Question

In terms of transition-state theory, account for the following solvent effects: $(a)$ The rate of solvolysis of a $3^{\circ} \mathrm{RX}$ increases as the polarity of the protic nucleophilic solvent $(\mathrm{SH})$ increases, e.g. $$ \mathrm{H}_2 \mathrm{O}>\mathrm{HCOOH}>\mathrm{CH}_3 \mathrm{OH}>\mathrm{CH}_3 \mathrm{COOH} $$ (b) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction $: \mathrm{Nu}^{-}+\mathrm{RX} \rightarrow \mathrm{RNu}+: \mathrm{X}^{-}$decreases slightly as the polarity of protic solvent increases. (c) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction : $\mathrm{Nu}+\mathrm{RX} \rightarrow \mathrm{RNu}^{+}+: \mathrm{X}^{-}$increases as the polarity of the solvent increases. $(d)$ The rate of reaction in $(b)$ is greatly increased in a polar aprotic solvent. $(e)$ The rate of the reaction in $(b)$ is less in nonpolar solvents than in aprotic polar solvents. See Table 7-2. (e) In nonpolar solvents, $\mathrm{Nu}^{-}$is less reactive because it is ion-paired with its countercation, $\mathrm{M}^{+}$. $\mathrm{S}_{\mathrm{N}} 2$ reactions with $\mathrm{Nu}^{-}$'s are typical of reactions between water-soluble salts and organic substrates that are soluble only in nonpolar solvents. These incompatible reactants can be made to mix by adding small amounts of phase-transfer catalysts, such as quaternary ammonium salts, $\mathrm{Q}^{+} \mathrm{A}^{-} . \mathrm{Q}^{+}$has a watersoluble ionic part and nonpolar $\mathrm{R}$ groups that tend to be soluble in the nonpolar solvent. Hence, $\mathrm{Q}^{+}$ shuttles between the two immiscible solvents while transporting $\mathrm{Nu}^{-}$, as $\mathrm{Q}^{+} \mathrm{Nu}^{-}$, into the nonpolar solvent; there $\mathrm{Nu}^{-}$quickly reacts with the organic substrate. $\mathrm{Q}^{+}$then moves back to the water while it transports the leaving group, $\mathrm{X}^{-}$, as $\mathrm{Q}^{+} \mathrm{X}^{-}$. Since the positive charge on the $\mathrm{N}$ of $\mathrm{Q}^{+}$is surrounded by the $\mathrm{R}$ groups, ion-pairing between $\mathrm{Nu}^{-}$and $\mathrm{Q}^{+}$is loose, and $\mathrm{Nu}^{-}$is quite free and very reactive.

Name: Problem 25, Chapter 7: Schaum's Outline of Organic Chemistry
Uploaded: 2021-10-25T08:18:10-08:00
Duration: 1 min 14 s
Channel: Sana Riaz

    In terms of transition-state theory, account for the following solvent effects: $(a)$ The rate of solvolysis of a $3^{\circ} \mathrm{RX}$ increases as the polarity of the protic nucleophilic solvent $(\mathrm{SH})$ increases, e.g.
$$
\mathrm{H}_2 \mathrm{O}>\mathrm{HCOOH}>\mathrm{CH}_3 \mathrm{OH}>\mathrm{CH}_3 \mathrm{COOH}
$$
(b) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction $: \mathrm{Nu}^{-}+\mathrm{RX} \rightarrow \mathrm{RNu}+: \mathrm{X}^{-}$decreases slightly as the polarity of protic solvent increases. (c) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction : $\mathrm{Nu}+\mathrm{RX} \rightarrow \mathrm{RNu}^{+}+: \mathrm{X}^{-}$increases as the polarity of the solvent increases. $(d)$ The rate of reaction in $(b)$ is greatly increased in a polar aprotic solvent. $(e)$ The rate of the reaction in $(b)$ is less in nonpolar solvents than in aprotic polar solvents.
See Table 7-2.

(e) In nonpolar solvents, $\mathrm{Nu}^{-}$is less reactive because it is ion-paired with its countercation, $\mathrm{M}^{+}$.
$\mathrm{S}_{\mathrm{N}} 2$ reactions with $\mathrm{Nu}^{-}$'s are typical of reactions between water-soluble salts and organic substrates that are soluble only in nonpolar solvents. These incompatible reactants can be made to mix by adding small amounts of phase-transfer catalysts, such as quaternary ammonium salts, $\mathrm{Q}^{+} \mathrm{A}^{-} . \mathrm{Q}^{+}$has a watersoluble ionic part and nonpolar $\mathrm{R}$ groups that tend to be soluble in the nonpolar solvent. Hence, $\mathrm{Q}^{+}$ shuttles between the two immiscible solvents while transporting $\mathrm{Nu}^{-}$, as $\mathrm{Q}^{+} \mathrm{Nu}^{-}$, into the nonpolar solvent; there $\mathrm{Nu}^{-}$quickly reacts with the organic substrate. $\mathrm{Q}^{+}$then moves back to the water while it transports the leaving group, $\mathrm{X}^{-}$, as $\mathrm{Q}^{+} \mathrm{X}^{-}$. Since the positive charge on the $\mathrm{N}$ of $\mathrm{Q}^{+}$is surrounded by the $\mathrm{R}$ groups, ion-pairing between $\mathrm{Nu}^{-}$and $\mathrm{Q}^{+}$is loose, and $\mathrm{Nu}^{-}$is quite free and very reactive.

