Problem 27 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

If the freezing point of a \(0.01\) molal aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is \(-0.0558^{\circ} \mathrm{C}\), the number of chloride(s) in the coordination sphere of the complex is \(\left[K_{f}\right.\) of water \(\left.=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]\)

Step-by-Step Solution

Answer

There are 2 chloride ions in the coordination sphere.

Step 1: Understand the freezing point depression formula

The freezing point depression formula is given by \[\Delta T_f = i \times K_f \times m\] where \(\Delta T_f\) is the change in freezing point, \(K_f\) is the freezing point depression constant of the solvent, \(m\) is the molality of the solution, and \(i\) is the van't Hoff factor representing the number of particles into which the solute dissociates.

Step 2: Calculate the freezing point depression

Given that the freezing point of the solution is \(-0.0558^{\circ}\ C\), and the freezing point of pure water is \(0^{\circ}\ C\), calculate \(\Delta T_f = 0 - (-0.0558) = 0.0558^{\circ}\ C\).

Step 3: Solve for the van't Hoff factor \(i\)

Substitute known values into the freezing point depression formula: \[0.0558 = i \times 1.86 \times 0.01\] Solve for \(i\): \[i = \frac{0.0558}{1.86 \times 0.01} = 3\] Thus, the van't Hoff factor \(i\) is 3.

Step 4: Determine the number of chloride ions

For a coordination complex, the increase in particles occurs from the dissociation into ions. Assuming the coordination complex formula is \([Co(NH_3)_xCl_y]Cl_z\), \(i = 3\) suggests that the compound dissociates into 3 ions. Since one \([Co(NH_3)_xCl_y]^+\) cation is released and the remaining ions must be chloride from the formula, the number of outer-sphere chloride ions that accounts for remaining ions is \(2\).

Key Concepts

Cobalt(III) Chloride Complex

The cobalt(III) chloride-ammonia complex is an intriguing compound with significant implications in the field of coordination chemistry. This complex is part of a category known as coordination compounds. These occur when metal ions form complexes with various ligands. Ligands are molecules or ions attached to a central metal atom. In this specific compound, cobalt (III), which implies a +3 oxidation state of cobalt, acts as the central metal ion.

Typically, ammonia (NH₃) acts as a ligand forming a bond with cobalt. This forms the coordination sphere. Another critical component involves chloride ions (Cl⁻). These can be either part of the coordination sphere directly bound to the cobalt or exist as counter ions outside the sphere. The role of these chloride ions in the complex is to balance charge or assist in complex formation.

• The behavior in aqueous solutions is crucial for calculations related to freezing point depression.
• The interactions within the complex significantly impact how the complex will dissociate in solution.

Van't Hoff Factor

The Van't Hoff factor, denoted as \( i \), is a crucial element when discussing colligative properties, which include freezing point depression. It reflects the level of solute dissociation into particles in solution. For electrolytes like our cobalt(III) chloride-ammonia complex, the dissociation into ions or molecules is represented numerically by \( i \).

In general terms:

• If \( i = 1 \), the substance does not dissociate and behaves as one particle in solution.
• If \( i > 1 \), this indicates an increase in the number of particles due to dissociation into multiple ions.

For the cobalt(III) chloride complex, the Van't Hoff factor was found to be 3. This is calculated using the freezing point depression formula \( \Delta T_f = i \times K_f \times m \). This tells us that each molecule of the complex dissociates into three ions in solution. This can be helpful to determine components like the outer-sphere chlorides which stabilize the charge around the complex.

Coordination Chemistry

Coordination chemistry is an area of chemistry that explores compounds consisting of a central metal atom bonded to surrounding molecules, or ligands.

These compounds are quite versatile, participating in varied reactions and forming unique structures. They are characterized by:

• The coordination number, which refers to the number of ligand atoms bonded to the central metal.
• The geometry of the complex, which describes how ligands arrange themselves around the metal atom.
• The types of ligands, which can range from simple ions to complex organic molecules.

These aspects tremendously influence the properties and reactivities of the complexes.

In coordination chemistry, the focus often shifts to analyzing how complexes interact in solutions, particularly in terms of dissociation and stability. The study of these reactions is fundamental in explaining behaviors such as those observed in freezing point depression experiments. Cobalt complexes specifically demonstrate fascinating behaviors due to varied oxidation states and coordination numbers, often leading to unexpected experimental observations.