Question

When cis-2-decalone is dissolved in ether containing a trace of \(\mathrm{HCl}\), an equilibrium is established with trans-2-decalone. The latter ketone predominates in the equilibrium mixture.

Short answer

Answer: The equilibrium mixture is influenced by the thermodynamic stability of the isomers. The trans-2-decalone predominates because it is more stable due to reduced steric interactions between the bulky alkyl groups.

Step-by-step solution

Understanding the reaction and reagents

Cis-2-decalone is a type of ketone with a cis-configuration of its two alkyl groups at the 2-position. In the presence of an acid like HCl, a reaction can take place that interconverts the cis and trans forms (isomers). Ether is a non-polar organic solvent, which does not participate directly in the reaction but provides an environment for the process to occur. A trace of HCl means that it is present in a very small amount, and it will act as a catalytic agent in this reaction.

Mechanism of cis to trans isomerization in ketones

The reaction mechanism undergoes the following steps: 1. Protonation of the carbonyl oxygen: The acidic hydrogen from HCl forms a bond with the carbonyl oxygen, resulting in an oxonium ion (a more electrophilic carbon). 2. Formation of intermediate: The protonated carbonyl group allows for a nucleophilic attack by one of the neighboring alkyl groups, forming a cyclic intermediate. 3. Alkyl group migration: As the reaction proceeds, the alkyl group undergoes migration, leading to a new carbonyl group formation. 4. Deprotonation: The newly protonated oxygen gets deprotonated by the solvent or a base, reforming the ketone. This series of steps ultimately converts the cis-2-decalone into trans-2-decalone.

Equilibrium favors trans-2-decalone

The trans-2-decalone predominates in the equilibrium mixture as it is the more thermodynamically stable isomer. This can be explained in terms of sterics - as in the trans isomer, the bulky alkyl groups are farther apart, reducing steric interactions and leading to a lower energy state compared to the cis isomer. In conclusion, the reaction of cis-2-decalone with a trace of HCl in ether solvent results in an equilibrium mixture that predominately contains the thermodynamically more stable trans-2-decalone isomer. This reaction mechanism involves protonation, alkyl group migration, and deprotonation steps, and the equilibrium is influenced by the stability of the isomers.

Key concepts

Cis-Trans Isomerism

Cis-trans isomerism, also known as geometric isomerism, is a form of stereoisomerism. It describes a scenario where two molecules have the same molecular formula but differ in the spatial arrangement of their functional groups.

In ketones, specifically, cis-trans isomerism can occur when there are two substituent groups on the same side of the molecule (cis) or opposite sides (trans). The existence of these isomers can significantly affect the chemical properties and reactivity of the compounds.

This is demonstrated in the case of the ketone exercise, with cis-2-decalone and trans-2-decalone. While they share the same molecular formula, their spatial arrangement around the carbonyl group leads to differences in their stability and, as a result, influences the position of the equilibrium when an isomerization reaction occurs.

Ketone Reaction Mechanism

The ketone reaction mechanism, particularly in isomerization processes, is characterized by several key steps. Initially, the presence of an acid catalyst, such as HCl, leads to the protonation of the carbonyl oxygen of the ketone. This step significantly increases the electrophilic character of the carbonyl carbon and sets the stage for further reaction.

Intermediate Creation

Following protonation, an alkyl group in close proximity can attack, forming a cyclic intermediate that is vital to the isomerization process.

Alkyl Migration

The intermediate then undergoes a crucial alkyl migration, which effectively shifts the position of functional groups, resulting in the conversion from cis to trans or vice versa. Finally, deprotonation occurs, and the ketone is restored.

Mechanistically, this series of steps is a dance of electrons and atoms shifting positions to lead us from the starting ketone to its isomerized counterpart.

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, meaning that the concentrations of reactants and products remain constant over time. This dynamic but stable state is perfectly illustrated in the isomerization of ketones.

When cis and trans isomers interconvert through the reaction mechanism, they eventually reach a point where both the forward (cis to trans) and reverse (trans to cis) reactions occur at the same pace. The equilibrium position is influenced by the stability of the products and reactants, which is often a consequence of steric and electronic factors.

In the given exercise, the equilibrium mixture predominantly contains trans-2-decalone because it is thermodynamically more stable, having less steric strain compared to the cis isomer. Understanding how various factors influence equilibrium provides students with insights into predicting which side of a reaction will be favored under different conditions.