Problem 130 - A Complete Resource Book in Chemistry for JEE Main

Question

Compare the \(\mathrm{C}-\mathrm{H}\) bond lengths of the following hydrocarbons: 1\. \(\mathrm{CH}_{3}-\mathrm{CH}_{3}\) 2\. \(\mathrm{CH}_{2}=\mathrm{CH}_{2}\) 3\. \(\mathrm{CH} \equiv \mathrm{CH}\)The decreasing order of \(\mathrm{C}-\mathrm{H}\) bond lengths is \(\begin{array}{ll}\text { (a) } 3,2,1 & \text { (b) } 1,23\end{array}\) (c) \(2,1,3\)

Step-by-Step Solution

Answer

The decreasing order of \(\mathrm{C}-\mathrm{H}\) bond lengths is (b) 1, 2, 3.

Step 1: Understanding Bond Types

To compare bond lengths, we need to understand the type of bonds involved in each hydrocarbon. In ethane (\(\mathrm{CH}_3-\mathrm{CH}_3\)), the \(\mathrm{C}-\mathrm{H}\) bonds are single bonds (\(\sigma\)-bonds). In ethylene (\(\mathrm{CH}_2=\mathrm{CH}_2\)), the \(\mathrm{C}-\mathrm{H}\) bonds are adjacent to a double bond (\(\sigma-\pi\) bonds). In acetylene (\(\mathrm{CH} \equiv \mathrm{CH}\)), the \(\mathrm{C}-\mathrm{H}\) bonds are adjacent to a triple bond (\(\sigma-2\pi\) bonds).

Step 2: Relating Bond Types to Bond Lengths

Single bonds are generally longer than double bonds, and double bonds are longer than triple bonds. This is because the more \(\pi\)-bonds present, the more the electrons in the bonds pull the atoms closer together, shortening the bond length.

Step 3: Ranking the Bond Lengths

Given the types of bonds: \(\mathrm{CH}_3-\mathrm{CH}_3\) has the longest \(\mathrm{C}-\mathrm{H}\) bond due to single bonds, \(\mathrm{CH}_2=\mathrm{CH}_2\) has shorter \(\mathrm{C}-\mathrm{H}\) bonds due to the double bond presence, and \(\mathrm{CH} \equiv \mathrm{CH}\) has the shortest \(\mathrm{C}-\mathrm{H}\) bond due to the presence of a triple bond. Hence, the order is 1 > 2 > 3.

Step 4: Selecting the Correct Option

From the ranking in the previous step, the correct decreasing order of \(\mathrm{C}-\mathrm{H}\) bond lengths is option (b): \(1, 2, 3\).

Key Concepts

single bonds

In organic chemistry, **single bonds** are the simplest type of chemical bond. They involve the sharing of one pair of electrons between two atoms. These are also known as sigma (c3) bonds. This single bond configuration generally allows for more rotational freedom which can impact the energy barrier to rotation or internal rotation within the molecule.

• Single bonds are versatile and common in organic compounds, providing basic connectivity between carbon atoms as well as other elements like hydrogen.
• Because they involve only one shared pair of electrons, the bond is longer and typically less strong when compared to double or triple bonds.

In the context of C-H bond lengths, like in ethane (cH_3-cH_3), single bonds lead to longer bond lengths. This is because there are fewer electrons pulling the bonded atoms closer, resulting in a longer distance between nuclei in the molecule.

double bonds

**Double bonds** consist of one sigma (c3) bond and one pi (c0) bond, involving the sharing of two pairs of electrons between two atoms. The presence of the pi bond restricts rotational freedom, making molecules with double bonds more rigid in structure.

• Compared to single bonds, double bonds are shorter and stronger. This is due to the additional electron density between the bonded atoms.
• In molecules like ethylene (cH_2=cH_2), the presence of a double bond means the C-H bond lengths are shorter than in single-bonded counterparts.

This shortening is because the additional overlapping of electron clouds pulls the bonded atoms closer than in single bonds. This characteristic influences how substances with double bonds behave chemically and physically.

triple bonds

When it comes to **triple bonds**, these involve one sigma (c3) bond combined with two pi (c0) bonds, sharing three pairs of electrons between two atoms. This results in an even greater restriction on rotation and increases rigidity.

• Triple bonds are the shortest and strongest of the three types of bonds, due to the high electron density pulling the atoms extremely close together.
• For example, in acetylene (cH cH), the C-H bond lengths are the shortest among the three examined hydrocarbons because of the triple bond's characteristics.

The presence of three shared pairs of electrons tightly holds the atoms in place, impacting the molecule's physical stability and chemical reactivity. This influences acetylene’s properties in applications like welding, where high temperatures require strong, stable bonds.