Question

Although the acid-dissociation constant for phenol $\left({\mathrm{C}}_6{\mathrm{H}}_5\mathrm{OH}\right)$ is listed in Appendix $\mathrm{D}$, the base-dissociation constant for the phenolate ion $\left({\mathrm{C}}_6{\mathrm{H}}_3{\mathrm{O}}^{-}\right)$is not. (a) Explain why it is not necessary to list both $K_a$ for phenol and $K_b$ for the phenolate ion. (b) Calculate $K_b$ for the phenolate ion. (c) Is the phenolate ion a weaker or stronger base than ammonia?

Short answer

The acid-dissociation constant (Ka) and base-dissociation constant (Kb) are related through the ion-product constant of water (Kw) using the expression $K_w=K_a\times K_b$. Therefore, it is not necessary to list both Ka and Kb values. The Ka for phenol is 1.3 × 10^-10, so the Kb for the phenolate ion is 7.7 × 10^-6, which is less than the Kb of ammonia (1.8 × 10^-5). Thus, the phenolate ion is a weaker base than ammonia.

Step-by-step solution

Explain the Relationship between Ka and Kb

The acid-dissociation constant (Ka) and base-dissociation constant (Kb) are related through the ion-product constant of water (Kw). The ion-product constant of water is given by the expression: $$K_w=K_a\times K_b$$ Since we are given the value of Ka and we know the value of Kw (1.0 × 10^-14 at 25°C), we can easily determine Kb using this relationship. Therefore, there is no need to list both Ka and Kb values for phenol and the phenolate ion.

Calculate Kb for the Phenolate Ion

To calculate Kb for the phenolate ion, we'll use the given Ka value for phenol and the ion-product constant for water (Kw). We can use the expression: $$K_b=\frac{K_w}{K_a}$$ Given, Ka for phenol is 1.3 × 10^-10 and Kw = 1.0 × 10^-14. Now we can plug in these values to calculate Kb: $$K_b=\frac{1.0\times {10}^{-14}}{1.3\times {10}^{-10}}$$ $$K_b=7.7\times {10}^{-6}$$ So, Kb for the phenolate ion is 7.7 × 10^-6.

Compare Kb of Phenolate Ion to Ammonia

Now we need to compare the Kb of the phenolate ion to the Kb of ammonia to determine if the phenolate ion is a stronger or weaker base. The Kb of ammonia is 1.8 × 10^-5. Since 7.7 × 10^-6 (Kb of phenolate ion) is less than 1.8 × 10^-5 (Kb of ammonia), we can conclude that the phenolate ion is a weaker base than ammonia.

Key concepts

Acid-Dissociation Constant (Ka)

The acid-dissociation constant, represented as Ka, is a quantitative measure of the strength of an acid in solution. It is defined as the equilibrium constant for the chemical reaction where an acid donates a proton to water, forming the conjugate base of the acid and a hydronium ion. This dissociation can be represented in a general chemical equation as:

Let's break it down into simpler terms. A higher Ka value signifies a stronger acid, as it indicates that the acid is more likely to donate its proton. For instance, to understand the relative strengths of acids, comparing their Ka values provides insights into which is more likely to participate in proton exchange. Understanding the concept of acid dissociation is crucial for predicting the behavior of acids in various chemical reactions.

Base-Dissociation Constant (Kb)

In parallel to Ka, the base-dissociation constant (Kb) measures the strength of a base. It represents the equilibrium position for the reaction of a base with water to produce the corresponding conjugate acid and a hydroxide ion. The base-dissociation reaction can be depicted as: The Kb value offers insight into the propensity of a base to accept a proton. A higher Kb value means the base is stronger, and more likely to react with H2O to form OH- ions, thus increasing the pH of the solution. Understanding Kb is essential for those studying chemistry to anticipate and explain the behavior of bases in various chemical contexts.

Ion-Product Constant of Water (Kw)

A fundamental concept in acid-base chemistry is the ion-product constant of water, known as Kw. It represents the equilibrium constant for the self-ionization of water, where two water molecules react to form a hydronium ion and a hydroxide ion: For pure water at 25°C, the Kw value is commonly known to be 1.0 × 10^-14. This value remains constant irrespective of changes in concentration of H3O+ and OH- ions, meaning that at equilibrium, the product of these ion concentrations will always equal Kw at a given temperature. Should the concentration of one ion increase, the other must decrease to maintain the constant Kw. This plays a significant role in understanding the interplay between pH, pOH, and the strength of acids and bases in a solution.

Phenol and Phenolate Ion Relationship

Moving on to an application of these concepts, let's examine the relationship between phenol and its conjugate base, the phenolate ion. Phenol is a weak acid that partially dissociates in solution, while the phenolate ion is its conjugate base formed when phenol donates a proton. The acid-dissociation constant for phenol is a measure of this reaction's extent, and it can be used to infer the basicity of the phenolate ion through the relationship with the ion-product constant of water (Kw).

The equilibrium constants Ka and Kb are inversely related, as shown by the formula Kw = Ka * Kb. Therefore, knowing Ka of phenol allows us to calculate the Kb for the phenolate ion. This is essential for predicting the behavior of the phenolate ion in chemical reactions, particularly when compared to other bases such as ammonia. By understanding this balance, one can discern why the phenolate ion is a weaker base than ammonia, which has a higher Kb value. This insight is critical when exploring reaction mechanisms and the potential outcomes of acid-base interactions in various chemical systems.