Problem 150 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct statements if the following are: (a) The bond angle of hybrid bonds increases as \(\mathrm{sp}^{3}<\) \(\mathrm{sp}^{2}<\mathrm{sp}\) (b) For hydrogen halides, bond length increases as \(\mathrm{HF}<\mathrm{HCl}<\mathrm{HBr}<\mathrm{HI}\) (c) Increasing order of bond energy: Single bond \(\leq\) Double bond \(<\) Triple bond.

Step-by-Step Solution

Answer

All three statements (a, b, and c) are correct based on principles of chemistry.

Step 1: Analyze Bond Angle in Hybridization

In hybrid orbitals, the bond angle is determined by the type of hybridization present. The order of bond angles in hybridization is based on the degree of s-orbital and p-orbital mixing: - In \(\mathrm{sp}\) hybridization, the orbitals are formed by an equal mix of s and p orbitals, resulting in a linear shape with bond angles of 180 degrees.- In \(\mathrm{sp}^{2}\) hybridization, the orbitals form a trigonal planar shape with bond angles of approximately 120 degrees.- In \(\mathrm{sp}^{3}\) hybridization, the orbitals form a tetrahedral shape with bond angles of approximately 109.5 degrees.Thus, the statement that the bond angle increases from \(\mathrm{sp}^{3} < \mathrm{sp}^{2} < \mathrm{sp}\) is correct.

Step 2: Understand Bond Length in Hydrogen Halides

Hydrogen halides are compounds of hydrogen with the halogens (F, Cl, Br, I). As you move down the halogen group, the size of the halogen atoms increases, leading to longer bond lengths.- \(\mathrm{HF}\) has the shortest bond length since fluorine is the smallest halogen.- As you go to \(\mathrm{HCl} < \mathrm{HBr} < \mathrm{HI}\), the bond length increases because chlorine, bromine, and iodine have progressively larger atomic sizes.Therefore, the order \(\mathrm{HF} < \mathrm{HCl} < \mathrm{HBr} < \mathrm{HI}\) is correct.

Step 3: Examine Bond Energy in Multiple Bonds

Bond energy is the energy required to break a bond between two atoms. Typically, as the bond type changes from single to double to triple, the bond becomes stronger, and more energy is required to break it.- A single bond consists of one pair of shared electrons and is usually the weakest.- A double bond is stronger than a single bond with two pairs of shared electrons.- A triple bond, with three pairs of shared electrons, is the strongest.Thus, the increasing order of bond energy is correctly given as Single bond \( \leq \) Double bond \( < \) Triple bond.

Key Concepts

Hybridization and Bond Angles

When discussing hybridization in chemistry, we are talking about the mixing of atomic orbitals to form new hybrid orbitals. These orbitals configure to help molecules form bonds with specified angles. The type of hybridization significantly influences these angles due to the s and p orbital mixing.
In

• sp hybridization, the orbitals are made from one s and one p orbital, forming a linear shape. The bond angle here is 180 degrees.
• sp² hybridization involves one s and two p orbitals, which turn into a trigonal planar shape. This creates bond angles of about 120 degrees.
• sp³ hybridization consists of one s and three p orbitals forming a tetrahedral shape with bond angles around 109.5 degrees.

Hence, the bond angle increases in the order of sp³ < sp² < sp. This progression reflects how the addition of more p orbitals compresses the angle compared to the fewer p orbital configurations.

Bond Lengths in Hydrogen Halides

Hydrogen halides are binary compounds made of hydrogen and a halogen, such as fluorine, chlorine, bromine, and iodine. An important consideration in these molecules is the bond length, which is the distance between the nuclei of the hydrogen and the halogen atoms.
As you move down the periodic table's halogen group:

• Fluorine, the smallest halogen, forms the shortest bond length with hydrogen in HF.
• Going to HCl and further down to HBr and HI, the bond length gradually increases.

This increase in bond length is due to the larger atomic radii of the respective halogens. Larger atoms mean their electrons and nuclei are further apart, causing the elongation of the bond length in hydrogen halides.

Bond Energy of Single, Double, and Triple Bonds

Bond energy is a measure of bond strength in a chemical bond, defined as the amount of energy necessary to break a bond between two atoms.
In general terms:

• A single bond, comprising one pair of shared electrons, is typically the weakest. It requires the least energy to break.
• Double bonds, with two pairs of electrons, present a stronger bond needing more energy to disrupt.
• Triple bonds, holding three pairs of electrons, are the strongest and demand the highest energy to break.

This hierarchy means that bond energy increases with the number of shared electron pairs: Single bond ≤ Double bond < Triple bond. The progressively higher bond energies reflect the increased interaction points, making bonds progressively stronger.