Problem 18 - Advanced Organic Chemistry. Part A. Structure and Mechanisms

Question

a. The gas phase basicity of substituted \(\alpha\)-methyl styrenes follows the YukawaTsuno equation with \(r^{+}=1.0\). The corresponding \(r^{+}\)for 1 -phenylpropyne is \(1.12\) and for phenylacetylene it is \(1.21\). How are these values related to the relative stability of the carbocations formed by protonation?

Step-by-Step Solution

Answer

Phenylacetylene forms the most stable carbocation, followed by 1-phenylpropyne, and then \(\alpha\)-methyl styrene based on their \(r^+\) values.

Step 1: Understanding Yukawa-Tsuno Equation

The Yukawa-Tsuno equation is an extension of the Hammett equation that includes resonance effects. The equation is used to evaluate the effects of substituents on reaction rates or equilibria, particularly for reactions involving the formation of a positive charge, such as carbocations. It consists of two parameters, \(\sigma\) (the substituent constant) and \(r^+\) (the resonance parameter).

Step 2: Analyze the Given Values

We have the \(r^+\) value for \(\alpha\)-methyl styrene as 1.0, for 1-phenylpropyne as 1.12, and for phenylacetylene as 1.21. These values indicate the degree to which resonance contributes to the stabilization of the intermediate carbocations.

Step 3: Relate r+ Values to Carbocation Stability

An \(r^+\) value greater than 1 suggests enhanced resonance stabilization in the carbocation, while a value less than 1 suggests less resonance stabilization. Here, phenylacetylene with an \(r^+\) of 1.21 indicates the highest resonance stabilization among the three, followed by 1-phenylpropyne and \(\alpha\)-methyl styrene.

Step 4: Conclude Stability Order

Based on the \(r^+\) values, the relative stability of the carbocations is ordered with phenylacetylene being the most stable, followed by 1-phenylpropyne, and \(\alpha\)-methyl styrene being the least stable. This reflects the increasing ability to distribute the positive charge over the substituent's pi system.

Key Concepts

Carbocation Stability

Carbocations are positively charged carbon atoms found as intermediates in many organic reactions. The stability of a carbocation is crucial in determining the rate and outcome of a reaction. The more stable the carbocation, the more likely it is to form.
Carbocation stability depends on several factors, such as the number of alkyl groups attached to the positively charged carbon. This is due to the inductive effect, where more alkyl groups can donate electron density to stabilize the charge.
The order of carbocation stability from least to most stable generally follows:

• Primary (attached to one carbon)
• Secondary (attached to two carbons)
• Tertiary (attached to three carbons)

However, resonance effects can shift this general order. Resonance allows the positive charge to be delocalized over a larger structure, increasing stability. This is why, as seen in the Yukawa-Tsuno analysis, different carbocations can exhibit varying levels of stability when resonance is involved.

Resonance Effects

Resonance is a fundamental concept in organic chemistry that explains how electrons can be distributed over two or more structures. This distribution or delocalization of electrons can greatly stabilize molecules, including carbocations.
When a molecule, like phenylacetylene, has a high resonance effect, the positive charge of a carbocation can be spread over an extended system. This delocalization reduces the energy of the system, making the carbocation more stable.
In the context of the Yukawa-Tsuno equation, resonance effects are quantified by the resonance parameter, \( r^+ \). A higher \( r^+ \) value signifies stronger resonance effects, leading to greater carbocation stabilization. These effects are evident in how the positive charge interacts with the substituents attached to the organic structure.
This is why, in the given exercise, the carbocation of phenylacetylene, with its highest \( r^+ \) value, is the most stable due to its significant resonance stabilization.

Substituent Effects

The presence and type of substituents on a molecule can drastically influence the properties of carbocations. Substituents can either donate or withdraw electron density from the carbocation, affecting its stability.
In the Yukawa-Tsuno framework, substituent effects are evaluated by the substituent constant, \( \sigma \), and its interaction with resonance effects denoted by \( r^+ \). Together, these parameters can predict how a substituent will impact the carbocation's stability.
For instance, electron-donating groups (EDGs) generally stabilize a carbocation by providing electron density to counteract the positive charge. Conversely, electron-withdrawing groups (EWGs) make a carbocation less stable by pulling electron density away.
Understanding these effects allows chemists to predict reaction pathways and design molecules with desired properties by carefully selecting and positioning substituents to achieve optimal carbocation stability.