Question

Is tert-butoxide anion a strong enough base to react with water? In other words, can a solution of potassium tert-butoxide be prepared in water? The \(\mathrm{p} K_{\mathrm{a}}\) of tert-butyl alcohol is approximately \(18 .\)

Short answer

Potassium tert-butoxide cannot be prepared in water; it reacts to form hydroxide ions.

Step-by-step solution

Define the Reaction

Understand the reaction in question. The tert-butoxide anion (\((CH_3)_3CO^-\)) is the conjugate base of tert-butyl alcohol \((CH_3)_3COH\). We are looking at the potential equilibrium reaction: \((CH_3)_3CO^- + H_2O \rightleftharpoons (CH_3)_3COH + OH^-\).

Use the pKa to Determine Base Strength

Given that the \( \mathrm{p}K_a \) of tert-butyl alcohol is 18, we can say that tert-butoxide anion is a strong base. Typically, strong bases are conjugate bases of weak acids, indicated by a high \( \mathrm{p}K_a \).

Assess the Feasibility of Dissolution in Water

Since tert-butoxide is a strong base, it will react with water by accepting a proton: \((CH_3)_3CO^- + H_2O \rightarrow (CH_3)_3COH + OH^-\). This means it cannot coexist with water without reacting.

Conclusion on Solution Preparation

Because tert-butoxide reacts readily with water to produce hydroxide ions \((OH^-)\) and tert-butyl alcohol, potassium tert-butoxide cannot be practically prepared in an aqueous solution.

Key concepts

Conjugate Base

In acid-base reactions, the concept of a conjugate base is essential. When an acid donates a proton \(H^+\), it forms its conjugate base. For tert-butyl alcohol \((CH_3)_3COH\), when it loses a proton, it forms the tert-butoxide anion \((CH_3)_3CO^-\). This anion now becomes the conjugate base of tert-butyl alcohol.
Understanding the concept of conjugate bases helps clarify the behavior of acids and bases in reactions.

• A stronger acid has a weaker conjugate base.
• A weaker acid has a stronger conjugate base.

In our scenario, tert-butoxide \((CH_3)_3CO^-\) is the stronger conjugate base derived from the weaker acid, tert-butyl alcohol, because of its relatively high \(\mathrm{p}K_a\) value of 18. Recognizing the characteristics of conjugate bases allows us to predict the outcomes of their interactions with water and other substances.

pKa value

The \( \mathrm{p}K_a \) value is a numerical representation that indicates the strength of an acid. It is calculated as the negative logarithm of the acid dissociation constant \( K_a \). A higher \( \mathrm{p}K_a \) signifies a weaker acid, while a lower \( \mathrm{p}K_a \) indicates a stronger acid. \( \mathrm{p}K_a \) values can thus help infer details about the base derived from the acid, also known as the conjugate base.
This is because a weak acid, like tert-butyl alcohol with a \( \mathrm{p}K_a \) of 18, will have a strong conjugate base in tert-butoxide \((CH_3)_3CO^-\). Knowing the \( \mathrm{p}K_a \) can guide us in predicting and explaining the reactivity patterns observed in acid-base reactions.

• High \( \mathrm{p}K_a \): weak acid, strong conjugate base.
• Low \( \mathrm{p}K_a \): strong acid, weak conjugate base.

This insight is crucial when assessing whether a base will accept a proton in a given reaction.

Base Strength

Base strength is an essential factor to consider in acid-base chemistry. It indicates how readily a base will accept a proton. Strong bases arise from the conjugate bases of weaker acids. In the context of tert-butoxide \( (CH_3)_3CO^- \), it is considered a strong base because it comes from a weak acid, tert-butyl alcohol, with a high \( \mathrm{p}K_a \) of 18.
This strong base will readily react with available protons, such as those in water \( H_2O \), to form the corresponding alcohol \( (CH_3)_3COH \) and hydroxide ions \( OH^- \).

• Strong bases quickly accept protons.
• Weak bases are less reactive in proton transfer.

Understanding base strength helps determine the feasibility of reactions and stability of solutions. Since tert-butoxide is a strong base, it makes it challenging to prepare a stable aqueous solution without reaction.

Equilibrium Reaction

An equilibrium reaction is essential in understanding the balance between reactants and products in a chemical equation. In the case of tert-butoxide and water, the reaction \( (CH_3)_3CO^- + H_2O \rightleftharpoons (CH_3)_3COH + OH^- \) represents an equilibrium reaction where there is a continuous, dynamic exchange between forward and reverse reactions.
This equilibrium illustrates the tendency of a strong base like tert-butoxide to shift the balance toward the products \( (CH_3)_3COH \) and \( OH^- \).

• In equilibrium, both reactants and products are present.
• The direction of the equilibrium can be influenced by the strength of acids and bases involved.

Because tert-butoxide shifts the equilibrium significantly towards forming hydroxide ions, preparing a potassium tert-butoxide solution in water results in rapid generation of these ions. This makes the solution unstable and unsuitable for certain applications, demonstrating the practical limits based on equilibrium dynamics.