Problem 41 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following order is correct for the size of \(\mathrm{Fe}^{3+}, \mathrm{Fe}\) and \(\mathrm{Fe}^{2+} ?\) (a) \(\mathrm{Fe}<\mathrm{Fe}^{2+}<\mathrm{Fe}^{3+}\) (b) \(\mathrm{Fe}^{2+}<\mathrm{Fe}^{3+}<\mathrm{Fe}\) (c) \(\mathrm{Fe}<\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}\) (d) \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}\)

Step-by-Step Solution

Answer

Option (d): \\(\mathrm{Fe}^{3+} < \mathrm{Fe}^{2+} < \mathrm{Fe}\\) is the correct order.

Step 1: Understanding Ionic and Atomic Sizes

The size of an ion or atom largely depends on the number of electrons and the nuclear charge. In general, cations (positive ions) are smaller than their neutral atoms because they have fewer electrons while the nuclear charge remains the same, pulling remaining electrons closer to the nucleus.

Step 2: Analyzing the Neutral Atom, Fe

The neutral atom, Fe, has electrons filling its various orbitals. The electron-nucleus attraction balances with electron-electron repulsion at this size. Since it has no extra or missing electrons, it maintains its typical atomic size.

Step 3: Comparing Ionic Sizes of Fe

When Fe loses electrons to form a cation, the size decreases due to increased effective nuclear charge. - \(\mathrm{Fe}^{2+}\): Loses two electrons, thus reducing electron-electron repulsion and size. - \(\mathrm{Fe}^{3+}\): Loses one more electron compared to \(\mathrm{Fe}^{2+}\), causing further reduction in size due to additional decrease in repulsion and increased effective nuclear attraction.

Step 4: Arranging Fe, Fe²⁺, and Fe³⁺ by Size

Comparing the ionic and atomic sizes: - \(\mathrm{Fe}^{3+}\) has the smallest size due to losing three electrons, resulting in very strong nuclear attraction.- \(\mathrm{Fe}^{2+}\) is larger than \(\mathrm{Fe}^{3+}\) as it loses only two electrons.- The neutral atom \(\mathrm{Fe}\) is the largest as it retains all its electrons, leading to greatest electron cloud size.

Step 5: Choosing the Correct Order

From the analysis, the correct order for the size is: \(\mathrm{Fe}^{3+} < \mathrm{Fe}^{2+} < \mathrm{Fe}\). This is option (d).

Key Concepts

Electron Configuration

Each atom and ion has a specific arrangement of electrons, known as its electron configuration. Understanding electron configuration helps explain why ions and atoms have different sizes. For Iron (Fe), its neutral form boasts a configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s². This configuration contains 26 electrons overall.

• When forming Fe²⁺, two electrons are removed, typically from the 4s orbital, so the configuration becomes 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶.
• Further, forming Fe³⁺ involves the loss of one more electron from the 3d orbital, leading to the configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵.

Removing electrons reduces electron-electron repulsion and alters the effective nuclear charge experienced by the remaining electrons, leading to changes in ionic sizes.

Effective Nuclear Charge

The concept of effective nuclear charge ( Z _eff) describes how the nucleus's positive charge affects an atom's or ion's electrons. In essence, Z _eff is the net positive charge felt by the electrons, accounting for both the actual nuclear charge and the repulsive effects of other electrons.
When an iron atom forms ions, it loses electrons which impacts the Z _eff. As iron loses electrons:

• From Fe to Fe²⁺, as two electrons are removed, the effective nuclear charge increases since there are fewer electrons to repel each other.
• The progression from Fe²⁺ to Fe³⁺ results in an even stronger Z _eff because the nuclear charge now acts on fewer spare electrons.

With fewer electrons, the effective nuclear charge draws the remaining electrons closer. This process makes ions like Fe³⁺ considerably smaller than both Fe²⁺ and the neutral Fe atom.

Atomic Radius

Atomic radius is a measure of the size of an atom. It is generally defined as the distance from the center of the nucleus to the outermost electrons. The atomic radius varies depending on several factors, including electron configuration and effective nuclear charge.
A neutral iron atom's size is largely due to its number of electrons balancing the pull from the nucleus. When iron loses electrons, as it does when forming Fe²⁺ and Fe³⁺:

• The atomic radius shrinks, as the loss of electrons increases the effective nuclear pull per remaining electron.
• With each electron removed, there is less repulsion among the remaining electrons, allowing the nucleus to pull them in closer.

Thus, Fe³⁺, having lost three electrons, exhibits the smallest atomic radius compared to Fe and Fe²⁺. This sequence of size decrease is a clear demonstration of how atomic radius is affected by electron removal and effective nuclear charge.