Problem 57 - A Complete Resource Book in Chemistry for JEE Main

Question

Arrange \(\mathrm{P}^{3-}, \mathrm{S}^{2-}, \mathrm{H}^{-}, \mathrm{I}^{-}\)in the order of increasing ionic radii (a) \(\mathrm{P}^{3-}, \mathrm{S}^{2-}, \mathrm{I}-, \mathrm{H}^{-}\) (b) \(\mathrm{S}^{2-}, \mathrm{P}^{3-}, \mathrm{H}^{-}, \mathrm{I}^{-}\) (c) \(\mathrm{S}^{2-}, \mathrm{H}^{-}, \mathrm{P}^{3-} \mathrm{I}^{-}\) (d) \(\mathrm{H}^{-}, \mathrm{S}^{2-}, \mathrm{P}^{3-}, \mathrm{I}^{-}\)

Step-by-Step Solution

Answer

The correct order is (d): \( \text{H}^{-}, \text{S}^{2-}, \text{P}^{3-}, \text{I}^{-} \).

Step 1: Understanding Ionic Radii

Ionic radii refer to the size of an ion, which is determined by the number of electrons and the nuclear charge. When an atom gains electrons and becomes a negative ion, its ionic radius increases due to electron-electron repulsion.

Step 2: Analyze the Isolated Ions

The ions provided are \( \text{P}^{3-}, \text{S}^{2-}, \text{H}^{-}, \text{I}^{-} \). These ions vary in their charge and atomic number, which will affect the ionic radii. Generally, within the same group, the ionic radius increases with an increase in atomic number.

Step 3: Comparison by Group and Period

\( \text{P}^{3-} \) and \( \text{S}^{2-} \) are in the same period. \( \text{I}^{-} \) is in the same group as \( \text{Cl}^{-} \), which is much larger due to its lower effective nuclear charge compared to \( \text{Cl}^{-} \). \( \text{H}^{-} \) is an outlier due to its single electron.

Step 4: Order by Ionic Radii Size

Ionic radii increase with added electrons and reduced nuclear pull. \( \text{P}^{3-} \) is larger than \( \text{S}^{2-} \) due to more electrons being added. \( \text{I}^{-} \) is larger than both because it is further down the group, resulting in a larger radius by default. \( \text{H}^{-} \) is typically smaller due to one electron and a high effective nuclear charge. Thus, the order is \( \text{H}^{-}, \text{S}^{2-}, \text{P}^{3-}, \text{I}^{-} \).

Step 5: Conclusion and Answer

Based on the ionic radius analysis, arrange in increasing order: \( \text{H}^{-}, \text{S}^{2-}, \text{P}^{3-}, \text{I}^{-} \). This matches option (d).

Key Concepts

Effective Nuclear Charge

The effective nuclear charge, often symbolized as \( Z_{eff} \), is a key concept that explains how strongly electrons are held by the nucleus of an atom. This concept is crucial for understanding ionic radii. Although atoms have a full nuclear charge, or \( Z \), the actual pull felt by an electron is less due to the shielding effect of other electrons, especially those in inner shells.
- In a multi-electron atom, electrons between the nucleus and the outer electrons repel each other.- This electron-electron repulsion reduces the overall nuclear charge experienced by outer electrons.- Consequently, the effective nuclear charge is less than the actual nuclear charge.
Calculating \( Z_{eff} \) helps in predicting the size of ions formed by an atom. A lower effective nuclear charge usually means electrons are more spread out, leading to a larger ionic radius, whereas a higher \( Z_{eff} \) means a tighter hold and a smaller radius.

Electron-Electron Repulsion

Electron-electron repulsion plays a significant role in determining the ionic radii of ions. When extra electrons are added to an atom, these negatively charged particles repel each other. This repulsion increases the size of the ion compared to its neutral atom form.
- More added electrons result in greater repulsive forces between electrons in an atom. - This repulsion tends to push electrons further away from each other, increasing the distance across the ion.
A classic example is anions, or negatively charged ions, which have gained electrons. In such cases, electron-electron repulsion is significant enough to expand the electronic cloud, leading to an increase in the ionic radius.

Periodic Trends

Periodic trends are consistent patterns observed in the periodic table, essential for predicting the behavior of elements, including ionic radii. Within a group (vertical column), ionic radii typically increase as you move down because each element has an additional electron shell compared to the element above it.
- Moving down a group, atomic number increases, adding more electron shells and increasing size. - Across a period (horizontal row), the addition of protons generally increases effective nuclear charge, drawing electrons closer and often reducing atomic size.
However, upon becoming ions, these trends might slightly differ due to changes in electronegativity and electron configuration. Still, these trends hold a general predictive power for estimating ionic sizes across the table.

Ionic Charges

Ionic charges have a direct influence on ionic size. Anions, negatively charged ions, are formed when an atom gains one or more electrons. This electron gain can drastically change the size of the ion due to increased electron-electron repulsion and alteration in effective nuclear charge.
- Anions like \( ext{P}^{3-} \), \( ext{S}^{2-} \), \( ext{H}^{-} \), and \( ext{I}^{-} \) are larger than their parent atoms.- More negative charge (larger number of added electrons) usually means a larger ionic radius.
On the other hand, cations (positively charged ions) typically become smaller than their neutral atoms because losing electrons reduces electron-electron repulsion and often increases \( Z_{eff} \), pulling the remaining electrons closer to the nucleus.