Problem 41 - A Complete Resource Book in Chemistry for JEE Main

Question

The C-C bond length of the following molecules are in the order (a) \(\mathrm{C}_{2} \mathrm{H}_{6}>\mathrm{C}_{2} \mathrm{H}_{4}>\mathrm{C}_{6} \mathrm{H}_{6}>\mathrm{C}_{2} \mathrm{H}_{2}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{2}<\mathrm{C}_{2} \mathrm{H}_{4}<\mathrm{C}_{6} \mathrm{H}_{6}<\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{6}>\mathrm{C}_{2} \mathrm{H}_{2}>\mathrm{C}_{6} \mathrm{H}_{6}>\mathrm{C}_{2} \mathrm{H}_{4}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{4}>\mathrm{C}_{2} \mathrm{H}_{6}>\mathrm{C}_{2} \mathrm{H}_{2}>\mathrm{C}_{6} \mathrm{H}_{6}\)

Step-by-Step Solution

Answer

The correct order is (a) f C_2H_6 > f C_2H_4 > f C_6H_6 > f C_2H_2.

Step 1: Identifying Bond Types

First, understand the type of bonds present in each molecule: - Ethane (f C_2H_6) has single bonds between carbon atoms. - Ethylene (f C_2H_4) has a double bond between carbon atoms. - Benzene (f C_6H_6) has resonance bonds (between single and double bonds). - Acetylene (f C_2H_2) has a triple bond between carbon atoms.

Step 2: Understanding Bond Lengths

Recall that the greater the number of bonds between two atoms, the shorter the bond length will typically be. Thus, single bonds are the longest, and triple bonds are the shortest.

Step 3: Arranging Bond Lengths

Based on the bond types: - f C_2H_6, with single C-C bonds, has the longest bond length. - f C_2H_4, with double C-C bonds, follows. - f C_6H_6, with resonance (intermediate between single and double), is next. - f C_2H_2, with triple bonds, has the shortest bond length.

Step 4: Comparing with Options

Compare the theoretical order obtained (f C_2H_6 > f C_2H_4 > f C_6H_6 > f C_2H_2) with the given options. The correct order matches option (a).

Key Concepts

Bond Length

Understanding bond length is crucial when studying chemical bonding. Bond length is the distance between the nuclei of two bonded atoms. It tells us how tightly or loosely atoms are held together. Several factors influence bond length, including bond type and the size of the atoms involved.

Here are some key points to remember about bond length:

• Single bonds are generally longer than double bonds.
• Double bonds are longer than triple bonds.
• The size of the atoms also affects bond length; larger atoms will typically result in a longer bond length.

For example, in the four molecules mentioned in the exercise, the C-C bond length decreases as the number of bonds (single, double, triple) increases between the carbon atoms. This is an essential concept in understanding how molecular structures are formed and how they influence the chemical and physical properties of substances.

Single, Double, and Triple Bonds

Chemical bonds can form in different ways depending on how many electrons are shared between atoms. These are categorized as single, double, and triple bonds, each representing different closeness and movement restrictions between atoms.

Let's explore the differences:

• Single Bonds: In single bonds, one pair of electrons is shared between two atoms. This results in the longest bond length but tends to be the weakest compared to double and triple bonds.
• Double Bonds: Double bonds involve two pairs of shared electrons. They are shorter and stronger than single bonds. An example is the C-C bond in ethylene ( C_2H_4 a).
• Triple Bonds: Triple bonds involve three pairs of shared electrons, making them the shortest and strongest. Acetylene ( C_2H_2 ) is a common molecule featuring a carbon-carbon triple bond.

It's important to note that as bond multiplicity increases (from single to triple bonds), the bond length decreases, leading to greater strength and stability of the bond. This concept is crucial for predicting how molecules behave during chemical reactions.

Hybridization in Molecules

Hybridization is a concept that explains how atomic orbitals mix to form new hybrid orbitals. This occurs when atoms bond to form molecules, allowing them to achieve optimal geometry for bonding.

Hybridization types depend on the types of bonds and the arrangement of atoms:

• sp³ Hybridization: Found in molecules with single bonds, such as ethane ( C_2H_6 ). Here, one s orbital combines with three p orbitals to form four equivalent sp³ hybrid orbitals. This results in a tetrahedral shape.
• sp² Hybridization: Present in molecules with double bonds, like ethylene ( C_2H_4 ). One s orbital mixes with two p orbitals, forming three sp² hybrid orbitals, often resulting in a trigonal planar shape.
• sp Hybridization: Occurs in molecules with triple bonds, such as acetylene ( C_2H_2 ). Here, one s orbital mixes with one p orbital to form two sp hybrid orbitals, resulting in a linear shape.

Understanding hybridization helps in predicting the shape and bond angles in molecules, which are vital for determining the reactions and interactions of organic compounds.