Question

Estimate the stabilization gained as a result of conjugation when 1,4 -pentadiene is converted to trans-1,3-pentadiene. Note that the answer is not as simple as comparing the heats of hydrogenation of 1,4 -pentadiene and trans-1,3pentadiene. Although the double bonds are moved from unconjugated to conjugated, the degree of substitution of one of the double bonds is also changed, in this case, from a monosubstituted double bond to a trans disubstituted double bond. To answer this question, you must separate the effect that is the result of conjugation from that caused by a change in the degree of substitution.

Short answer

Answer: The stabilization gained as a result of conjugation when 1,4-pentadiene is converted to trans-1,3-pentadiene is estimated to be 0 kJ/mol.

Step-by-step solution

Understanding the structures of 1,4-pentadiene and trans-1,3-pentadiene

First, draw the structures of 1,4-pentadiene and trans-1,3-pentadiene. Notice the double bonds' positions and the degree of substitution on the double bonds. 1,4-pentadiene: H2C=CH-CH2-CH=CH2 (two unconjugated double bonds) trans-1,3-pentadiene: H2C=CH-CH=CH-CH3 (two conjugated double bonds)

Determine the changes in the structure

In the conversion from 1,4-pentadiene to trans-1,3-pentadiene, the degree of substitution of one of the double bonds change, as well as the double bonds become conjugated. Initially, one of the double bonds is monosubstituted in 1,4-pentadiene (H2C=CH), whereas this double bond becomes disubstituted in trans-1,3-pentadiene (H2C=CH-CH).

Calculate the energies required for hydrogenation of each compound

The heats of hydrogenation (∆H) for alkene depend on the degree of substitution. The heat of hydrogenation for terminal alkenes is higher than that of internal alkenes. ∆H values: - Terminal (monosubstituted) alkene: 125 kJ/mol - Internal (disubstituted) alkene: 120 kJ/mol 1,4-pentadiene: Two terminal alkenes: H2C=CH and H2C=CH2 ∆H_total(1,4-pentadiene) = 2 * 125 kJ/mol = 250 kJ/mol trans-1,3-pentadiene: One terminal alkene (H2C=CH) and one internal alkene (H2C=CH-CH) ∆H_total(trans-1,3-pentadiene) = 125 kJ/mol + 120 kJ/mol = 245 kJ/mol

Determine the effect of conjugation from that caused by a change in the degree of substitution

Now that we know the heats of hydrogenation for 1,4-pentadiene and trans-1,3-pentadiene, we can calculate the stabilization energy associated with conjugation. However, we must first account for the change in the degree of substitution. If we convert the monosubstituted alkene in 1,4-pentadiene to a disubstituted alkene, we get the energy required for this change: Energy_change = 125 kJ/mol - 120 kJ/mol = 5 kJ/mol So, the stabilization energy associated with conjugation can be estimated as: Stabilization_energy = ∆H_total(1,4-pentadiene) - ∆H_total(trans-1,3-pentadiene) - Energy_change Stabilization_energy = 250 kJ/mol - 245 kJ/mol - 5 kJ/mol = 0 kJ/mol Therefore, the stabilization gained as a result of conjugation when 1,4-pentadiene is converted to trans-1,3-pentadiene is estimated to be 0 kJ/mol.

Key concepts

Heats of Hydrogenation

Understanding the heats of hydrogenation is vital for estimating the stability of different alkenes. This measure indicates the energy released when an alkene is converted to an alkane by the addition of hydrogen. In general, the more substituted an alkene is, the less heat it releases upon hydrogenation, suggesting greater intrinsic stability.

For example, a terminal (monosubstituted) alkene like H₂C=CH₂ typically has a higher heat of hydrogenation (around 125 kJ/mol) compared to an internal (disubstituted) alkene such as H₂C=CH-CH (around 120 kJ/mol). These values are a reflection of the alkene's structural and electronic environment. When assessing the stability of alkenes that undergo a transformation, such as in the problem with 1,4-pentadiene and trans-1,3-pentadiene, it's essential to consider these heats of hydrogenation to tease apart the effects of conjugation and substitution on the overall stability.

Alkene Substitution

When talking about alkene substitution, we refer to the number and position of alkyl groups attached to the double bond. This has a significant effect on the alkene's reactivity and stability. For instance, terminal alkenes have one alkyl group, classifying them as monosubstituted, while internal alkenes with two alkyl groups are disubstituted.

Alkene substitution alters the heat of hydrogenation, as seen in the comparison between monosubstituted and disubstituted alkenes—the latter being slightly more stable due to the additional alkyl group providing hyperconjugative stabilization and reducing the energy released in hydrogenation. In the conversion process of 1,4-pentadiene to trans-1,3-pentadiene, this distinction is critical because it changes a terminal alkene to an internal one, influencing the stability and reactivity of the molecule.

1,4-Pentadiene

The molecule 1,4-pentadiene contains two non-conjugated double bonds. These alkenes are known as terminal alkenes because the double bonds exist at the ends of the carbon chain. With each double bond being monosubstituted, the cumulative heat of hydrogenation for 1,4-pentadiene is calculated by summing the individual heats for each double bond.

In the step-by-step exercise, it was calculated as 250 kJ/mol by adding the identical heat of hydrogenation of two separate terminal alkenes. As students work to compare this molecule with trans-1,3-pentadiene, they must understand that the double bonds here don't interact in a way that stabilizes the molecule, which is different from conjugated systems.

Trans-1,3-Pentadiene

Trans-1,3-pentadiene, in contrast to 1,4-pentadiene, features two conjugated double bonds. This configuration allows for a degree of overlap in the p-orbitals, which lets electrons delocalize along the carbon skeleton. This delocalization generally results in increased stability and a lower heat of hydrogenation.

In the given problem, the heat of hydrogenation for trans-1,3-pentadiene is computed by considering one terminal alkene and one internal alkene, leading to a combined heat of 245 kJ/mol. This reflects one effect of conjugation, which is often to lower the overall energy of the system. However, as shown in the exercise, when comparing it to 1,4-pentadiene, the alteration in alkene substitution must also be considered to accurately assess the stabilization energy due to conjugation.