Problem 18 - A Complete Resource Book in Chemistry for JEE Main

Question

Which will have smallest heat of hydrogenation per mole? (a) cis-2-butene (b) trans-2-butene (c) 1,3 -butadiene (d) 1 -butene

Step-by-Step Solution

Answer

1,3-butadiene (c) has the smallest heat of hydrogenation per mole due to resonance stabilization.

Step 1: Understanding Heat of Hydrogenation

Heat of hydrogenation refers to the heat released when one mole of an unsaturated compound reacts with hydrogen to become saturated. More stable alkenes will have a smaller heat of hydrogenation due to their lower initial energy states.

Step 2: Stability of Alkenes and Conjugated Dienes

The stability of alkenes can be compared based on their structure. Conjugated dienes, like in compounds with alternating double bonds, have increased stability due to resonance. Therefore, 1,3-butadiene will be more stable than non-conjugated alkenes like cis-2-butene, trans-2-butene, and 1-butene.

Step 3: Comparing the Stability of Trans vs Cis Alkenes

Between cis-2-butene and trans-2-butene, trans isomers are more stable due to less steric hindrance between substituent groups. Thus, trans-2-butene will have a smaller heat of hydrogenation compared to cis-2-butene.

Step 4: Evaluate Each Option

Now, evaluate each compound: (a) cis-2-butene will have higher heat of hydrogenation than trans-2-butene due to less stability. (b) trans-2-butene will have lower heat of hydrogenation than cis-2-butene. (c) 1,3-butadiene, being a conjugated diene, will be more stable and have the lowest heat of hydrogenation due to resonance stabilization. (d) 1-butene, being an isolated double bond, is less stable than trans-2-butene but more stable than 1-butene.

Key Concepts

Stability of Alkenes

Alkenes are hydrocarbons that contain carbon-carbon double bonds. Their stability depends on several structural factors. Generally, the more substituted a double bond is, the more stable the alkene. Substitution refers to the number of carbon groups attached to the double-bonded carbons.

More substituted alkenes have lower heats of hydrogenation because they are more stable. In simpler terms, when you hydrogenate an alkene, more heat is released if the alkene was less stable to begin with.

To put it simply, compare the number of attached groups:

• Tetrasubstituted > Trisubstituted > Disubstituted > Monosubstituted

Consequently, trans-2-butene is more stable than cis-2-butene due to its trans configuration, which reduces steric hindrance.

Conjugated Dienes

Conjugated dienes are alkenes with two double bonds separated by one single bond, like 1,3-butadiene. This specific arrangement allows the p-orbitals from the alternating double bonds to overlap.

This overlapping lets electrons delocalize over the entire system, providing additional stability via a phenomenon called conjugation.

Due to this stability, conjugated dienes have smaller heats of hydrogenation compared to isolated dienes or simple alkenes. The presence of conjugation means that less energy is needed to maintain the molecule's stable state without saturating it with hydrogen.

Resonance Stabilization

Resonance stabilization is a concept where a molecule can be represented by two or more structures that differ only in the arrangement of electrons.

In the case of conjugated dienes like 1,3-butadiene, resonance contributes significantly to stability because the electron delocalization spreads out charge and lessens energy levels.

The overlap of p-orbitals in conjugated dienes facilitates this, allowing the compound to adopt a resonance hybrid form. Such electronic arrangements are helpful in lowering the energy and hence increasing the stability of the molecule, contributing to a lower heat of hydrogenation.

Cis-Trans Isomerism

Cis-trans isomerism affects the stability of alkenes primarily through steric factors.

In a cis-isomer (like cis-2-butene), the substituents on either side of the double bond are on the same side, creating more steric strain and thus making them less stable.

On the other hand, trans-isomers have substituents on opposite sides, which minimizes steric hindrance and leads to greater stability.

• For example, trans-2-butene is more stable than its cis counterpart due to this reduced steric interference.

This difference in stability due to isomerism directly influences their heats of hydrogenation, with trans forms generally releasing less energy upon hydrogenation compared to cis forms.