Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{CO}_{3}\right] \mathrm{ClO}_{4}\) The coordination number, oxidation number, number of d electrons and number of unpaired d electrons on the metal are, respectively (a) \(6,3,6,0\) (b) \(6,3,6,3\) (c) \(6,0,6,3\) (d) \(6,2,6,3\)

Step-by-Step Solution

Answer

(b) 6, 3, 6, 3.

Step 1: Identify the Coordination Number

The coordination number is the number of ligand atoms that are bonded to the central metal atom. In the complex \([\text{Cr(NH}_3)_5\text{CO}_3]\text{ClO}_4\), the ligands are \(5\text{NH}_3\) and \(\text{CO}_3^{2-}\), totaling to 6 ligands. Thus, the coordination number is 6.

Step 2: Determine the Oxidation State of Chromium

Set up the equation to find the oxidation state of chromium. The perchlorate ion, \(\text{ClO}_4^-\), contributes a \(-1\) charge. Ammonia \((\text{NH}_3)\) is a neutral ligand and contributes 0 charge. Carbonate \((\text{CO}_3^{2-})\) contributes \(-2\) charge. Let \(x\) be the oxidation state of chromium: \[ x + 0 + (-2) + (-1) = 0 \] Solve for \(x\): \[ x - 3 = 0 \] \[ x = +3 \] Thus, the oxidation state of chromium is +3.

Step 3: Calculate the Number of d-Electrons

Chromium in its elemental form has an electron configuration of \([\text{Ar}] 3d^5 4s^1\). To find the number of d-electrons in the complex, we consider the oxidation state of +3:- Oxidation reduces the number of electrons, so remove 3 electrons starting from the highest energy orbital.- The configuration becomes \([\text{Ar}] 3d^3\).Thus, there are 3 d-electrons.

Step 4: Determine the Number of Unpaired d-Electrons

With 3 electrons in the 3d subshell \( (3d^3) \), place them in the orbitals according to Hund's rule: 1. Each of the 3 electrons occupies separate orbitals because it minimizes repulsion.This results in 3 unpaired d-electrons.

Key Concepts

Coordination Number

In coordination chemistry, the **coordination number** of a metal complex is crucial for understanding its geometry and properties. It refers to the total number of bonds formed between the central metal atom and the ligand atoms. Take the chromium complex \[ \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{CO}_{3}\right] \mathrm{ClO}_{4} \], for example.
Here, the term *ligands* encapsulates any molecule or ion that donates a pair of electrons to the metal atom to form a coordination bond.

• In this complex, the ligands are five ammonia molecules \( (\mathrm{NH}_3) \), bonded directly to the metal atom, and one carbonate ion \( (\mathrm{CO}_3^{2-}) \).
• Both ligands result in a coordination number of **6** for the metal atom, chromium.
• This indicates a hexa-coordination, which is often associated with an octahedral shape.

Understanding the coordination number helps predict the 3D structure, crucial for envisioning the behavior and reactions of the complex under various chemical conditions.

Oxidation State

The **oxidation state** of a metal within a complex is a number that indicates the effective charge the metal bears after accounting for contributions from the ligands.
For the complex \[ \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{CO}_{3}\right] \mathrm{ClO}_{4} \], determining the oxidation state of chromium involves simple charge arithmetic.

• Ammonia ligands are neutral, contributing zero to the charge.
• The carbonate ion contributes an \( -2 \) charge, while \( \mathrm{ClO}_4^- \), being a single anion outside the coordination sphere, adds another \( -1 \).
• To balance this, the oxidation state of chromium \( (x) \) can be determined by equating: \( x - 3 = 0 \, \ x = +3 \).

The result, an oxidation state of **+3**, points to the fact that chromium has donated three electrons, making this complex potentially interesting for redox reactions.

d-Electron Count

In determining the **d-electron count** of a metal complex, one must assess how many of the valence electrons remain in the d orbitals, considering the metal's oxidation state. For chromium with an atomic configuration \[ [\mathrm{Ar}] \ 3d^5 \ 4s^1 \]:

• First, account for the chromium's oxidation state of \( +3 \), which occurs by removing three electrons, initially from the outermost orbitals.
• This deduction results in a revised configuration of \[ [\mathrm{Ar}] \ 3d^3 \], indicating that **three d-electrons** remain.

The calculation of d-electron count is essential as these electrons play a decisive role in bonding, color, magnetism, and reactivity of the complex.

Unpaired Electrons

The presence of **unpaired electrons** in a metal complex's d-orbitals greatly influences its magnetic properties. To determine the number of unpaired electrons, consider the filling of these orbitals according to Hund's rule, prioritizing the minimization of electron repulsion by maximizing unpaired spins.
For the chromium complex, \[ 3d^3 \]:

• The three d-electrons occupy separate 3d orbitals.
• Each electron rests in its own orbital due to Hund's Rule, resulting in **three unpaired electrons**.

These unpaired electrons render the complex paramagnetic, meaning it will be attracted to a magnetic field, a vital consideration in many applications, including materials science and catalysis.