)\), the chloride ions \((Cl^-)\) react with the silver ions \((Ag^+)\) to form a white precipitate of silver chloride \((AgCl)\):

\(Cl^- + Ag^+ \longrightarrow AgCl\)

For every mole of \([Co(NH_3)_6]Cl_3\), 3 moles of chloride ions are available to form 3 moles of \(AgCl\). This confirms that there are 3 chloride ions dissociated from the compound.

Electrolysis:

During electrolysis, the ions in solution participate:

The complex ion \([Co(NH_3)_6]^{3+}\) acts as a cation.

The chloride ions \(Cl^-\) act as anions.

Thus, the total number of ions produced in the solution, which are involved in the electrolysis, is:

1 ion from \([Co(NH_3)_6]^{3+}\)

3 ions from \(3Cl^-\)

Final Conclusion:

The total number of ions produced during the electrolysis of \([Co(NH_3)_6]Cl_3\) is 4.