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

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

Step 1: Understand Mulliken's definition of electronegativity

Mulliken's definition of electronegativity refers to the average of the ionization energy (IP) and electron affinity (EA) of an element. It provides a quantitative measure of the tendency of an atom to attract a bonding pair of electrons.

Step 2: Analyze each given equation

Let's look at each answer option: (a) suggests multiplying IP and EA, (b) suggests dividing IP by EA, (c) suggests averaging IP and EA, and (d) suggests subtracting EA from IP. We need to check which of these reflects Mulliken's definition.

Step 3: Verify correct equation with Mulliken's definition

According to Mulliken, the electronegativity (EN) is given by the average of the ionization energy and the electron affinity. Therefore, the correct equation is \[\mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2}\] which corresponds to option (c).

Step 4: Finalize and confirm correct option

Option (c), \(\mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2}\), correctly represents Mulliken's definition of electronegativity. Thus, the proper equation is identified.

Key Concepts

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons within a chemical bond. Mulliken's approach takes a different path by calculating the average of two properties: ionization energy and electron affinity. By doing so, Mulliken's electronegativity provides a more quantifiable and comprehensive measure.

• Ionization energy represents how much energy it takes to remove an electron from an atom.
• Electron affinity indicates how much energy is released when an electron is added to a neutral atom.

For Mulliken's model, electronegativity is derived from these two energies, fitting naturally into the equation \[\text{EN} = \frac{\text{IP} + \text{EA}}{2}\]This formula captures the balance between the reluctance to lose an electron and the eagerness to gain one. It makes electronegativity a handy tool in predicting how atoms interact in compounds.

Ionization Energy

Ionization energy (IP) is crucial in understanding how elements behave in reactions. It measures the energy needed to remove the outermost electron from a neutral atom.

• High ionization energy indicates an atom holds onto its electrons tightly. Such elements, like noble gases, have full outer electron shells, making them stable and non-reactive.
• Low ionization energy suggests that an atom gives up its electrons more readily, often found in metals like sodium and potassium.

Factors affecting ionization energy include the charge on the nucleus, the energy levels of electrons, and the shielding effect. Generally, moving across a period on the periodic table, ionization energy increases, while moving down a group, it decreases.

Electron Affinity

Electron affinity (EA) defines the change in energy when an electron is added to a neutral atom, forming a negative ion.

• A positive electron affinity value means the process is exothermic; an atom releases energy when it gains an electron.
• If the value is negative or low, this indicates less tendency to gain electrons.

In the periodic table, electron affinities become more negative from left to right across a period. This trend reflects how nonmetals like halogens readily accept electrons to achieve a full valence shell, contrasting with metals that prefer to lose electrons. Together with ionization energy, electron affinity provides insight into an element's electronegativity, helping predict chemical behavior.