Schaum's Outline of Organic Chemistry

George Hademenos,… 3rd Edition

Chapter 7, Problem 25

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Solved by Expert Sana Riaz

10/25/2021

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Transition-state theory explains how the rate of a chemical reaction is influenced by the energy barrier between reactants and products. The transition state is the highest energy state along the reaction path, and the rate of reaction depends on how easily this Show more…

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In terms of transition-state theory, account for the following solvent effects: $(a)$ The rate of solvolysis of a $3^{\circ} \mathrm{RX}$ increases as the polarity of the protic nucleophilic solvent $(\mathrm{SH})$ increases, e.g. $$ \mathrm{H}_2 \mathrm{O}>\mathrm{HCOOH}>\mathrm{CH}_3 \mathrm{OH}>\mathrm{CH}_3 \mathrm{COOH} $$ (b) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction $: \mathrm{Nu}^{-}+\mathrm{RX} \rightarrow \mathrm{RNu}+: \mathrm{X}^{-}$decreases slightly as the polarity of protic solvent increases. (c) The rate of the $\mathrm{S}_{\mathrm{N}^2}$ reaction : $\mathrm{Nu}+\mathrm{RX} \rightarrow \mathrm{RNu}^{+}+: \mathrm{X}^{-}$increases as the polarity of the solvent increases. $(d)$ The rate of reaction in $(b)$ is greatly increased in a polar aprotic solvent. $(e)$ The rate of the reaction in $(b)$ is less in nonpolar solvents than in aprotic polar solvents. See Table 7-2. (e) In nonpolar solvents, $\mathrm{Nu}^{-}$is less reactive because it is ion-paired with its countercation, $\mathrm{M}^{+}$. $\mathrm{S}_{\mathrm{N}} 2$ reactions with $\mathrm{Nu}^{-}$'s are typical of reactions between water-soluble salts and organic substrates that are soluble only in nonpolar solvents. These incompatible reactants can be made to mix by adding small amounts of phase-transfer catalysts, such as quaternary ammonium salts, $\mathrm{Q}^{+} \mathrm{A}^{-} . \mathrm{Q}^{+}$has a watersoluble ionic part and nonpolar $\mathrm{R}$ groups that tend to be soluble in the nonpolar solvent. Hence, $\mathrm{Q}^{+}$ shuttles between the two immiscible solvents while transporting $\mathrm{Nu}^{-}$, as $\mathrm{Q}^{+} \mathrm{Nu}^{-}$, into the nonpolar solvent; there $\mathrm{Nu}^{-}$quickly reacts with the organic substrate. $\mathrm{Q}^{+}$then moves back to the water while it transports the leaving group, $\mathrm{X}^{-}$, as $\mathrm{Q}^{+} \mathrm{X}^{-}$. Since the positive charge on the $\mathrm{N}$ of $\mathrm{Q}^{+}$is surrounded by the $\mathrm{R}$ groups, ion-pairing between $\mathrm{Nu}^{-}$and $\mathrm{Q}^{+}$is loose, and $\mathrm{Nu}^{-}$is quite free and very reactive.

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Key Concepts

SN1 and SN2 Reaction Mechanisms

The reaction mechanism—whether SN1 or SN2—dictates how solvent effects influence the overall rate. In SN1 reactions, which proceed via carbocation intermediates, polar protic solvents stabilize both the intermediate and the transition state, often accelerating the reaction. However, in SN2 reactions, where a single concerted step involves simultaneous bond-making and bond-breaking, solvent effects such as nucleophile solvation and ion pairing can markedly affect reactivity; polar aprotic solvents favor faster reactions by minimizing solvation of the nucleophile.

Phase-Transfer Catalysis

Phase-transfer catalysis bridges the gap between reactants in different phases by using a catalyst that can transport an ion from an aqueous (or polar) phase into an organic (or nonpolar) phase. The catalyst, typically a quaternary ammonium salt, forms a loose ion pair with the nucleophile, enhancing its solubility in the organic phase and making it more available for reaction. This process significantly increases the reaction rate by effectively overcoming the solubility and ion pairing issues in heterogeneous mixtures.

Ion Pairing and Reactivity

Ion pairing occurs when a charged nucleophile associates closely with a counterion, particularly in nonpolar or weakly polar solvents. This pairing reduces the effective concentration of free nucleophilic species available to participate in reactions, thereby decreasing the reaction rate. Understanding ion pairing is crucial because it explains why nucleophiles in some solvents are less reactive despite being thermodynamically favorable for the reaction.

Solvent Polarity Effects

Solvent polarity has a profound influence on the reactivity of chemical processes by stabilizing or destabilizing the transition state and intermediates. Polar solvents can stabilize charged or highly polar transition states through solvent-solute interactions, such as dipole-dipole interactions or hydrogen bonding, which reduces the activation energy and accelerates the reaction rate. The relative solvating power of the solvent is critical in reactions involving ionic species or polar transition states.

Transition State Theory

Transition State Theory explains reaction rates by focusing on the energy barrier between reactants and products – the transition state. It asserts that a reaction’s rate increases when the transition state is stabilized relative to the reactants. Solvent effects play a pivotal role in this stabilization by interacting with charged or polar groups present in the transition state, thereby lowering the activation energy required for the reaction.

Nucleophile Solvation

The degree to which a nucleophile is solvated by the surrounding solvent impacts its reactivity. Protic solvents, characterized by their ability to hydrogen-bond, strongly solvate anionic nucleophiles, often leading to a reduction in their effective nucleophilicity in SN2 reactions. In contrast, polar aprotic solvents, which lack hydrogen-bond donors, solvate cations more effectively than anions, leaving the nucleophile less hindered and more reactive towards electrophilic centers.

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