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

Step 1: Understand Ionic Radius

Ionic radius refers to the size of an ion. Ions with more electrons generally have larger radii due to increased electron-electron repulsion, while cations with fewer electrons are smaller.

Step 2: Recognize Ion Trends

The trend for ionic radii across the periodic table is that as you add electrons to an ion (as in forming anions from atoms), the ion becomes larger. So, generally, anions with more negative charge will have larger radii.

Step 3: Compare Ionic Sizes Based on Charge

The ions are \(\text{P}^{3-}\), \(\text{S}^{2-}\), \(\text{I}^{-}\), and \(\text{H}^{-}\). \(\text{P}^{3-}\) has the most added electrons and therefore is the largest, followed by \(\text{S}^{2-}\), then \(\text{I}^{-}\). \(\text{H}^{-}\) is typically very small compared to others.

Step 4: Analyze Options for Order

Using the ionic radius understanding, \(\text{H}^{-}\) should be the smallest and \(\text{P}^{3-}\) the largest of the set. Arranging in order of increasing radius gives: \(\text{H}^{-} < ext{S}^{2-} < ext{P}^{3-} < ext{I}^{-}\).

Key Concepts

Periodic Table Trends

Understanding ionic radii and their trends on the periodic table is crucial for arranging ions by size. Generally, as you move down a group on the periodic table, ionic radii increase. This is because new electron shells are added as you move from one period to the next, making the ions larger. Meanwhile, as you move across a period from left to right, the trend is for ionic radii to decrease. This shrinking effect is due to the increasing positive charge of the nucleus, which pulls electrons closer even if a new shell isn’t added.

However, when an atom gains electrons to become an anion, its size increases. This is due to additional electrons increasing electron-electron repulsion. In comparison, losing electrons to form cations results in smaller ions, since there are fewer electron-electron repulsions and less electron shielding occurs.

To put is simply:

• Moving down a group increases radius
• Forming anions increases size compared to neutral atoms
• Moving across a period rightwards generally decreases the radius

Anions and Cations

Ions can be broadly categorized into two groups: anions and cations. Anions are negatively charged ions, formed when atoms gain electrons. Cations are positively charged ions, formed when atoms lose electrons.

When atoms become anions, the gain of electrons increases electron-electron repulsion, causing the ion to expand. Anions are typically larger than their parent atoms. The more electrons gained, the larger the anion due to increased repulsion among electrons in the same space.

Conversely, when atoms form cations, they lose electrons. This loss reduces electron-electron repulsion and the electron shielding effect from outer electrons, so the cation becomes smaller than its parent atom. An interesting detail is that ions of the same element with higher charges are smaller, as they have more protons pulling on fewer electrons.

Key points to remember:

• Anions (negative) are larger than their neutral atoms due to extra electrons
• Cations (positive) are smaller than their neutral atoms due to electron loss
• More electrons in an anion means a larger ionic radius

Electron-electron Repulsion

Electron-electron repulsion is a crucial concept when discussing the size of ions and their trend behaviors. When electrons are added to an atom or ion, they take up nearby spaces, leading to repulsions among electrons in proximity to each other.

These repulsions cause the ion to swell, as electrons naturally repel each other due to their like charges. This swelling effect is why, in general, anions (which have more electrons than their parent atoms) boast larger ionic radii. In contrast, cations, having fewer electrons, experience less repulsion and are smaller.

Moreover, electron-electron repulsion also affects the degree of the radius increase or decrease as you add or remove electrons to ions of elements within similar groups or periods of the periodic table.

In summary:

• Electron-electron repulsion causes ions to expand when they gain electrons
• More electrons in the same space heighten repulsions, causing larger radius in anions
• Removing electrons diminishes repulsion, leading to smaller ionic size in cations