Problem 176 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following facts about the complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) is wrong? (a) The complex gives white precipitate with silver nitrate solution. (b) The complex involves \(\mathrm{d}^{2} \mathrm{sp}^{3}\) hybridisation, and is octahedral in shape. (c) The complex is an outer orbital complex. (d) The complex is paramagnetic.

Step-by-Step Solution

Answer

Option (c) is wrong because the complex is an inner orbital complex, not an outer orbital complex.

Step 1: Analyze the complex structure

The complex given is \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \). It consists of a chromium ion coordinated to six ammonia ligands, making it an octahedral complex. The chloride ions are counter ions that can participate in reactions outside the coordination sphere.

Step 2: Determine precipitate with silver nitrate

Silver nitrate reacts with free chloride ions to form a white precipitate of silver chloride \( \text{AgCl} \). The complex has three chloride ions that can be displaced by silver ions to give this reaction, thus (a) is correct.

Step 3: Determine hybridization and geometry

The coordination number of chromium in the complex is 6 due to its binding with six ammonia ligands. As it forms an octahedral coordination, the hybridization is \(d^2sp^3\), which matches (b), as the central metal ion uses two of its d orbitals, one s orbital, and three p orbitals in hybridization.

Step 4: Classify the complex type

An outer orbital complex involves d orbitals from the outermost (n)d shell. For \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \), the electrons fill lower energy 3d orbitals, not outer 4d orbitals, indicating it is an inner orbital complex rather than an outer orbital complex. Thus, (c) is incorrect.

Step 5: Confirm magnetic properties

Determine the number of unpaired electrons. Chromium in the +3 oxidation state ([Ar] 3d\(^3\)) is expected to have 3 unpaired electrons, making the complex paramagnetic, confirming (d) is correct.

Key Concepts

Hybridisation

Hybridisation is crucial in determining the geometry and bonding in coordination complexes. When we talk about hybridisation, it refers to the mixing of atomic orbitals to form new hybrid orbitals that correspond to the geometry of the molecule.
In the complex \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \), chromium is the central ion, surrounded by six ammonia ligands. This leads to an octahedral shape.
For the formation of this complex, chromium exhibits \( \mathrm{d}^{2}\mathrm{sp}^{3} \) hybridisation:

• Two of the 3d orbitals are used, allowing space for the ligands to coordinate.
• One 4s and three 4p orbitals also mix to accommodate the six ligands symmetrically.

The result is an octahedral geometry, which is a common shape for complexes with a coordination number of six. Understanding these orbital movements and arrangements helps explain why complexes have specific shapes and properties.

Coordination Complex

A coordination complex forms when a metal ion bonds with one or more ligands. These ligands donate electron pairs to the metal, resulting in a coordinated structure. The complex \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \) is a great example.
In this complex, the chromium ion acts as the coordination center. It's surrounded by six ammonia (\(\mathrm{NH}_3\)) ligands which donate their lone pairs of electrons to chromium, forming coordinate covalent bonds.
This type of complex often displays specific geometric structures like octahedral, tetrahedral, or square planar, depending on the number and type of ligands. In our example, with six ligands, the structure is octahedral, efficiently packed around the central chromium.

• The ammonia ligands are within the coordination sphere.
• The chloride ions are outside and can react with other molecules like silver nitrate, proving the presence of ionizable counter ions.

Understanding such complexes is key in applications ranging from catalysis to colorimetric analysis in chemistry.

Magnetic Properties

The magnetic properties of a coordination complex depend on the number of unpaired electrons in the metal center. Unpaired electrons create a magnetic moment, which can lead to paramagnetic behavior.
For the complex \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \), chromium has an oxidation state of +3. This corresponds to the electronic configuration of \([\mathrm{Ar}] 3d^3\) for the chromium(III) ion.
With three unpaired electrons in the 3d orbitals, this complex is paramagnetic:

• Paramagnetism arises due to these unpaired electrons aligning with external magnetic fields.
• This is distinct from diamagnetism, where all electrons are paired, leading to no net magnetic moment.

Recognizing the paramagnetic characteristics of complexes is useful for understanding their reactivity and spectral properties, among other physical data.