Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

When two oppositely charged ions approach each other, the ion smaller in size attracts outermost electrons of the other ion and repels its nuclear charge. The electron cloud of anion no longer remains symmetrical but is elongated towards the cation. Due to that, sharing of electrons occur between the two ions to some extent and the bond shows some covalent character. The value of dipole moment can be used for determining the amount of ionic character in a bond. Thus, percentage ionic character = \(\frac{\text { Experimental value of dipole moment }}{\text { Theoretical value of dipole moment }} \times 100\) The dipole moment of \(\mathrm{LiH}\) is \(1.964 \times 10^{-29} \mathrm{C} . \mathrm{m}\). and the interatomic distance between \(\mathrm{Li}\) and \(\mathrm{H}\) in this molecule is \(1.596 \AA\). What is the \% ionic character in \(\mathrm{LiH}\) ? (a) \(76.8 \%\) (b) \(60.25 \%\) (c) \(15.5 \%\) (d) \(26.2 \%\)

Step-by-Step Solution

Answer

The percentage ionic character of LiH is approximately 76.8%, which matches option (a).

Step 1: Understand the Formula

The problem requires us to find the percentage ionic character of a bond using the dipole moment. The given formula is: \[ \text{Percentage Ionic Character} = \frac{\text{Experimental value of dipole moment}}{\text{Theoretical value of dipole moment}} \times 100 \] We must use the provided experimental value and calculate the theoretical dipole moment.

Step 2: Calculate Theoretical Dipole Moment

The theoretical dipole moment is calculated by considering one electron (charge = \(1.6 \times 10^{-19} \text{C}\)) transferred over the interatomic distance. Given the interatomic distance in lithium hydride (\(\mathrm{LiH}\)) is \(1.596 \times 10^{-10} \text{m}\), the theoretical dipole moment is: \[ \mu_{\text{theoretical}} = q \times d = (1.6 \times 10^{-19} \text{C}) \times (1.596 \times 10^{-10} \text{m}) = 2.5536 \times 10^{-29} \text{C.m} \]

Step 3: Calculate Percentage Ionic Character

Now that we have the theoretical dipole moment, use the given experimental dipole moment to calculate the percentage ionic character: \[ \text{Percentage Ionic Character} = \frac{1.964 \times 10^{-29} \text{C.m}}{2.5536 \times 10^{-29} \text{C.m}} \times 100 = 76.9\% \]

Step 4: Choose the Closest Answer

After calculating the percentage ionic character, we found it to be approximately \(76.9\%\). Thus, the closest answer choice provided is \(76.8\%\), option (a).

Key Concepts

Dipole Moment

The concept of the dipole moment is central to understanding molecular polarity. A dipole moment arises in a molecule when there is a separation of positive and negative charges. In simple terms, it's like one end of the molecule is slightly negative, and the other end is slightly positive. This results in a measurable 'moment', a vector quantity, which provides insight into the molecular polarity.
A dipole moment is calculated as the product of charge (\( q \) in coulombs) and distance (\( d \) in meters) between the charges. Thus, the formula is:\[\mu = q \times d\]When the dipole moment is high, it often indicates that the molecule has a significant polarity, which means it can interact strongly with other polar molecules. This is an important property in predicting how molecules will behave in different environments:

• Strong dipole moments can result in higher boiling points.
• Molecules with dipole moments can dissolve better in polar solvents.
• Important in dictating the strength of intermolecular forces in a compound.

Ions

Ions are atoms or molecules that have gained or lost one or more electrons, resulting in a net electrical charge. When an atom loses an electron, it becomes positively charged, and when it gains an electron, it becomes negatively charged.
This concept is essential when examining chemical bonding:

• Cations: Positively charged ions. Formed when an atom loses electrons, usually metals.
• Anions: Negatively charged ions. Formed when an atom gains electrons, typically nonmetals.

In ionic compounds, ions are held together by electrostatic forces. This interaction results in the formation of ionic bonds. The size and charge of the ions greatly influence the bond's properties and can also affect the polar characteristics of the resulting molecule:

• Larger ions tend to form less polar bonds due to the greater distance between charges.
• Higher charges on ions often lead to stronger ionic bonds.

Percentage Ionic Character

The percentage ionic character provides a means to understand how ionic or covalent a bond is within a molecule. It helps to measure the degree to which electrons are fully transferred between atoms in a bond, as opposed to being shared.
To find the percentage ionic character, we can use the dipole moment—both experimental and theoretical values:

• Experimental dipole moment: Measured using actual experimental methods.
• Theoretical dipole moment: Calculated assuming complete charge transfer, as if one unit of charge was fully transferred over the bond length.

The formula used is:\[\text{Percentage Ionic Character} = \frac{\text{Experimental Dipole Moment}}{\text{Theoretical Dipole Moment}} \times 100\]This formula helps in gauging the actual nature of chemical bonds. A higher percentage means the bond behaves more like an ionic bond, while a lower percentage shows more covalent character. Understanding this helps predict properties like solubility, melting point, and electrical conductivity—attributes often crucial in chemical applications such as drug design and materials science.