The distance between the two adjacent carbon atoms is largest in butane.

Explanation:

Butane is a hydrocarbon compound with the molecular formula C4H10. It consists of a chain of four carbon atoms bonded together, with each carbon atom also bonded to hydrogen atoms.

In butane, the carbon atoms are connected by single covalent bonds, which allow for rotation around the carbon-carbon bond axis. This rotation is known as torsional rotation.

Torsional Rotation:

Torsional rotation refers to the rotation of one part of a molecule around a single bond axis with respect to another part of the molecule. In the case of butane, the rotation occurs around the carbon-carbon single bond axis.

When the molecule is in the eclipsed conformation, the hydrogen atoms attached to the carbon atoms on one end of the butane molecule are aligned with the hydrogen atoms on the other end. This results in increased repulsion between the electron clouds of the hydrogen atoms, causing a higher energy state.

Staggered Conformation:

In the staggered conformation, the hydrogen atoms attached to the carbon atoms are not aligned with each other. This results in a lower energy state compared to the eclipsed conformation.

Effect on Carbon-Carbon Distance:

In the eclipsed conformation, the carbon atoms are closer to each other due to the increased repulsion between the hydrogen atoms. This results in a shorter distance between the adjacent carbon atoms.

On the other hand, in the staggered conformation, the carbon atoms are farther apart because the hydrogen atoms are not aligned, reducing the repulsion between them. This results in a longer distance between the adjacent carbon atoms.

Conclusion:

In butane, the ability of the molecule to undergo torsional rotation allows for the carbon atoms to be in a staggered conformation, resulting in the largest distance between the two adjacent carbon atoms compared to the other compounds mentioned (benzene, ethene, and ethyne).