Problem 32 - A Complete Resource Book in Chemistry for JEE Main

Question

Ionic radius (in A) of \(\mathrm{As}^{3+}, \mathrm{Sb}^{3+}\) and \(\mathrm{Bi}^{3+}\) follow the order (a) \(\mathrm{As}^{3+}>\mathrm{Sb}^{3+}>\mathrm{Bi}^{3+}\) (b) \(\mathrm{Sb}^{3+}>\mathrm{Bi}^{3+}>\mathrm{As}^{3+}\) (c) \(\mathrm{Bi}^{3+}>\mathrm{As}^{3+}>\mathrm{Sb}^{3+}\) (d) \(\mathrm{Bi}^{3+}>\mathrm{Sb}^{3+}>\mathrm{As}^{3+}\)

Step-by-Step Solution

Answer

(d) \(\mathrm{Bi}^{3+} > \mathrm{Sb}^{3+} > \mathrm{As}^{3+}\).

Step 1: Understanding the Trend

In the periodic table, ionic radius tends to increase as we move down a group. This is because each row down adds a new electron shell, making the ions larger.

Step 2: Identifying the Group

Arsenic (As), Antimony (Sb), and Bismuth (Bi) all belong to Group 15 of the periodic table. They are in the same group but different periods, with Bi being the lowest and As the highest in the group.

Step 3: Analyzing the Ionic Radii

Since atomic size increases as we move down a group, the ionic radius follows the same trend. Therefore, the size order should mirror their arrangement in the group from top to bottom: \[ ext{As}^{3+} < ext{Sb}^{3+} < ext{Bi}^{3+}.\] This is due to Bismuth having more electron shells than Antimony or Arsenic, resulting in a larger ionic radius.

Step 4: Selecting the Correct Option

Given the ionic radius order of \[ ext{As}^{3+} < ext{Sb}^{3+} < ext{Bi}^{3+},\] we choose the answer that reflects Bismuth having the largest ionic radius, followed by Antimony and then Arsenic. This corresponds to choice (d): \[ ext{Bi}^{3+} > ext{Sb}^{3+} > ext{As}^{3+}.\]

Key Concepts

Periodic Table

The periodic table is a cornerstone of chemistry, providing a systematic arrangement of all known chemical elements. Each element is placed according to its atomic number, which is the number of protons in its nucleus. The table is structured in rows, called periods, and columns, known as groups or families. Each element's position on this table not only reflects its atomic number but also gives insights into recurring chemical properties.

As you move across a period from left to right, elements become less metallic and more nonmetallic in character. Meanwhile, as you move down a group, elements exhibit similar chemical properties. This makes the periodic table an invaluable tool for predicting element behavior and understanding the trends like ionic radius and atomic size.

Group Trends

Group trends refer to the predictable patterns that appear within specific columns, or groups, in the periodic table. As elements in a group share the same number of valence electrons, they often display similar chemical behaviors. Moving down a group, there are notable trends such as the increase in atomic size and ionic radius.

This increase is attributed to the added electron shells as you progress down the group. Hence, atoms lower in the group are generally larger than those at the top. Understanding these trends is crucial when predicting behaviors such as ionic sizes and the chemical reactivity of elements.

Electron Shells

Electron shells are the paths or energy levels that electrons follow around an atom's nucleus. Each shell can hold a limited number of electrons, determined by the formula \(2n^2\), where \(n\) is the shell level. As you move down a group in the periodic table, each element has one more electron shell than the one before it.

This addition of shells plays a pivotal role in increasing the size of the atom as you go down the group. More shells mean a more spread-out electron cloud, leading to a larger atomic radius. Understanding the concept of electron shells is essential for grasping why elements have different sizes and ionic charges.

Atomic Size

Atomic size, or atomic radius, is the distance from an atom's nucleus to its outermost electron shell. This parameter is crucial as it influences the chemical properties of an element. In the periodic table, atomic size increases as you move down a group. This is due to the addition of more electron shells, which increase the distance between the nucleus and the outermost shell.

Conversely, atomic size decreases as you move from left to right across a period, because the increased nuclear charge pulls the electron cloud closer to the nucleus. For Group 15 elements like Arsenic, Antimony, and Bismuth, we see larger atomic sizes when moving from top to bottom within the group.

Group 15 Elements

Group 15 of the periodic table is known as the Nitrogen group or Pnictogens, comprising Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), and Bismuth (Bi). These elements share common properties, such as having five valence electrons, which influences their ability to form bonds.

With increasing atomic number, these elements exhibit higher atomic and ionic sizes due to additional electron shells. For example, - Nitrogen is a gas with small atomic size,
while Bismuth is a dense metal with a larger atomic size.
This progression within the group highlights the effect of increasing electron shells on atomic and ionic radii, as elements become heavier and larger with more complex electron clouds.