Question

There is another kind of rotation possible in 1,3 -butadienethat about the \(\mathrm{C}(1)-\mathrm{C}(2)\) or \(\mathrm{C}(3)-\mathrm{C}(4)\) bonds. We might guess that the barrier to this rotation would be little different from that for rotation in a typical double bond but, as a former president of the United States once said, "that would be wrong." In 1,3-butadiene, it takes only \(52 \mathrm{kcal} / \mathrm{mol}(217 \mathrm{~kJ} / \mathrm{mol})\) to do this rotation, some \(14 \mathrm{kcal} / \mathrm{mol}(59 \mathrm{~kJ} / \mathrm{mol})\) less than the barrier of \(66 \mathrm{kcal} / \mathrm{mol}\) \((276 \mathrm{~kJ} / \mathrm{mol})\) for rotation in ethylene. Explain.

Short answer

The conjugation in 1,3-butadiene reduces the rotational barrier compared to ethylene, resulting in a lower energy requirement for rotation.

Step-by-step solution

Understand the Molecules

First, understand the compounds involved. 1,3-butadiene is a conjugated diene with double bonds between C(1)-C(2) and C(3)-C(4). Ethylene consists of a single double bond between two carbon atoms.

Compare Rotations

The energy barrier for rotation around the C(1)-C(2) or C(3)-C(4) bonds in 1,3-butadiene is given as 52 kcal/mol, whereas for plain C=C rotation in ethylene, it is 66 kcal/mol.

Role of Conjugation

Conjugation in 1,3-butadiene stabilizes intermediate structures during rotation, effectively lowering the barrier by delocalizing electrons across the pi-system, hence the lower rotational barrier.

Elaborate on Energy Differences

The difference between the rotational barriers is 66 kcal/mol - 52 kcal/mol = 14 kcal/mol. This indicates stabilization due to conjugation in 1,3-butadiene that is not present in ethylene.

Key concepts

1,3-Butadiene

1,3-Butadiene is a conjugated diene, meaning it has two double bonds separated by a single bond. In this molecule, the double bonds are located between Carbon atoms 1 and 2 (C(1)=C(2)) and Carbon atoms 3 and 4 (C(3)=C(4)). This structure allows for the possibility of different kinds of rotations, such as the rotation around C(1)-C(2) or C(3)-C(4) bonds.

This type of rotation is particularly interesting because the energy barrier for this rotation is significantly lower than what one might expect from a simple double bond. In 1,3-butadiene, the rotation barrier is only 52 kcal/mol. This is a crucial point to understand because most simple double bonds have higher rotational barriers due to the need to break the pi-bond during rotation.

Ethylene

Ethylene is a much simpler molecule compared to 1,3-butadiene. It consists of just two carbon atoms connected by a single double bond (C=C). This simplicity makes ethylene a useful benchmark for comparing rotational barriers. In ethylene, the energy barrier for rotation about the double bond is 66 kcal/mol.

This high barrier is due to the need to break the pi-bond to allow rotation. In a double bond, the pi-bond locks the carbon atoms into a fixed position, preventing rotation. Breaking this bond requires significant energy, thus resulting in a higher rotational barrier compared to that of 1,3-butadiene.

Conjugation

Conjugation is a critical concept in understanding why 1,3-butadiene has a lower rotational barrier compared to ethylene. Conjugation occurs when alternating single and double bonds allow for the delocalization of pi-electrons across the molecule. This delocalization of electrons provides extra stability to the molecule.

In the case of 1,3-butadiene, conjugation stabilizes the intermediate structures formed during the rotation around C(1)-C(2) or C(3)-C(4) bonds. Because the electrons are spread out over a larger area, the molecule gains additional stability that a non-conjugated system like ethylene does not have. This extra stability translates into a lower energy requirement for rotation, hence the lower rotational barrier of 52 kcal/mol for 1,3-butadiene compared to 66 kcal/mol for ethylene.