Problem 93 - Chemistry: An Atoms-Focused Approach

Question

Which has the longer carbon-carbon bond: acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) or ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) ?\)

Step-by-Step Solution

Answer

Explain your answer. Answer: Ethane has a longer carbon-carbon bond length than acetylene. This is because acetylene has a stronger triple bond between its carbon atoms, which results in a shorter bond length, while ethane has a weaker single bond between its carbon atoms, leading to a longer bond length.

Step 1: Identify the types of carbon-carbon bonds in acetylene and ethane

In acetylene, the two carbon atoms are bound together by a triple covalent bond. This means that there are three bonds between the carbon atoms. In ethane, the two carbon atoms are bound together by a single covalent bond, meaning there is only one bond between the carbon atoms.

Step 2: Relate bond strength and types of carbon-carbon bonds

In general, the bond strength increases as we move from a single bond to a double bond to a triple bond. Therefore, the triple bond in acetylene will be stronger than the single bond in ethane.

Step 3: Describe the relationship between bond strength and bond length

Bond strength and bond length are inversely proportional to each other. A stronger bond will have a shorter bond length, while a weaker bond will have a longer bond length.

Step 4: Compare the carbon-carbon bond lengths in acetylene and ethane

As we established above, acetylene has a stronger carbon-carbon triple bond compared to ethane's single bond. Therefore, acetylene has a shorter carbon-carbon bond length compared to ethane. So, ethane has a longer carbon-carbon bond length than acetylene.

Key Concepts

Acetylene

Acetylene, with the chemical formula \(\mathrm{C}_{2}\mathrm{H}_{2}\), is a hydrocarbon that is characterized by a triple bond between its two carbon atoms. This triple bond is a defining feature of acetylene, making it a member of the alkyne family—compounds known for having at least one carbon-carbon triple bond. The triple bond in acetylene is made up of one sigma \((\sigma)\) bond and two pi \((\pi)\) bonds. This configuration results in a very strong and tightly bonded pair of carbons, pulling them closer together. Thus, acetylene has a very short carbon-carbon bond length.

• The structure of acetylene makes it very linear, with a bond angle of 180 degrees around the carbon atoms.
• It's this straight line structure that contributes to its unique chemical properties and short bond length.

This short bond length is due to the strength of the bonds; stronger bonds pull atoms closer, making acetylene's triple bond more compressed compared to other types of carbon bonds, like those found in alkanes.

Ethane

Ethane, bearing the chemical formula \(\mathrm{C}_{2}\mathrm{H}_{6}\), is a simple alkane that consists of a single bond between its two carbon atoms. This single covalent bond is a sigma \((\sigma)\) bond, where the electrons are shared directly between the two carbons, allowing for rotation around the bond axis.

• In ethane, each carbon atom forms three more single bonds with hydrogen atoms, completing the typical tetrahedral geometry of alkanes.
• This geometry allows for maximal spacing between bonded atoms, making ethane more flexible in terms of molecular shape.

Because the single bond is not as strong as a triple bond, the carbon-carbon bond in ethane is longer. Unlike the stiff and strong triple bond in acetylene, the single bond in ethane allows for a more extensive range of motion and is relatively weaker, resulting in a longer bond length.

Triple Bond vs Single Bond

Understanding the differences between triple and single bonds is crucial in chemistry. A triple bond, like that in acetylene, is composed of one sigma \((\sigma)\) and two pi \((\pi)\) bonds. This combination makes the bond incredibly strong and, therefore, shorter.

• Triple bonds prevent rotation around the bond axis due to the presence of pi bonds, which lock the atoms in a linear alignment.
• The strength of these bonds results in compact and resilient structures.

In contrast, a single bond, such as in ethane, involves only one sigma bond. The electrons are shared equally along the internuclear axis, allowing for free rotation and flexibility. This results in a weaker interaction between atoms, manifesting in a longer bond length.

• Single bonds offer rotational freedom, which is crucial for many biological structures and chemical reactions.
• While they are longer and weaker, their flexibility offers unique advantages in terms of molecule conformation and reactivity.

Thus, we see that while the strength and structure of multiple bonds limit movement, they offer robust chemical stability, whereas single bonds provide adaptability and dynamic motion.