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) e^{3+}<e^{2+}<e

Step 1: Understand the Concept

Atomic size depends on the number of electrons and proton-electron interactions. Cations (e^{3+} and e^{2+} ) generally have a smaller size compared to neutral atoms (e ) due to the loss of electrons, which reduces electron-electron repulsion.

Step 2: Compare e and e^{3+}

e is the neutral atom with the original number of electrons. e^{3+} has lost three electrons, increasing effective nuclear charge where protons pull the remaining electrons closer, leading to a smaller atomic radius compared to e .

Step 3: Compare e^{2+} and e^{3+}

e^{2+} is a cation formed by the loss of two electrons, while e^{3+} has lost three. With one more electron removed, e^{3+} has an even higher effective nuclear charge, making it smaller than e^{2+} .

Step 4: Compile the Order Based on Size

Since e^{3+} is smaller than e^{2+} , and e^{2+} is smaller than e , the correct order of increasing size is e^{3+}<e^{2+}<e .

Key Concepts

Cations

When an atom loses one or more electrons, it becomes a cation. Cations are positively charged due to the loss of negatively charged electrons, which results in an overall positive charge. The formation of a cation reduces the atomic size because:

• There is less electron-electron repulsion in the atom.
• The remaining electrons are pulled closer to the nucleus due to increased effective nuclear charge.

This process leads to a smaller radius for cations compared to their neutral counterparts. For example, Fe, when it loses two electrons to form Fe^{2+}, or three electrons to form Fe^{3+}, will have a decreased size due to these effects. Understanding cations is crucial for grasping trends in atomic size and behavior.

Electron Configuration

The electron configuration of an atom refers to the distribution of electrons in its atomic orbitals. This configuration determines many chemical properties and reactions of an element. When an element forms a cation, its electron configuration changes as electrons are removed. For Fe (iron), the neutral atom has an electron configuration of \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2\). Upon losing two electrons to form Fe^{2+}, the electron configuration becomes \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^6\). If it loses three electrons to become Fe^{3+}, it further loses another electron, leading to \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5\). Notice how the loss of electrons alters the electron configuration and how this affects the atom's properties, such as size.

Effective Nuclear Charge

Effective nuclear charge is the net positive charge experienced by electrons in an atom. It accounts for both the actual nuclear charge (the total charge of the protons) and the actual electron shielding effect (electrons repelling each other). When an atom becomes a cation, by losing electrons, the effective nuclear charge experienced by the remaining electrons increases. This is because:

• The number of protons remains the same.
• There are fewer electron-electron repulsions as electrons are lost.

Thus, the remaining electrons are pulled more strongly towards the nucleus, reducing the atomic radius. In the case of Fe^{3+}, which has lost three electrons, the effective nuclear charge is much higher than in Fe or Fe^{2+}. This results in a smaller atomic size for Fe^{3+} than for Fe^{2+} or the neutral Fe atom. Understanding effective nuclear charge is crucial for predicting and explaining changes in atomic size and reactivity.