Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

A \(0.01 \mathrm{M}\) complex of \(\mathrm{CoCl}_{2}\) and \(\mathrm{NH}_{3}\) (molar ratio \(1: 4\) ) is found to have effective molarity of \(0.02 \mathrm{M}\) (evaluated from colligative property). What is the formula of the complex? (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{3}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}\)

Step-by-Step Solution

Answer

The formula of the complex is \([\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl}\) (option a).

Step 1: Identify Given Values

We are given a complex with a concentration of \(0.01 \text{ M}\) and an effective molarity obtained from colligative property is \(0.02 \text{ M}\). The molar ratio of \(\text{CoCl}_2\) to \(\text{NH}_3\) is \(1:4\).

Step 2: Understand the Formula Options

We have four options for the formula of the complex: - Option (a): \(\left[ \text{Co}\left(\text{NH}_3\right)_4 \text{Cl}_2 \right]\text{Cl}\) - Option (b): \(\left[\text{Co}\left(\text{NH}_3\right)_3 \text{Cl}_3\right]\) - Option (c): \(\left[ \text{Co}\left(\text{NH}_3\right)_4 \right]\text{Cl}_3\) - Option (d): \(\left[ \text{Co}\left(\text{NH}_3\right)_5 \text{Cl}\right]\text{Cl}\)

Step 3: Calculate the i Factor (Van't Hoff Factor)

The Van't Hoff factor, \(i\), is calculated by dividing the effective molarity by the actual molarity: \[ i = \frac{0.02 \text{ M}}{0.01 \text{ M}} = 2 \].This indicates that the complex dissociates into two ions in solution.

Step 4: Analyze Dissociation of Complexes

Analyze each option to see which one dissociates into two ions:- (a) \([\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl}\) \( \rightarrow [\text{Co}(\text{NH}_3)_4\text{Cl}_2]^+ + \text{Cl}^- \) : 2 ions- (b) \([\text{Co}(\text{NH}_3)_3\text{Cl}_3]\) : Non-ionizing- (c) \([\text{Co}(\text{NH}_3)_4]\text{Cl}_3\) \( \rightarrow [\text{Co}(\text{NH}_3)_4]^{3+} + 3\text{Cl}^- \) : 4 ions- (d) \([\text{Co}(\text{NH}_3)_{5}\text{Cl}]\text{Cl}\) \( \rightarrow [\text{Co}(\text{NH}_3)_{5}\text{Cl}]^{2+} + \text{Cl}^- \) : 2 ions

Step 5: Identify the Correct Formula

Options (a) and (d) give us a dissociation into two ions, matching our calculated \(i = 2\). Since the molar ratio of \(\text{CoCl}_2\) to \(\text{NH}_3\) is 1:4, option (a) \(\left[ \text{Co}\left(\text{NH}_3\right)_4 \text{Cl}_2 \right]\text{Cl}\) is the correct complex formula as it involves 4 \(\text{NH}_3\) ligands.

Key Concepts

Van't Hoff Factor

In the context of chemical complexes, the Van't Hoff factor, represented by the symbol \(i\), is crucial for understanding how a compound dissociates in solution. It helps us understand the number of particles that a solute divides into when dissolved. This factor is calculated by dividing the effective concentration by the original concentration of the solution.

For example, if a complex initially at \(0.01\text{ M}\) exhibits a colligative property suggesting an effective molarity of \(0.02\text{ M}\), the Van't Hoff factor would be \( i = \frac{0.02\text{ M}}{0.01\text{ M}} = 2 \).

This value of 2 indicates that the complex dissociates into two particles when in solution. Understanding \(i\) is essential for predicting the behavior of substances in solution, especially for coordination complexes that can dissociate into multiple ions.

Ion Dissociation

Ion dissociation is the process by which an ionic compound separates into its individual ions when in solution. This is particularly significant in coordination chemistry, where complex compounds often dissociate into multiple ions.

When we analyze a given complex, we need to determine how it breaks down. For instance, a complex like \([ ext{Co}( ext{NH}_3)_4 ext{Cl}_2] ext{Cl}\) dissociates as follows:
- \[ [ ext{Co}( ext{NH}_3)_4 ext{Cl}_2]^+ + ext{Cl}^- \] (producing two ions)

Understanding this process is critical for predicting outcomes in chemical reactions, as well as for calculating related properties such as boiling point elevation and freezing point depression, which are dependent on the number of particles in solution.

Coordination Chemistry

Coordination chemistry involves compounds that feature central metal atoms bonded to surrounding molecules or ions, known as ligands. These complexes can exhibit diverse configurations and behaviors depending on their structure.

Take, for instance, a cobalt complex with \( ext{NH}_3\) ligands. The number and type of ligands, along with the metal center, define the properties and reactivity. Optional formulae such as \[ ext{Co} ext{Cl}_2 ext{(NH}_3)_4 \] present the distinct chemical challenges based on their dissociation patterns in aqueous solutions.

The field also explores how these complexes influence chemical processes through their structural framework and interaction with other compounds. Coordination chemistry is essential in areas such as catalysis, material science, and bioinorganic chemistry.

Colligative Properties

Colligative properties are physical changes that result from the dissolution of a solute in a solvent. They depend solely on the number of solute particles in a solution and not on the identity of the particles.

Some primary colligative properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. These changes provide indirect insight into the behavior of solutions and the nature of dissolved electrolytes.

For example, the effective molarity derived from a colligative property serves as a hint about ion dissociation, as seen in the Van't Hoff factor recovery of a cobalt complex. Being able to measure these properties allows chemists to infer significant molecular information about solute phenomena in solvents.