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

(d) Fe^{3+} < Fe^{2+} < Fe

Step 1: Understanding Atomic and Ionic Sizes

The size of an atom or ion is determined by the number of protons and electrons and the electron configuration. When an atom loses electrons to form a cation (positive ion), the size generally decreases due to a reduced electron-electron repulsion and increased effective nuclear charge per electron.

Step 2: Analyze Iron Atom  extbf{Fe}

The neutral iron atom (Fe) has an atomic number of 26, which means it has 26 electrons. This gives it a certain size based on the electron cloud spread around the nucleus.

Step 3: Examine  extbf{Fe}^ extbf{2+} Ion

When Fe loses two electrons to form Fe^{2+}, it becomes a cation. It now has 24 electrons, with the loss of electrons reducing the cloud's spread and allowing the nucleus to attract the remaining electrons more strongly, thus decreasing its size compared to the neutral atom.

Step 4: Examine  extbf{Fe}^ extbf{3+} Ion

Fe^{3+} is formed when Fe loses three electrons. It has only 23 electrons, further reducing repulsion among them. The increased positive charge holds the electrons even tighter, making Fe^{3+} the smallest in size.

Step 5: Conclusion on Sizes

Based on the analysis, Fe^{3+} is the smallest due to losing three electrons, followed by Fe^{2+} with two electrons lost, and Fe, being neutral, is the largest. Hence, the correct order of size is Fe^{3+} < Fe^{2+} < Fe.

Key Concepts

Cations

Cations are positively charged ions formed when an atom loses one or more of its electrons. This loss of electrons results in a reduction of the size of the electron cloud around the nucleus. Here are some important points about cations:

• The formation of a cation involves the loss of negatively charged electrons, and this decreases the number of electrons in the atom.
• With fewer electrons, there is reduced electron-electron repulsion, allowing the remaining electrons to be pulled closer to the positively charged nucleus.
• The process of forming cations increases the effective nuclear charge, leading to a smaller atomic or ionic radius than the neutral atom.

When analyzing cations like \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \), it's clear that losing more electrons will generally lead to a smaller ionic size due to the increased attraction between the remaining electrons and the nucleus.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom or ion's atomic orbitals. Understanding electron configuration is key to predicting and explaining the size of atoms and ions:

• Electron configuration affects the atom's size by determining how electrons are distributed over different energy levels and sublevels.
• For a neutral iron atom, \( \mathrm{Fe} \), the electron configuration is \([\mathrm{Ar}]\, 3d^6 4s^2\), reflecting 26 electrons surrounding the nucleus.
• When forming \( \mathrm{Fe}^{2+} \), two electrons are removed, typically from the 4s subshell, resulting in an electron configuration of \([\mathrm{Ar}]\, 3d^6\).
• For \( \mathrm{Fe}^{3+} \), another electron is removed from the 3d subshell, leading to a configuration of \([\mathrm{Ar}]\, 3d^5\).

The electron configuration changes lead to a decrease in electron-electron repulsion and allow for a tighter hold on the remaining electrons, contributing to a decrease in ionic size.

Effective Nuclear Charge

Effective nuclear charge (often abbreviated as \( Z_{\text{eff}} \)) is a concept that helps us understand how much of a positive charge from the nucleus is "felt" by the outer electrons. It's crucial when discussing atomic and ionic sizes:

• \( Z_{\text{eff}} \) can be thought of as the net positive charge experienced by an electron in a multi-electron atom.
• As electrons are removed to form cations, the reduced electron shielding means \( Z_{\text{eff}} \) increases.
• This increase in \( Z_{\text{eff}} \) results in stronger attraction between the nucleus and the remaining electrons, pulling them closer.
• This means smaller atomic or ionic radii for cations compared to their neutral counterparts.

In the case of \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \), the loss of electrons increases \( Z_{\text{eff}} \), making \( \mathrm{Fe}^{3+} \) smaller than \( \mathrm{Fe}^{2+} \) or the neutral \( \mathrm{Fe} \) atom.