Problem 159 - A Complete Resource Book in Chemistry for JEE Main

Question

The increasing order of the ionic radii of the given isoelectronic species is: (a) \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{S}^{2-}\) (b) \(\mathrm{S}^{2-}, \mathrm{Cl}^{2}, \mathrm{Ca}^{2+}, \mathrm{K}^{+}\) (c) \(\mathrm{Cl}^{-}, \mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{S}^{2-}\) (d) \(\mathrm{K}^{+}, \mathrm{S}^{2}, \mathrm{Ca}^{2+}, \mathrm{Cl}^{-}\)

Step-by-Step Solution

Answer

The correct order is (a) \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{S}^{2-}\).

Step 1: Identify the Isoelectronic Species

First, recognize that all the given species are isoelectronic, meaning they have the same number of electrons. These species are: \(\text{Ca}^{2+}, \text{K}^+, \text{Cl}^-, \text{S}^{2-}\), each having 18 electrons.

Step 2: Determine the Nuclear Charge

Next, find the nuclear charge (number of protons) for each species: \(\text{Ca}^{2+}\) has 20 protons, \(\text{K}^+\) has 19 protons, \(\text{Cl}^-\) has 17 protons, \(\text{S}^{2-}\) has 16 protons.

Step 3: Understand the Trend in Ionic Radii

Understand that for isoelectronic species, ionic radius decreases as the nuclear charge increases because the electrons are pulled closer to the nucleus. Thus, the ion with the highest nuclear charge will have the smallest radius.

Step 4: Arrange the Ions by Increasing Radii

Using the nuclear charges, arrange the ions in increasing order of ionic radii: \(\text{Ca}^{2+} \) (smallest radius) < \(\text{K}^+\) < \(\text{Cl}^-\) < \(\text{S}^{2-}\) (largest radius).

Step 5: Match with Given Options

Compare the order found in step 4 with the given options. The correct order is found in option (a): \(\text{Ca}^{2+}\), \(\text{K}^+\), \(\text{Cl}^-\), \(\text{S}^{2-}\).

Key Concepts

Isoelectronic Species

When we talk about isoelectronic species, we refer to different atoms or ions that possess the same number of electrons. This means they all have the same electronic configuration, but often differ in their nuclear charges because they have a different number of protons.

• Consider the ions: \( \text{Ca}^{2+}, \text{K}^+, \text{Cl}^-, \text{S}^{2-} \).
• Each of these ions has exactly 18 electrons, making them isoelectronic.

Despite the same number of electrons, these species vary because they come from different elements on the periodic table. This difference affects properties like ionic radius, because the number of protons in each nucleus pulls on the electrons differently.
Understanding isoelectronic species is crucial as it sets the foundation for comparing different ionic properties, such as ionic radii and reactivity, in a more structured way.

Nuclear Charge

Nuclear charge refers to the total charge within an atomic nucleus, dictated by the number of protons present. Given that like charges repel and opposite charges attract, nuclear charge greatly influences the size and properties of ions.

• For \( \text{Ca}^{2+} \), it has a nuclear charge of 20+, meaning 20 protons are in the nucleus.
• \( \text{K}^+ \) has 19 protons.
• \( \text{Cl}^- \) has 17 protons.
• \( \text{S}^{2-} \) has 16 protons.

The trend that emerges is that the species with the higher nuclear charge will exert a stronger pull on the electrons, pulling them closer.
This concept explains why isoelectronic ions decrease in size as their nuclear charge increases - the electrons are more tightly held by the nucleus.
So, when determining the size among isoelectronic species, always compare their nuclear charges first.

Periodic Trends

Periodic trends refer to general patterns or tendencies in the properties of elements across the periodic table. These trends help predict the behavior of elements and their ions based on their positions on the table.

• One important trend is that atomic and ionic sizes decrease across a period (left to right) due to an increasing nuclear charge which pulls electrons closer.
• Conversely, within a group (moving top to bottom), atoms and ions become larger as additional electron shells are added.

For isoelectronic species, the trend in ionic radii is primarily driven by nuclear charge rather than typical periodic trends of atomic size. This is because, as the nuclear charge increases while electron count stays the same, the same number of electrons are drawn closer, resulting in a smaller ionic radius.
Therefore, among isoelectronic ions, despite their differing positions on the periodic table, it is essential to focus on nuclear charge to predict their relative sizes.