Question

The given order is not a correct for their: $$ \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}>\mathrm{CH}_{2}=\mathrm{CH}_{2} $$ (A) Heat of hydrogenation (B) Bond length of \(\mathrm{C}=\mathrm{C}\) bond (C) Heat of hydrogenation per mole of \(\mathrm{H}_{2}\) (D) Heat of combustion

Short answer

The given order is incorrect for option (B) Bond length of \(\mathrm{C}=\mathrm{C}\) bond, because smaller alkene molecules have a slightly shorter carbon-carbon double bond length than larger ones due to less steric hindrance and more s-orbital overlap, resulting in a stronger pi bond.

Step-by-step solution

(A) Heat of hydrogenation

Heat of hydrogenation is the energy released when a molecule with a double bond reacts with hydrogen to form a molecule with only single bonds. The more stable a molecule is, the less energy will be released during hydrogenation. As we go from 1-butene to ethene, the number of carbons involved in the double bond decreases, so the energy released when hydrogenated would decrease. Therefore, the given order is correct for heat of hydrogenation.

(B) Bond length of \(\mathrm{C}=\mathrm{C}\) bond

Smaller alkene molecules have a slightly shorter carbon-carbon double bond length than larger ones due to less steric hindrance and more s-orbital overlap, resulting in a stronger pi bond. Since 1-butene is a larger molecule than ethene, the bond length of the \(\mathrm{C}=\mathrm{C}\) bond in 1-butene should be larger than that in ethene. In this case, the given order is incorrect.

(C) Heat of hydrogenation per mole of \(\mathrm{H}_{2}\)

Since heat of hydrogenation is the energy released when a molecule with a double bond reacts with hydrogen, the heat of hydrogenation per mole of \(\mathrm{H}_{2}\) would be directly proportional to heat of hydrogenation. Thus, the given order is correct for heat of hydrogenation per mole of \(\mathrm{H}_{2}\).

(D) Heat of combustion

Heat of combustion is the amount of heat released when a molecule is fully combusted. In general, larger molecules release more heat during combustion. However, as 1-butene and ethene only differ by the position of the double bond and not the size, their heat of combustion will be similar. Hence, the given order is also correct for heat of combustion. Based on the analysis, we find that the given order is incorrect for the bond length of \(\mathrm{C}=\mathrm{C}\) bond, which makes the correct answer option (B).

Key concepts

Heat of Hydrogenation

Heat of hydrogenation refers to the energy released when an alkene (a molecule with a carbon-carbon double bond) is transformed into an alkane (a molecule with only single bonds) by adding hydrogen.
This reaction helps chemists understand the stability of different alkenes. When hydrogen gas is added to an alkene, the double bond breaks and the hydrogen atoms add, converting the molecule into a saturated compound. The amount of energy released during this process is inverse to the stability of the alkene:

• A more stable alkene will release less energy, resulting in a lower heat of hydrogenation.
• A less stable alkene, which has more energy stored in the double bond, will release more energy upon hydrogenation.

This means that alkenes with more substituents or bulkier groups around the double bond tend to be more stable and have lower heats of hydrogenation. The original problem indicated an order based on the number of carbons and how they participate in the double bond, implying that the energy released and thus heat of hydrogenation decreases from 1-butene to ethene.

Bond Length in Alkenes

Bond length in alkenes is determined by the nature of the bonds between carbon atoms. In general, carbon-carbon double bonds (\(C=C\)) are shorter than carbon-carbon single bonds due to the presence of one sigma bond and one pi bond. However, the length of the \(C=C\) bond can vary due to several factors:

• Steric hindrance: Larger alkene molecules may experience crowding around the double bond, slightly increasing bond length compared to smaller alkenes.
• Orbital overlap: Alkenes with better overlap of sp²-hybridized orbitals can achieve stronger pi bonds, which may result in shorter bond lengths.

For instance, ethene, being a smaller molecule, experiences less steric hindrance, allowing for a stronger and shorter \(C=C\) bond than that observed in 1-butene. The original solution identified that the order given was incorrect for bond length, as larger 1-butene should have a longer bond compared to ethene.

Heat of Combustion

Heat of combustion describes the total amount of energy released when a molecule is completely oxidized to produce carbon dioxide and water. This property helps gauge the energy content of different hydrocarbons. For alkenes like 1-butene and ethene, the combustion equation generally yields a similar amount of energy since both consist mostly of carbon and hydrogen:

• Heat of combustion tends to be greater for larger hydrocarbons as they contain more carbon and hydrogen bonds.
• The positional differences of the double bond in molecules like 1-butene and ethene minimally affect the heat of combustion.

Thus, the heats of combustion for 1-butene and ethene should be comparable, as both have nearly the same number of carbon and hydrogen atoms. The original analysis supported this, indicating that the given order was correct for the heat of combustion, aligning with the expectations for such small hydrocarbons.