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 (a) \([\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}] \mathrm{Cl}\).

Step 1: Understand the Problem

We have a 0.01 M solution of a complex with a 1:4 molar ratio of CoCl2 to NH3. This complex shows an effective molarity of 0.02 M due to colligative properties. We need to find which of the given formulas corresponds to the complex.

Step 2: Analyze the Effective Molarity

The measured effective molarity of 0.02 M means the solution behaves as if there are twice as many particle entities as in a 0.01 M solution. This suggests that upon dissolution, the complex dissociates into two separate ions or species.

Step 3: Analyze Molar Ratio and Options

The molar ratio is 1:4, indicating that the complex contains one Co atom bonded with four NH3 molecules. Reviewing the options, we need to identify which complex matches the ratio and dissociates into two parts upon dissolving.

Step 4: Match with Options

Option (a) has formula \([\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}] \mathrm{Cl}\). After dissociation, it becomes \([\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}]^+\) and one \(\mathrm{Cl}^-\), which are two species, matching the 0.02 M effective molarity. This option fits the criteria.

Key Concepts

Complex Formation

Complex formation is a fascinating interaction in coordination chemistry. It involves a central metal ion, like cobalt \((\mathrm{Co})\), surrounded by molecules or ions called ligands. In our context, ammonia \(\left(\mathrm{NH}_3\right)\) serves as the ligand. Here's how it all comes together.
The metal ion, typically a positively charged entity, attracts these ligands, which usually have lone pairs of electrons to offer via coordinate covalent bonds. As a result, the complex forms a stable structure, reflecting its coordination number. The coordination number represents the number of ligand atoms directly bonded to the central metal. In our exercise, with a molar ratio of 1 metal ion to 4 ammonia molecules, the complex indeed shows a coordination number of 4, indicating a unique arrangement.

Understanding these interactions sheds light on why different ligands might be favored, or lead to different complexes if substituted. Elements like cobalt can engage multiple ligands, creating a series of stable, variably-charged complexes, which express general formula varieties, contributing to their vast applications in areas like catalysis and chemical synthesis.

Colligative Properties

Colligative properties are intriguing as they depend solely on the number of dissolved particles in a solution, not their identity. These include properties like boiling point elevation, freezing point depression, osmotic pressure, and, relevant to our context, effective molarity.
When a complex dissolves, it dissociates into various ions or molecules, increasing particle count. This increase is what elevates the effective molarity. The more particles present, the more pronounced the colligative effects. For example, a solution with a measured effective molarity of 0.02 M suggests it behaves like one with twice the particle entities than initially expected from its 0.01 M measurement.

• This dissociation and increase create significant shifts in colligative properties, highlighting the core role of particle count versus the chemical nature of the solute.

By focusing on particle numbers, colligative properties offer clues about the degree and mode of a complex's dissociation, as in our example where simple molarity was effectively doubled.

Dissociation of Complexes

When it comes to the dissociation of complexes, such as the one formed between cobalt and ammonia, understanding how and why they break apart in solution provides great insight. Dissociation refers to the separation of the complex into smaller, separate entities, usually ions, when dissolved.
In the given exercise, the complex dissociates into two species, suggested by its doubled effective molarity. This means that, once dissolved, \[[\mathrm{Co}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl}\] separates into a positive complex ion \[\lm{e.g., [\mathrm{Co}(\mathrm{NH}_3)_4 \mathrm{Cl}_2]^+}\] and a chloride ion \(\mathrm{Cl}^-\).

• The process is influenced by a variety of factors, including concentration, temperature, and the stability of the resultant ions.
• It’s an equilibrium, often favoring dissociation strongly if stable ion pairs result, as evident from colligative observations.

This dissociation not only informs on what forms in solution but also on chemical reactivity, potential for further reactions, and properties seen in measurable experiments, such as those assessing conductivity or colligative effects.