Question

Column-I Column-II (Alkenes) (Heat of combustion in \(\mathrm{kcal} / \mathbf{m o l}\) ) (A) 3,4 -dimethyl pent-l-ene (P) 1160 (B) \(2.3\)-dimethyl pent-2-ene (Q) 980 (C) 3-methyl hept-2-ene (R) 920 (D) 3-ethyl-pent-2-ene (S) 875

Short answer

The correct matches between alkenes and their heat of combustion are: (A) 3,4-dimethylpent-1-ene ⟶ (Q) 980 kcal/mol, (B) 2,3-dimethylpent-2-ene ⟶ (P) 1160 kcal/mol, (C) 3-methylhept-2-ene ⟶ (S) 875 kcal/mol, and (D) 3-ethyl-pent-2-ene ⟶ (R) 920 kcal/mol.

Step-by-step solution

Draw Structures of Alkenes

First, let's draw the structures of the given alkenes in Column-I: (A) 3,4-dimethylpent-1-ene: \(H_3C{-}CH=C(CH_3)_2{-}CH_3\) (B) 2,3-dimethylpent-2-ene: \(H_3C{-}C(CH_3)=C(CH_3){-}CH_2{-}CH_3\) (C) 3-methylhept-2-ene: \(H_3C{-}CH_2 {-}C(CH_3)=CH{-}CH_2{-}CH_2{-}CH_3\) (D) 3-ethyl-pent-2-ene: \(H_3C{-}CH_2{-}C(CH_2CH_3)=CH{-}CH_2{-}CH_3\)

Determine Stability

Now, let's consider the stability of these alkenes. In general, more substituted alkenes are more stable due to hyperconjugation and steric factors. (A) 3,4-dimethylpent-1-ene: This alkene has a trisubstituent carbon. (B) 2,3-dimethylpent-2-ene: This alkene has a tetrasubstituent carbon. (C) 3-methylhept-2-ene: This alkene has a disubstituent carbon. (D) 3-ethyl-pent-2-ene: This alkene has a trisubstituent carbon. Considering the substitution pattern, we can arrange the alkenes in terms of their stability: (B) > (A) ≈ (D) > (C)

Relate Stability to Heat of Combustion

Since more stable alkenes have less energy, their combustion will release more heat. Therefore, alkenes with higher heat of combustion are more stable. Now, let's match the heat of combustion values to the alkenes in Column-I based on the stability ranking: (B) 2,3-dimethylpent-2-ene: Heat of Combustion = 1160 kcal/mol (P) (A) 3,4-dimethylpent-1-ene: Heat of Combustion = 980 kcal/mol (Q) (D) 3-ethyl-pent-2-ene: Heat of Combustion = 920 kcal/mol (R) (C) 3-methylhept-2-ene: Heat of Combustion = 875 kcal/mol (S) Hence, the correct matches are: (A) ⟶ (Q) (B) ⟶ (P) (C) ⟶ (S) (D) ⟶ (R)

Key concepts

Stability of Alkenes

The stability of alkenes is an essential concept in understanding their reactivity and physical properties, including the heat of combustion. In general, the stability of an alkene increases with the number of alkyl substituents attached to the double bonded carbons. This is due to several factors, including hyperconjugation and the release of steric strain.

In the given exercise, the stability order of the alkenes was determined based on their substitution patterns. Alkenes that are more substituted, such as those with tetrasubstituted or trisubstituted carbons, are typically more stable. For instance, 2,3-dimethylpent-2-ene (B), with a tetrasubstituent carbon, was considered to be the most stable, followed by the trisubstituted alkenes (A and D), and finally 3-methylhept-2-ene (C) with a disubstituent carbon.

This stability affects the heat of combustion; more stable alkenes have lower potential energy and therefore release more energy when they undergo combustion. This relationship is crucial when predicting the heat of combustion values for different alkenes.

Substitution Patterns in Organic Compounds

Substitution patterns refer to the arrangement of atoms or groups of atoms attached to the carbon skeleton of organic molecules. These patterns greatly influence the chemical behavior of the compound. In alkenes, the location and number of alkyl substituents attached to the carbon-carbon double bond determine the molecule's physical and chemical properties.

In the step-by-step solution of the exercise, the alkene's stability was predicted based on its substitution pattern. For example, a tetrasubstituted double bond in an alkene, where four carbon groups are attached to the double bond, is more stable due to increased hyperconjugation, compared to a disubstituted double bond. The enhancement of stability with increased substitution can also be explained in terms of the inductive effect, where electron-donating alkyl groups push electron density towards the double bond strengthening it.

Effect of Substitution on Heat of Combustion

When evaluating the heat of combustion, the rule of thumb is that the more substituted the alkene, the higher the heat of combustion. This is because a more substituted alkene is lower in potential energy, and during combustion, a larger energy difference exists between the reactants and the products, leading to the release of more heat.

Hyperconjugation and Steric Effects

Hyperconjugation and steric effects are two fundamental concepts that help explain the stability of organic molecules, particularly alkenes. Hyperconjugation refers to the delocalization of electrons from a sigma bond (usually C-H or C-C) to an adjacent empty or partially filled p-orbital or pi-system. This electron delocalization stabilizes the molecule and is more pronounced in alkenes with greater alkyl substitution.

Steric effects involve repulsive interactions between atoms or groups of atoms which are brought into close proximity. These can influence reactivity and stability. In the context of alkenes, steric strain can decrease stability; however, in the absence of overly bulky groups, minor steric hindrance can actually contribute to stability by preventing the molecule from reacting too readily.

Combining these ideas, the exercise improvement in understanding the heat of combustion in alkenes could benefit from a comparison of hyperconjugation and steric effects. An alkene with strong hyperconjugation but not overwhelmed by steric hindrance would be expected to be quite stable and thus have a higher heat of combustion, as evidenced by the provided exercise solutions.