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 \(\mathrm{LiH}\) is \(76.8\%\), which is option (a).

Step 1: Understand the Formula

The problem provides a formula to calculate the percentage of ionic character: \( \text{% Ionic Character} = \frac{\text{Experimental value of dipole moment}}{\text{Theoretical value of dipole moment}} \times 100 \). To use this formula, we need both the experimental and theoretical values of the dipole moment.

Step 2: Determine Experimental Dipole Moment

The experimental dipole moment is given as \(1.964 \times 10^{-29} \mathrm{C} \cdot \mathrm{m}\). This is the value we will use for the numerator in our formula to calculate the percentage of ionic character.

Step 3: Calculate Theoretical Dipole Moment

The theoretical dipole moment, in case of a complete ionic bond, can be calculated by using the product of the elementary charge (\( e = 1.602 \times 10^{-19} \text{C} \)) and the interatomic distance. The interatomic distance between \(\text{Li}\) and \(\text{H}\) is given as \(1.596 \AA = 1.596 \times 10^{-10} \text{m}\). Therefore, the theoretical dipole moment = \(e \times \text{distance} = 1.602 \times 10^{-19} \text{C} \times 1.596 \times 10^{-10} \text{m}\).

Step 4: Calculate Theoretical Dipole Moment Value

Perform the multiplication: \[ \text{Theoretical Dipole Moment} = 1.602 \times 10^{-19} \times 1.596 \times 10^{-10} = 2.556792 \times 10^{-29} \text{C} \cdot \text{m} \]

Step 5: Calculate Percentage Ionic Character

Insert the experimental and theoretical dipole moment values into the formula: \[ \text{Percentage Ionic Character} = \frac{1.964 \times 10^{-29}}{2.556792 \times 10^{-29}} \times 100 \] Perform the division and multiplication to obtain the percentage value.

Step 6: Final Calculation

Calculating, we get:\[ \text{Percentage Ionic Character} = \frac{1.964}{2.556792} \times 100 = 76.8 \% \] So, the ionic character in \(\text{LiH}\) is \(76.8\%\).

Key Concepts

Dipole Moment

The dipole moment is a measure of the polarity of a chemical bond within a molecule. It occurs when there's a separation of electric charge, leading to a molecule having a positive and negative end. This separation of charge results in a vector quantity pointing from the negative to the positive charge. The magnitude of a dipole moment is calculated by multiplying the amount of charge by the distance between the charges, typically represented in units of Debye or Coulomb-meters.
Understanding dipole moment is important because it helps us assess how ionic or covalent a bond is. For example, a completely ionic bond would have a higher theoretical dipole moment value compared to a covalent bond where electrons are shared more equally. Real molecules often display dipole moments that indicate a mix of ionic and covalent characteristics, which can be calculated using specific formulas.

Ionic Bonds

Ionic bonds are formed through the electrostatic attraction between oppositely charged ions. This occurs typically between a metal and a non-metal where one atom donates its electrons to another, resulting in positively charged cations and negatively charged anions.
The strength and nature of ionic bonds heavily depend on the size of the ions and their charges. Smaller ions with higher charges will result in stronger ionic bonds due to increased attraction forces. In practical terms, ionic bonds result in the formation of crystalline solid structures, like table salt (NaCl), that demonstrate high melting and boiling points due to the strong attractions between the ions.
Ionic bonds can also influence the dipole moment of a molecule. In scenarios where the ionic character is high, the dipole moment will reflect the strong electrostatic interactions present, hence giving insight into the bond's characteristics.

Covalent Bonds

Covalent bonds involve the sharing of valence electrons between atoms, typically non-metals, resulting in a mutual attraction and the formation of molecules. In contrast to ionic bonds, the shared electrons in covalent bonds mean there is not a complete transfer from one atom to another.
There can be varying degrees of covalent character in a bond depending on how equally the electrons are shared. Perfectly nonpolar covalent bonds occur when both atoms exert equal force on the shared electrons, leading to no permanent dipole moment.
However, most covalent bonds are polar, with one atom pulling more on the electrons than the other, resulting in partial charges. This behavior introduces a dipole moment in the molecule, indicating some ionic character. Understanding the nature of covalent versus ionic bonds within molecules helps predict and explain molecular behavior and properties.

Anion-Cation Interactions

The interactions between anions and cations are central to understanding ionic compounds. These interactions are purely electrostatic, with cations (positive ions) and anions (negative ions) attracting each other to form ionic bonds.
Anion-cation interactions play a crucial role in determining the physical properties of ionic compounds, such as solubility, melting point, and electrical conductivity when in solution.

• Anions, being larger, tend to have their electron clouds distorted by smaller and more positively charged cations, leading to a polarization effect.
• This distortion can cause the electron cloud to stretch towards the cation, introducing a slight covalent character to the ionic bond.

Such interactions are significant in predicting the behavior of complex ionic networks and in understanding how various elements bond to form compounds with unique properties.