Problem 75 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following does not obey EAN rule? (a) \(\mathrm{V}(\mathrm{CO})_{6}\) (b) \(\mathrm{Mn}_{2}(\mathrm{CO})_{10}\) (c) \(\mathrm{Fe}(\mathrm{CO})_{5}\) (d) \(\mathrm{K}_{4} \mathrm{Fe}(\mathrm{CN})_{6}\)

Step-by-Step Solution

Answer

(c) \( \text{Fe(CO)}_5 \) obeys the EAN rule; the others do not.

Step 1: Identify EAN Rule

The Effective Atomic Number (EAN) rule states that for a metal complex, the sum of the metal's electrons and the electrons donated by the ligands should ideally be equal to the atomic number of the nearest noble gas.

Step 2: Calculate EAN for V(CO)6

Vanadium has an atomic number of 23, so it has 23 valence electrons. Each CO ligand donates 2 electrons, so 6 CO ligands donate 12 electrons. Therefore, the EAN of \( \text{V(CO)}_6 \) is \( 23 + 12 = 35 \). The nearest noble gas is Krypton, which has an atomic number of 36, so this does not obey the EAN rule.

Step 3: Calculate EAN for Mn2(CO)10

Manganese has an atomic number of 25, so each Mn atom has 25 valence electrons. Each CO ligand donates 2 electrons, so 10 CO ligands (shared by 2 Mn atoms) donate 20 electrons. Each Mn atom in Mn2(CO)10 shares 10 CO ligands, adding 10 electrons: \( \text{EAN} = 25 + 10 = 35 \). The nearest noble gas is Krypton, which has an atomic number of 36, so this does not obey the EAN rule, but for illustration purposes, calculation above assumes all CO are shared equally with both Mn involved in direct CO bonding.

Step 4: Calculate EAN for Fe(CO)5

Iron has an atomic number of 26, so it has 26 valence electrons. Each CO ligand donates 2 electrons, so 5 CO ligands donate 10 electrons. Therefore, the EAN of \( \text{Fe(CO)}_5 \) is \( 26 + 10 = 36 \). The nearest noble gas is Krypton, which has an atomic number of 36, so this does obey the EAN rule.

Step 5: Calculate EAN for K4Fe(CN)6

Iron has an atomic number of 26, so it has 26 valence electrons. The complex bears a \(4^+\) charge from \(\text{K}_4\), hence reducing Iron's electron by 4 to 22. Each CN ligand donates 2 electrons, so 6 CN ligands donate 12 electrons. The EAN of \( \text{Fe in K}_4\text{Fe(CN)}_6 \) is \( 22 + 12 = 34 \). The nearest noble gas to match is poor, so it does not fit traditional EAN analysis exactly but considers charge and electronic symmetry achieving noble gas structure.

Key Concepts

Effective Atomic Number

The Effective Atomic Number (EAN) is a concept used to determine the stability of a metal complex. To calculate the EAN, you sum up the number of electrons that come from the metal itself with the electrons that ligands donate. The resulting sum should ideally match the atomic number of the nearest noble gas. This concept is often used to predict whether a particular metal complex will display stability.
In practice, if the EAN equals the atomic number of the nearest noble gas, the metal complex is considered to have a complete electronic configuration that usually confers stability and low reactivity. However, exceptions do exist, and some complexes do not strictly adhere to the EAN rule while remaining stable because of factors like steric effects or additional stability from electronic arrangements other than the predicted noble gas resemblance.

Metal Complexes

Metal complexes are intriguing structures formed when a central metal atom, often a transition metal, bonds with molecules or ions known as ligands. These ligands sit around the metal center and are bound through coordinate covalent bonds, where both electrons come from the ligand.
These complexes can display a wide array of geometries and properties due to their specific arrangements. The nature and number of ligands influence the stability and properties of the complex, as well as its electron count, which plays a role in determining whether it follows the EAN rule. Understanding the EAN provides insight into predicting possible configurations and stability attributes of metal complexes.

Ligand Donation

Ligand donation is an essential concept within coordination chemistry that deals with the number of electrons ligands contribute when binding to a metal in a complex. Each type of ligand has a fixed donation power, where it supplies a set number of electrons to form covalent bonds with the metal center.
For example, the cyanide ion (CN) and carbon monoxide (CO) are both common ligands known for their ability to donate two electrons each. This donation helps elevate the metal's electron count and moves it toward mimicking a noble gas configuration if the EAN rule holds.
Thus, a ligand's donating capacity directly affects the overall electron configuration and stability. When examining the electron donation from ligands, it becomes clearer whether the complex adheres to the EAN rule through achieving or approaching a noble gas electron structure.

Noble Gas Configuration

Achieving a noble gas configuration is often the goal for metal complexes as it signifies reaching a full complement of electrons, akin to that of noble gases. Noble gases, located at the far right of the periodic table, have complete valence electron shells and are remarkably stable.
For a metal complex to be classified as having a noble gas configuration, the combined electrons from the metal atom and the donating ligands must mirror the total electron count of a noble gas. Metals like iron or manganese in complexes aim to reach configurations similar to Krypton, with an atomic number of 36.
This mimicry of noble gas configurations generally implies a lower energy state, making the complex more stable and typically less reactive. Thus, achieving a noble gas configuration is a natural check for chemistry students to understand the potential stability of a metal complex.