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: (a) \(3,2,1\) (b) \(1,2,3\) (c) \(2,1,3\) (d) \(3,1,2\)

Short answer

The order is 1, 2, 3, so the answer is (b).

Step-by-step solution

Identify Bond Types

First, identify the types of bonds present in each hydrocarbon. In ethane (\(\mathrm{CH}_{3}-\mathrm{CH}_{3}\)), the \(\mathrm{C}-\mathrm{H}\) bond is a single bond. In ethene (\(\mathrm{CH}_{2}=\mathrm{CH}_{2}\)), it is a double bond. In ethyne (\(\mathrm{CH} \equiv \mathrm{CH}\)), it is a triple bond.

Understand Bond Length Relationship

Remember that bond length is inversely related to bond strength. Single bonds are the longest, while triple bonds are the shortest due to greater electron sharing and thus greater bond strength.

Evaluate Bond Lengths

Based on bond types: in \(\mathrm{CH}_{3}-\mathrm{CH}_{3}\) (single bond), the \(\mathrm{C}-\mathrm{H}\) bond length is the longest. In \(\mathrm{CH}_{2}=\mathrm{CH}_{2}\) (double bond), it is shorter. In \(\mathrm{CH} \equiv \mathrm{CH}\) (triple bond), it is the shortest.

Arrange in Decreasing Order

Arrange the hydrocarbons in order of decreasing \(\mathrm{C}-\mathrm{H}\) bond length: \(\mathrm{CH}_{3}-\mathrm{CH}_{3}\) (single bond), \(\mathrm{CH}_{2}=\mathrm{CH}_{2}\) (double bond), and \(\mathrm{CH} \equiv \mathrm{CH}\) (triple bond), yielding the sequence: 1, 2, 3.

Select the Correct Answer

Compare the sequence 1, 2, 3 with the provided options. The correct option is (b) \(1, 2, 3\).

Key concepts

Single Bond

In the world of chemistry, a single bond is the simplest type of covalent bond. This is where two atoms share a pair of electrons. In hydrocarbons like ethane (\(\mathrm{CH}_{3}-\mathrm{CH}_{3}\)), the \(\mathrm{C}-\mathrm{H}\) bond is a prime example of a single bond. Here, carbon and hydrogen each share one electron, creating a bond between them.
Single bonds are characterized by their relative simplicity and length. Among different bond types, single bonds are the longest in terms of distance between two bonded atoms.
This is because the electron sharing is minimal compared to multiple bonds, resulting in weaker attractive forces drawing the atoms together.

Double Bond

Double bonds occur when two atoms share two pairs of electrons. This results in a bond that is both stronger and shorter than a single bond. In ethene (\(\mathrm{CH}_{2} = \mathrm{CH}_{2}\)), the carbon-to-hydrogen interaction features such a double bond.
This connective power results from more shared electrons in the bond, which pulls the atoms closer than a single bond can.
A double bond adds rigidity to the molecular structure, limiting the rotation around the bond and affecting the molecule's geometry. The strength and shorter length are what differentiate double bonds from single ones.

Triple Bond

A triple bond is a type of covalent bonding where three pairs of electrons are shared between two atoms. Ethyne (\(\mathrm{CH} \equiv \mathrm{CH}\)) is an example of a molecule with a triple carbon-hydrogen bond. This type of bond is the strongest and shortest among all three categories, due to the maximal sharing of electrons.
Triple bonds introduce significant atom-to-atom attraction, thus bringing them into very close proximity compared to single or double bonds.
This stronger interaction results in higher bond energy, making triple bonds more robust but also less flexible, greatly affecting the molecule's stability and reactivity.

Bond Strength

Bond strength is an important property that signifies how tightly atoms are held together. It is generally proportional to the number of shared electron pairs between atoms. Therefore, as you move from a single bond to a triple bond, the bond strength increases.

• Single bonds have the least bond strength since they share only one pair of electrons.
• Double bonds are stronger due to two pairs of shared electrons, conferring better stability.
• Triple bonds are the strongest because they involve three pairs of electrons.

A higher bond strength equates to higher energy required to break the bond, which also means less reactivity under normal conditions.

Bond Length Relationship

The bond length relationship highlights an inverse correlation between bond length and bond strength. In simpler terms, the stronger the bond, the shorter the distance between the bonded atoms. This crucial relationship helps in understanding why, in hydrocarbons:

• Single bonds are the longest, due to weaker attraction from fewer shared electrons.
• Double bonds are moderately shorter because they share two pairs of electrons, pulling the atoms closer.
• Triple bonds are the shortest since three shared pairs bring the atoms extremely close.

Understanding this relationship helps in predicting molecular shapes and reactivity, as shorter, stronger bonds like triple bonds make molecules more rigid.