Problem 20 - Basic Principles of Organic Chemistry

Question

Optically active sodium 2-bromopropanoate is converted to sodium 2-hydroxypropanoate in water solution. The product has the same stereochemical configuration at \(\mathrm{C}_{2}\) as the starting material and the reaction rate is independent of added \(\mathrm{OH}^{\ominus}\) at moderate concentrations. At higher concentrations of \(\mathrm{OH}^{\ominus}\), the rate becomes proportional to the \(\mathrm{OH}^{\ominus}\) concentration and the 2-hydroxypropanoate formed has the opposite configuration to the starting material. Write appropriate mechanisms to explain these facts. Give your reasoning.

Step-by-Step Solution

Answer

Moderate \(\mathrm{OH}^{\ominus}\): S\(_N1\) mechanism; high \(\mathrm{OH}^{\ominus}\): S\(_N2\) mechanism with inversion.

Step 1: Identify Initial Observations

The reaction involves an optically active sodium 2-bromopropanoate converting to sodium 2-hydroxypropanoate. At moderate concentrations of \(\mathrm{OH}^{\ominus}\), the product retains the same stereochemistry at \(\mathrm{C}_2\). At higher \(\mathrm{OH}^{\ominus}\) concentrations, the stereochemistry is inverted.

Step 2: Mechanism at Moderate Concentrations

At moderate \(\mathrm{OH}^{\ominus}\) concentrations, the reaction proceeds through an S\(_N1\) mechanism. In this mechanism, the bromine atom detaches slowly, forming a carbocation intermediate. Water then attacks this intermediate, resulting in sodium 2-hydroxypropanoate with the same stereochemistry due to internal nucleophilic substitution (retains stereochemistry).

Step 3: Mechanism at High Concentrations

At higher \(\mathrm{OH}^{\ominus}\) concentrations, the reaction proceeds via an S\(_N2\) mechanism. In this scenario, the \(\mathrm{OH}^{\ominus}\) ion directly displaces the bromide in a concerted reaction. During this substitution, inversion of the stereochemical center occurs, leading to a product with the opposite configuration.

Step 4: Reasoning Behind Mechanisms

The independence of reaction rate from \(\mathrm{OH}^{\ominus}\) concentration at moderate levels suggests a carbocation intermediate (S\(_N1\)) where the nucleophile doesn’t affect the rate. At high \(\mathrm{OH}^{\ominus}\) concentrations, the rate dependency and stereochemistry inversion suggest a direct backside attack (S\(_N2\)), leading to inversion.

Key Concepts

S_N1 mechanism

The S\(_N1\) mechanism is a two-step nucleophilic substitution process. It is called "unimolecular" because the rate-determining step depends only on the concentration of the substrate, not the nucleophile. This mechanism typically involves:\

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• Formation of a carbocation: The process starts with the slow detachment of the leaving group, which in our exercise is the bromide ion. This creates a positively charged carbocation intermediate, which is crucial for the next step.
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• Nucleophilic attack: In the exercise, water acts as the nucleophile. It attacks the carbocation, leading to the formation of the product. This approach enables substitution without altering the stereochemistry at the carbon center.
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\The S\(_N1\) mechanism is favored in polar protic solvents, like water, since they stabilize the carbocation formed and facilitate the leaving of the bromide ion. In the given exercise, the product retains the stereochemistry because the attack of the nucleophile is symmetrical around the planar carbocation, which is ultimately the reason for retention of configuration.

S_N2 mechanism

The S\(_N2\) mechanism describes a one-step bimolecular nucleophilic substitution. In this concerted process, the nucleophile attacks simultaneously as the leaving group departs. Key aspects include:\

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• Backside attack: The nucleophile, here the \(\mathrm{OH}^{\ominus}\) ion, approaches from the opposite side of the leaving group, which in the exercise is the bromide ion, thus ensuring a direct swap.
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• Stereochemical inversion: The simultaneous attack and departure result in the flipping of the molecule's spatial arrangement, akin to an umbrella flipping inside out. Thus, the stereochemistry at the configuration center is inverted.
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\The S\(_N2\) mechanism often occurs in polar aprotic solvents where nucleophiles are unsolvated and more reactive. In our exercise, the increase in \(\mathrm{OH}^{\ominus}\) concentration facilitates its role as the nucleophile, leading to the requisite stereochemical inversion and a rate dependent on both substrate and nucleophile concentrations.

Nucleophilic substitution

Nucleophilic substitution involves the replacement of a leaving group by a nucleophile. It is crucial in transforming functional groups in organic molecules and follows either an S\(_N1\) or an S\(_N2\) pathway depending on conditions. \

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• Substrate: The nature of the substrate is pivotal. Tertiary substrates often undergo S\(_N1\) due to stable carbocation formation, while primary substrates prefer S\(_N2\) due to less steric hindrance.
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• Nucleophile: A strong nucleophile tends to push towards an S\(_N2\) mechanism due to its ability to efficiently attack the electrophilic carbon.
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• Solvent: Polar protic solvents stabilize carbocations, favoring S\(_N1\), while polar aprotic solvents enhance nucleophilicity and favor S\(_N2\).
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\In our exercise, the key to understanding the reaction lies in the balance between nucleophile concentration and solvent interaction, highlighting how different conditions promote different substitution mechanisms and thereby affect the stereochemistry of the product.