Question

The enthalpy of hydrogenation for 1-pentene is \(-126 \mathrm{~kJ} / \mathrm{mol}\). The enthalpy of hydrogenation for 1,3 -pentadiene is \(-230 \mathrm{~kJ} / \mathrm{mol}\). Hence, estimate the resonance (delocalization) energy of 1,3 -pentadiene. (A) \(+4 \mathrm{~kJ} / \mathrm{mol}\) (B) \(+22 \mathrm{~kJ} / \mathrm{mol}\) (C) \(-4 \mathrm{~kJ} / \mathrm{mol}\) (D) \(-22 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

The resonance (delocalization) energy of 1,3-pentadiene is estimated to be \( -22 \ \mathrm{kJ/mol} \). (D)

Step-by-step solution

Understand given enthalpies of hydrogenation

For 1-pentene, the enthalpy of hydrogenation is -126 kJ/mol, and there is only one double bond present in the molecule. For 1,3-pentadiene, the enthalpy of hydrogenation is -230 kJ/mol, and there are two double bonds present in the molecule.

Compare enthalpies of hydrogenation per double bond

Since there are two double bonds in 1,3-pentadiene, for every double bond broken, the enthalpy of hydrogenation would be half the total enthalpy of hydrogenation for the whole molecule. In other words, we would have: Enthalpy of hydrogenation per double bond in 1,3-pentadiene = \(\frac{-230 \ \mathrm{kJ/mol}}{2}\) = -115 kJ/mol

Calculate the difference in the enthalpy of hydrogenation between 1-pentene and 1,3-pentadiene per double bond

Now, we will subtract the enthalpy of hydrogenation per double bond in 1-pentene and that in 1,3-pentadiene: Difference = Enthalpy of hydrogenation per double bond in 1-pentene - Enthalpy of hydrogenation per double bond in 1,3-pentadiene Difference = (-126 kJ/mol) - (-115 kJ/mol) = -11 kJ/mol

Estimate the resonance energy

The negative difference in enthalpy (-11 kJ/mol) indicates that there is resonance present in the 1,3-pentadiene molecule, which stabilizes it. Thus the resonance or delocalization energy is -11 kJ/mol per double bond. Since there are two double bonds in 1,3-pentadiene, the total resonance energy is: Total resonance energy = -11 kJ/mol × 2 = -22 kJ/mol From the given options, the correct answer is: (D) -22 kJ/mol

Key concepts

Enthalpy of Hydrogenation

Enthalpy of hydrogenation is a measure of the energy change when hydrogen is added to a molecule with double bonds. This process involves the conversion of double bonds into single bonds by adding hydrogen. The enthalpy of hydrogenation provides insights into the stability of a molecule. Specifically, it reveals how much energy is released during this transformation.
For example, in the case of 1-pentene, the enthalpy of hydrogenation is equal to -126 kJ/mol. This energy value tells us that when hydrogen is added to its one double bond, a significant amount of energy is released, indicating the bond's stability.
In comparison, 1,3-pentadiene has an enthalpy of hydrogenation of equal to -230 kJ/mol for the molecule. Since this compound contains two double bonds, its enthalpy per bond can be calculated as -115 kJ/mol. This distinction suggests that the two double bonds in 1,3-pentadiene are slightly more stable than the single double bond in 1-pentene.
Understanding enthalpy of hydrogenation helps assess the stability of compounds, particularly those with resonance structures, as less energy released per bond indicates greater stability.

Double Bonds

Double bonds are a type of covalent bond where two pairs of electrons are shared between two atoms. These bonds are stronger than single bonds and hold atoms together more tightly, which makes them significant in the structure and stability of organic compounds. Double bonds are often represented by two lines between chemical symbols, such as C=C for a carbon-carbon double bond.
The presence of double bonds in hydrocarbons like 1-pentene and 1,3-pentadiene influences both their reactivity and stability. In terms of chemical reactions, double bonds are known to be sites of higher reactivity, participating readily in reactions such as hydrogenation and polymerization.
Double bonds not only affect the reactivity but also the shape and symmetry of molecules. For example, when there are multiple double bonds, like in 1,3-pentadiene, the molecule can exhibit resonance, where electrons in double bonds are delocalized across the molecule and reduce the overall energy level. This is crucial in stabilizing molecules that have alternating single and double bonds.

1,3-Pentadiene

1,3-Pentadiene is a hydrocarbon with the chemical formula C\(_5\)H\(_6\). It is characterized by two double bonds between the first and second, and the third and fourth carbon atoms. This configuration, often referred to as 'conjugated double bonds,' allows for electron delocalization across the molecule, a phenomenon known as resonance.
This resonance provides additional stability to the molecule beyond what would be predicted by the presence of two separate, isolated double bonds. The enthalpy of hydrogenation for 1,3-pentadiene being less per double bond than predicted is evidence of this added stability.
The structure and stability of 1,3-pentadiene have practical implications in various chemical processes, including its use as a monomer in the production of synthetic rubbers. Its resonance stabilization influences how it participates in chemical reactions, making it a valuable compound in industrial applications.
Thus, when assessing compounds like 1,3-pentadiene, it's essential to consider the dual effects of conjugation on both stability and reactivity, as well as their implications in synthetic chemistry.