Problem 164 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

Set (a) is isoelectronic with all ions having 18 electrons.

Step 1: Understanding Isoelectronic Species

Isoelectronic species are atoms and ions that have the same number of electrons. To determine which set of ions is isoelectronic, we need to find the electron configuration of each ion.

Step 2: Determine Electron Configuration for Set (a)

The ions in set (a) are \(\mathrm{K}^+\), \(\mathrm{Ca}^{2+}\), \(\mathrm{Sc}^{3+}\), and \(\mathrm{Cl}^-\). Calculate their electron configurations:- \(\mathrm{K}\) is 19 electrons, so \(\mathrm{K}^+\) is 18 electrons.- \(\mathrm{Ca}\) is 20 electrons, so \(\mathrm{Ca}^{2+}\) is 18 electrons.- \(\mathrm{Sc}\) is 21 electrons, so \(\mathrm{Sc}^{3+}\) is 18 electrons.- \(\mathrm{Cl}\) is 17 electrons, so \(\mathrm{Cl}^-\) is 18 electrons.

Step 3: Verify Electron Configuration for Set (b)

The ions in set (b) are \(\mathrm{Na}^+\), \(\mathrm{Ca}^{2+}\), \(\mathrm{Sc}^{3+}\), and \(\mathrm{F}^-\):- \(\mathrm{Na}\) is 11 electrons, so \(\mathrm{Na}^+\) is 10 electrons.- \(\mathrm{Ca}^{2+}\) (as calculated in Step 2) has 18 electrons.- \(\mathrm{Sc}^{3+}\) has 18 electrons (as calculated in Step 2).- \(\mathrm{F}\) is 9 electrons, so \(\mathrm{F}^-\) is 10 electrons.

Step 4: Check Electron Configuration for Set (c)

The ions in set (c) are \(\mathrm{K}^+\), \(\mathrm{Cl}^-\), \(\mathrm{Mg}^{2+}\), and \(\mathrm{Sc}^{3+}\):- \(\mathrm{K}^+\) and \(\mathrm{Cl}^-\) both have 18 electrons (as calculated in Step 2).- \(\mathrm{Mg}\) is 12 electrons, so \(\mathrm{Mg}^{2+}\) is 10 electrons.- \(\mathrm{Sc}^{3+}\) has 18 electrons (as calculated in Step 2).

Step 5: Examine Electron Configuration for Set (d)

The ions in set (d) are \(\mathrm{Na}^+\), \(\mathrm{Mg}^{2+}\), \(\mathrm{Al}^{3+}\), and \(\mathrm{Cl}^-\):- \(\mathrm{Na}^+\) and \(\mathrm{Mg}^{2+}\) have 10 electrons (as calculated in previous steps).- \(\mathrm{Al}\) is 13 electrons, so \(\mathrm{Al}^{3+}\) is 10 electrons.- \(\mathrm{Cl}^-\) has 18 electrons (as calculated in Step 2).

Step 6: Identify the Isoelectronic Set

Based on the calculations: - Set (a): All ions have 18 electrons. - Set (b): Mixed electron counts (10, 10, 18, 18). - Set (c): Mixed electron counts, but two have 18 (18, 18, 10, 18). - Set (d): Mixed electron counts, but three have 10 (10, 10, 10, 18). Since all ions in set (a) have the same electron count, they are isoelectronic.

Key Concepts

Electron Configuration

Electron configuration is a systematic way of describing the distribution of electrons in an atom's electron shells. Electrons fill orbitals in a specific order following the Aufbau principle, which generally states: fill lower energy levels first before moving to higher ones. The electron configuration of an atom can be represented by listing its occupied electron orbitals.
For example, let's consider a neutral potassium atom (K), which has 19 electrons. Its electron configuration is written as: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1\]Electrons are added to subshells according to the specified order until all electrons are placed.
When forming ions, atoms gain or lose electrons to achieve a stable electron arrangement, often aiming for a noble gas configuration. In this process, electron configurations help determine how many electrons must be added or removed.

Ionic Species

Ionic species refer to atoms or molecules that have gained or lost electrons, leading to a net positive or negative charge. This charge imbalance occurs because the number of protons in an atom remains constant while electrons are added or removed to form ions.
- Cations are positively charged ions and occur when an atom loses electrons. For example, when potassium (K) loses one electron, it forms a K^+ ion. - Anions are negatively charged ions formed by gaining electrons. For instance, chlorine (Cl) becomes Cl^- when it gains an electron.
Ionic species are crucial in chemistry as their interactions form ionic bonds, resulting in ionic compounds with unique properties. Identifying ionic species helps in knowing the nature of the compounds they form.

Chemical Ions

Chemical ions play a fundamental role in the formation of substances and their interactions. Ions are simply atoms or molecules that possess a net electrical charge due to the loss or gain of one or more electrons. This charged state drastically alters the chemical behavior of an atom.

• The type and magnitude of an ion's charge determine its chemical reactivity and how it combines with other ions to form compounds.
• For instance, the ion Na^+ (sodium) is common in table salt, where it pairs with the chloride ion Cl^- to form NaCl.

It's important to recognize how ions interact and impact various chemical phenomena, from the properties of acids and bases to the electrical conductivity of solutions.

Atomic Number Determination

The atomic number of an element is vital as it defines the element's identity in the periodic table. It corresponds to the number of protons in an atom's nucleus, which remains unchanged regardless of the ionic state.
For example, potassium (K) has an atomic number of 19, indicating it possesses 19 protons. Even if potassium forms a K^+ ion, losing one electron, its atomic number stays the same since protons are unaffected.

• The atomic number serves as a unique identifier for each element.
• It helps determine the position of an element in the periodic table and its chemical properties.

Understanding atomic numbers is critical for predicting elemental behavior and recognizing how elements and ions interact in chemical reactions.