Question

For each of the questions, four choices have been provided. Select the correct alternative. Arrange the following in increasing order of their bond lengths. \(\mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{C} \equiv \mathrm{C}\) (a) \(\mathrm{C} \equiv \mathrm{C}<\mathrm{C}=\mathrm{C}<\mathrm{C}-\mathrm{C}\) (b) \(\mathrm{C}=\mathrm{C}<\mathrm{C}-\mathrm{C}<\mathrm{C} \equiv \mathrm{C}\) (c) \(C=C

Short answer

Question: Arrange the following carbon-carbon bonds in increasing order of bond length: single bond (C-C), double bond (C=C), and triple bond (C≡C). Answer: C≡C < C=C < C-C

Step-by-step solution

Understand bond lengths in different bonds

The length of a bond is inversely proportional to the bond strength or the number of bonds shared between the atoms. As the number of bonds shared between the atoms increases, the bond length decreases. Therefore, we can infer that single bonds are longer than double bonds, and double bonds are longer than triple bonds.

Arrange the carbon-carbon bonds in increasing order of bond length

Based on the understanding from step 1, we can arrange the given bonds, \(\mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{C} \equiv \mathrm{C}\), in increasing order of bond length as follows: \(\mathrm{C} \equiv \mathrm{C}<\mathrm{C}=\mathrm{C}<\mathrm{C}-\mathrm{C}\).

Compare the arrangement with the provided options

Comparing the arrangement of bond lengths from step 2 with the four given options, we can see that it matches with option (a). Thus, the correct answer is (a) \(\mathrm{C} \equiv \mathrm{C}<\mathrm{C}=\mathrm{C}<\mathrm{C}-\mathrm{C}\).

Key concepts

Carbon-Carbon Bonds

Understanding the nature of carbon-carbon bonds is fundamental to the study of organic chemistry. Carbon, a versatile element, is capable of forming different types of bonds with other carbon atoms, namely single bonds (C-C), double bonds (C=C), and triple bonds (C≡C). These varying bond types are due to the ability of carbon to share pairs of electrons with other carbon atoms, forming covalent bonds.

A single bond is formed when two carbon atoms share one pair of electrons, a double bond shares two pairs, and a triple bond shares three pairs. With each additional pair shared, the carbon atoms are pulled closer together due to increased attractive forces. This alters the bond's properties, including its length and strength, which is critical to the structure and reactivity of organic compounds.

Significance in Organic Structures

Within an organic molecule, these varying types of carbon bonds impact the molecule's shape and stability. As an example, the rigidity of double bonds plays a crucial role in the structure of unsaturated fats, whereas longer single bonds allow for more flexibility found in saturated fats. This impacts not only the physical properties but also how these molecules interact biologically.

Bond Strength

The strength of a bond is an indication of how much energy is required to break the bond apart. It is a critical factor in determining a molecule's stability and reactivity. Bond strength is directly influenced by the number of electron pairs being shared in the covalent bond. Thus, a single bond, which involves only one pair of electrons, is weaker than a double bond that involves two pairs of electrons, and a triple bond is the strongest among the three, involving three pairs of electrons.

These strength differences are due to the increased electrostatic interactions between the shared pairs of electrons and the nuclei of the bonding atoms. As more electrons are shared, the atoms in a molecule are held together more tightly, resulting in a shorter and stronger bond. The concept that stronger bonds tend to be shorter is not merely a trend, but a reflection of stronger forces pulling the atoms closer together.

Impact on Chemical Reactions

Understanding bond strength is essential when predicting the reactivity of molecules. Chemical reactions often involve breaking and forming bonds. Stronger bonds, such as those found in triple-bonded carbons, typically require more energy to break and thus can influence the conditions under which a chemical reaction will proceed.

Bond Length Inversely Proportional

There is a fundamental concept in chemistry that the length of a bond between two atoms is inversely proportional to the strength of the bond. This implies that as the bond becomes stronger, the distance between the two atoms becomes shorter. This relationship is due to the nature of atomic forces and electron interactions in a bond.

When comparing carbon-carbon bonds, the triple bond (as in ethyne or acetylene) has the shortest length due to its high electron density, causing a stronger pull between the nuclei. In contrast, single bonds as found in ethane, have the longest bond length since they share fewer electrons and hence have a weaker pull between the bonding nuclei.

Visualization of Bond Length and Strength

To visualize this, imagine a rubber band being stretched between two points. With more force (akin to bond strength), the rubber band will extend less (representing shorter bond length). Conversely, less force allows the rubber band to stretch more (resulting in a longer bond length). This inverse relationship helps us deduce the physical structure of molecules from their theoretical bond properties and thus is a pivotal concept in the interpretation of molecular architecture and chemical behavior.