Problem 147 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one the following sets of ions represents the collection of isoelectronic species? (a) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{F}-\) (b) \(\mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{Mg}^{2+}, \mathrm{Sc}^{3+}\) (c) \(\mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Cl}^{-}\) (d) \(\mathrm{Na}^{+}, \mathrm{Mg}^{2+}, \mathrm{Al}^{3+}, \mathrm{Cl}-\)

Step-by-Step Solution

Answer

Set (c) is the isoelectronic set.

Step 1: Definition of Isoelectronic Species

Isoelectronic species are different ions or atoms that have the same number of electrons. This implies that the sum of protons minus the charge for the ions should result in the same total number of electrons for isoelectronic species.

Step 2: Analyze Set (a)

Calculate the number of electrons:- \(\mathrm{Na}^{+}\): Element Na has 11 protons, so \(11 - 1 = 10\) electrons.- \(\mathrm{Ca}^{2+}\): Element Ca has 20 protons, so \(20 - 2 = 18\) electrons.- \(\mathrm{Sc}^{3+}\): Element Sc has 21 protons, so \(21 - 3 = 18\) electrons.- \(\mathrm{F}^{-}\): Element F has 9 protons, so \(9 + 1 = 10\) electrons.The electrons are not the same, so these ions are not isoelectronic.

Step 3: Analyze Set (b)

Calculate the number of electrons:- \(\mathrm{K}^{+}\): Element K has 19 protons, so \(19 - 1 = 18\) electrons.- \(\mathrm{Cl}^{-}\): Element Cl has 17 protons, so \(17 + 1 = 18\) electrons.- \(\mathrm{Mg}^{2+}\): Element Mg has 12 protons, so \(12 - 2 = 10\) electrons.- \(\mathrm{Sc}^{3+}\): Element Sc has 21 protons, so \(21 - 3 = 18\) electrons.The electrons are not the same, so these ions are not isoelectronic.

Step 4: Analyze Set (c)

Calculate the number of electrons:- \(\mathrm{K}^{+}\): Element K has 19 protons, so \(19 - 1 = 18\) electrons.- \(\mathrm{Ca}^{2+}\): Element Ca has 20 protons, so \(20 - 2 = 18\) electrons.- \(\mathrm{Sc}^{3+}\): Element Sc has 21 protons, so \(21 - 3 = 18\) electrons.- \(\mathrm{Cl}^{-}\): Element Cl has 17 protons, so \(17 + 1 = 18\) electrons.All ions have 18 electrons. Therefore, these ions are isoelectronic.

Step 5: Confirm Isoelectronic Set

By confirming that each ion in Set (c) has 18 electrons, we identify it as the only isoelectronic set. Verify that no other sets have been identified as isoelectronic, confirming that Set (c) is the correct choice.

Key Concepts

Electron Configuration

When we talk about electron configuration, we're referring to how electrons are distributed within the orbitals of an atom or ion. Electrons fill available atomic orbitals in a specific order, mainly starting from the lowest energy level. This order is determined by the principles of quantum mechanics and is commonly arranged following the sequence of the periodic table.

The electron configuration plays a crucial role in defining the chemical behavior of an element. For example, the configuration helps determine how atoms interact with each other and form bonds.

• The number of electrons equal to protons in a neutral atom fills the orbitals according to the Aufbau principle.
• For ions, electrons are added or removed from the outermost shell, according to the charge.

Understanding electron configurations is essential for predicting the properties of isoelectronic species, which have identical electron configurations despite being different atoms or ions.

Protons and Electrons Calculation

Calculating the number of protons and electrons is fundamental in understanding chemical species. The atomic number, found on the periodic table, tells us the number of protons in an element. For neutral atoms, the number of electrons equals the number of protons.

When dealing with ions, the calculation slightly changes due to the charge of the ion. Here's how you can calculate the number of electrons:

• For positive ions (cations), subtract the ion charge from the atomic number to find the number of electrons.
• For negative ions (anions), add the ion charge to the atomic number.

By performing these calculations for each ion within a set, you can determine if they're isoelectronic, meaning they have the same number of electrons. This is crucial in many areas of chemistry, such as predicting reactions and bonding.

Chemical Ions

Chemical ions are atoms or molecules that have gained or lost one or more electrons, giving them a positive or negative charge. Understanding ions is essential for explaining a wide array of chemical processes, interactions, and reactions.

There are two main types of ions:

• Cations: Positively charged ions that have fewer electrons than protons.
• Anions: Negatively charged ions that have more electrons than protons.

In the context of isoelectronic species, ions that have the same number of electrons exhibit similar chemical behavior, even if they have different numbers of protons and thus represent different elements. This concept helps us categorize ions and predict their atomic arrangement and reactivity in various chemical environments.