Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one is the most likely structure of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is \(1 / 3\) of total chlorine of the compound is precipitated by adding \(\mathrm{AgNO}_{3}\) to its aqueous solution? (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{3}\right] .\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\) (b) \(\mathrm{CrCl}_{3}-6 \mathrm{H}_{2} \mathrm{O}\) (c) \(\left[\mathrm{CrCl}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\right] \mathrm{Cl}_{2} \cdot \mathrm{H}_{2} \mathrm{O}\) (d) \(\left[\mathrm{CrCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] . \mathrm{Cl} .{ }_{2} \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The structure is \(\left[\mathrm{CrCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] \cdot \mathrm{Cl} \cdot 2 \mathrm{H}_{2} \mathrm{O}\).

Step 1: Understanding Coordination Complexes

Coordination complexes consist of a central metal atom or ion surrounded by molecules or ions, termed ligands. For compounds like \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), the metal chromium (\(\mathrm{Cr}\)) may form a complex with water and chloride ions.

Step 2: Analyzing Chloride Precipitation

When \(\mathrm{AgNO}_3\) is added to a solution containing chloride ions, it reacts with free chloride ions (not those complexed to the metal) to form \(\mathrm{AgCl}\) precipitate. Since \(\frac{1}{3}\) of total chlorine is precipitated, only one out of three chloride ions per \(\mathrm{Cr}\) is free in the solution.

Step 3: Choosing the Correct Structure

For the structure where \(\frac{1}{3}\) of total chlorine is precipitated, one out of three chlorine atoms must be free because of it not being part of the complex. The structure \(\left[\mathrm{CrCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] \cdot \mathrm{Cl} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) contains two chloride ions within the coordination sphere and one chloride ion outside the coordination sphere.

Key Concepts

Central Metal Atom

In a coordination complex, the term "central metal atom" refers to the metal ion that acts as the core of the entire structure. This metal atom, like chromium (Cr) in our given compound \( \mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O} \), plays a crucial role as it defines the coordination center around which the rest of the molecules or ions are arranged.

The central metal atom's properties, such as its oxidation state, size, and electronic configuration, heavily influence how it interacts with other atoms or groups to form the complex.

• It determines the strength and number of bonds that can form.
• It dictates the geometry of the complex, affecting aspects like bond angles and the overall 3D shape of the complex.

Central metal atoms usually have empty d-orbitals which allow them to form coordinate bonds with ligands, the surrounding molecules or ions.

Ligands

Ligands are the molecules or ions that attach themselves to the central metal atom, forming the coordination sphere of the complex. They act as donors of electron pairs to the metal ion, forming *coordinate covalent bonds*.

Types of ligands vary greatly, ranging from small ions like chloride (\( \mathrm{Cl}^- \)) and water (\( \mathrm{H}_2 \mathrm{O} \)) in our example to large, complex molecules.

• Monodentate Ligands: Attach through one donor atom (e.g., water).
• Bidentate or Polydentate Ligands: Can attach through two or more atoms, creating more complex bonds.

In \( \left[\mathrm{CrCl}_2\left(\mathrm{H}_2 \mathrm{O}\right)_4\right] \cdot \mathrm{Cl} \cdot 2 \mathrm{H}_2 \mathrm{O} \), the ligands such as \( \mathrm{Cl}^- \) inside the brackets form part of the coordination sphere, binding tightly to chromium. Outside-the-bracket chloride ions and water molecules, meanwhile, do not form part of the immediate coordination sphere with the chromium, affecting properties like *solubility* and *reactivity* with external compounds.

Chloride Precipitation

Chloride precipitation is an essential concept, especially when analyzing compounds like coordination complexes in an aqueous solution. This concept revolves around the interaction between free chloride ions and silver nitrate (\( \mathrm{AgNO}_3 \)).

When \( \mathrm{AgNO}_3 \) is added to the solution, it reacts with free chloride ions (those not bonded within the coordination sphere) to form a white precipitate of silver chloride (\( \mathrm{AgCl} \)).

• This precipitation is a common method to identify the *presence* and *amount* of free chloride ions in solution.
• The occurrence of a precipitate upon addition of \( \mathrm{AgNO}_3 \) suggests that the chloride ions are not internally bonded in the coordination complex.

In our problem, since \( \frac{1}{3} \) of total chloride precipitates, we know that one chloride ion is outside the coordination sphere. This information helps us deduce the correct complex structure as being \( \left[\mathrm{CrCl}_2\left(\mathrm{H}_2 \mathrm{O}\right)_4\right] \cdot \mathrm{Cl} \cdot 2 \mathrm{H}_2 \mathrm{O} \), where two chlorides are ligands and one is free, hence precipitated by \( \mathrm{AgNO}_3 \).