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) \(\mathrm{EN}=\frac{\mathrm{IP}}{\mathrm{EA}}\) (c) \(\mathrm{EN}=\frac{\mathrm{IP}+\mathrm{EA}}{2}\) (d) \(\mathrm{EN}=\mathrm{IP}-\mathrm{EA}\)

Short answer

Option (c): \(\mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2}\).

Step-by-step solution

Understanding the Mulliken Electronegativity

Mulliken proposed a way to calculate the electronegativity (EN) of an element using the ionization energy (IP) and electron affinity (EA). His approach considers both the tendency of an atom in a molecule to attract electrons towards itself (EA) and the energy required to remove an electron (IP).

Equation Verification

According to Mulliken's definition of electronegativity, the formula is given by the average of ionization energy and electron affinity: \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \).

Comparison with Given Options

Now compare this formula \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \) to the options provided in the exercise: \(\mathrm{EN} = \mathrm{IP} \times \mathrm{EA}\), \(\mathrm{EN} = \frac{\mathrm{IP}}{\mathrm{EA}}\), \(\mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2}\), and \(\mathrm{EN} = \mathrm{IP} - \mathrm{EA}\).

Correct Choice Identification

The formula \( \mathrm{EN} = \frac{\mathrm{IP} + \mathrm{EA}}{2} \) matches exactly with option (c). Therefore, the correct equation according to Mulliken is option (c).

Key concepts

Ionization Energy

Ionization energy refers to the amount of energy needed to remove an electron from an atom or ion in its gaseous state. It is a fundamental concept in chemistry because it helps predict how an element will behave in a chemical reaction.
Ionization energy can vary depending on the electron and the atom's properties. Here are some important points to remember:

• The first ionization energy is the energy needed to remove one electron, resulting in a cation with a charge of +1.
• As more electrons are removed, the ionization energy tends to increase since the electrons are being removed from an increasingly positive ion.
• Elements on the right side of the periodic table typically have higher ionization energies than those on the left, due to a greater effective nuclear charge holding the electrons tightly.

Understanding ionization energy helps in analyzing how atoms interact and how strongly they hold on to their electrons.

Electron Affinity

Electron affinity measures the energy change that occurs when an electron is added to a neutral atom in the gaseous state. Essentially, it quantifies an atom's tendency to gain an electron. It is a key concept for understanding chemical bonds and reactivity.
Here are a few things to note about electron affinity:

• When an atom gains an electron and releases energy, its electron affinity is positive. This indicates the atom's tendency to accept the electron.
• Generally, nonmetals have higher electron affinities than metals, which aligns with their tendency to gain electrons during chemical reactions.
• Electron affinity values are typically highest in the upper right portion of the periodic table because atoms there have smaller radii and stronger nuclear charge.

By understanding electron affinity, you can better predict how atoms will act in different chemical environments.

Electronegativity Calculation

Electronegativity is the measure of an atom's ability to attract and hold onto electrons within a chemical bond. Mulliken proposed a formula to calculate electronegativity using both ionization energy (IP) and electron affinity (EA).
To compute Mulliken electronegativity, use the following formula:
\[ \text{EN} = \frac{\text{IP} + \text{EA}}{2} \]
This formula indicates that electronegativity is the average of an atom's ionization energy and electron affinity. It implies that both the tendency to lose an electron (IP) and the tendency to gain an electron (EA) contribute equally to how strongly an atom can attract electrons.
Important aspects of the Mulliken electronegativity calculation include:

• Higher ionization energy and electron affinity lead to greater electronegativity, indicating stronger electron attraction.
• This method provides a more nuanced understanding than some other models by involving two factors rather than just one.
• Mulliken electronegativity is best used for comparing elements within the same group or period.

By using Mulliken's approach, you can more accurately estimate an element's electronegativity and predict its behavior in chemical reactions.