Problem 40 - A Complete Resource Book in Chemistry for JEE Main

Question

Let electronegativity, ionization energy and electronicaffinity be represented as EN, IP and EA respectively. Which one of the following equation is correct according to Mulliken? (a) \(\mathrm{EN}=\mathrm{IP} \times \mathrm{EA}\) (b) \(\mathrm{EN}=\mathrm{IP} / \mathrm{EA}\) (c) \(\mathrm{EN}=\frac{\mathrm{IP}+\mathrm{EA}}{2}\) (d) \(\mathrm{EN}=\mathrm{IP}-\mathrm{EA}\)

Step-by-Step Solution

Answer

The correct equation according to Mulliken is option (c): \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \).

Step 1: Understanding Mulliken Electronegativity

Mulliken's approach to electronegativity suggests that the electronegativity (EN) of an atom can be thought of as the average of two other properties: ionization energy (IP) and electron affinity (EA). This gives a measure of how much an atom wants to attract electrons.

Step 2: Identify Potential Formula

Based on Mulliken's concept, the electronegativity is given by the average of ionization energy and electron affinity. This can be represented by the equation: \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \).

Step 3: Match with Given Options

Let's compare the Mulliken equation \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \) with the provided options. The correct option should match this equation.

Step 4: Select the Correct Option

Comparing the equation to the options provided: - (a) \( \mathrm{EN} = \mathrm{IP} \times \mathrm{EA} \) does not match.- (b) \( \mathrm{EN} = \mathrm{IP} / \mathrm{EA} \) does not match.- (c) \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \) matches exactly.- (d) \( \mathrm{EN} = \mathrm{IP} - \mathrm{EA} \) does not match.Therefore, the correct option is (c).

Key Concepts

Electronegativity

Electronegativity is a fundamental concept in chemistry. It describes how strongly an atom can attract and hold onto electrons when it is part of a compound. In general, elements with high electronegativity are good at attracting electrons.

Electronegativity varies across the periodic table. Meaningful patterns include:

• It increases across a period from left to right.
• It decreases down a group from top to bottom.

Mulliken's method involves considering both ionization energy and electron affinity. According to Mulliken, electronegativity can be estimated by averaging these two properties because both reflect an atom's tendency to attract electrons.

Understanding electronegativity is crucial for predicting molecule behavior, bonding types, and molecular interactions.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. It indicates how tightly an atom holds its electrons.

Key characteristics of ionization energy include:

• High ionization energy means an atom holds onto its electrons strongly, making it harder to remove them.
• It tends to increase across a period as the nuclear charge increases, drawing electrons closer.
• It generally decreases down a group where electrons are further from the nucleus due to additional electron shells.

Ionization energy is integral in determining reactivity, especially for metals and nonmetals. It influences how easily an atom can form positive ions, which is vital in Mulliken's electronegativity equation, reflecting the atom's reluctance to give away electrons.

Electron Affinity

Electron affinity measures the amount of energy released when an electron is added to an atom. It provides insight into how much an atom desires more electrons.

Notable aspects include:

• Atoms with high electron affinity gain electrons more readily, releasing more energy in the process.
• Like ionization energy, electron affinity generally increases across periods and varies throughout groups.
• Halogens, with their nearly full outer shells, have high electron affinities, eager to gain additional electrons for a stable configuration.

In Mulliken's calculation, electron affinity complements ionization energy by showing how keen an atom is to attract and hold additional electrons. This tendency is crucial for understanding the atom's behavior. By combining these energies, Mulliken effectively estimates electronegativity, offering a clearer picture of atomic interactions.