Question

Consider the equation: \(\mathrm{HA}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\) \(\mathrm{A}^{-}(a q)\). a. If water is a better base than \(\mathrm{A}^{-}\), which way will equilibrium lie? b. If water is a better base than \(\mathrm{A}^{-}\), does this mean that HA is a strong or a weak acid? c. If water is a better base than \(\mathrm{A}^{-}\), is the value for \(K_{\mathrm{a}}\) greater or less than \(1 ?\)

Short answer

a. The equilibrium will lie to the right. b. HA is a strong acid. c. \(K_a > 1\).

Step-by-step solution

Identify the reaction and the given condition

For the given reaction: HA(aq) + H2O(l) ⇌ H3O+(aq) + A⁻(aq) We are given the condition: Water is a better base than A⁻. Our goal is to analyze the reaction equilibrium, acid strength, and determine if Ka is greater or less than 1.

Determine the equilibrium direction

If water is a better base than A⁻, it means it will be more willing to accept a proton than A⁻. In this scenario, the reaction will favor the side where water acts as a base, and it will more readily react with the acid (HA), taking a proton and forming H3O+. As a result, the equilibrium will lie to the right, forming more H3O+ and A⁻ ions. a. So, the equilibrium will lie to the right.

Determine whether HA is a strong or weak acid

If water is a better base than A⁻, the dissociation of HA will be easier since water is more willing to accept the proton. Consequently, HA will readily give up its proton in the presence of water, suggesting that HA is a strong acid. b. This means that HA is a strong acid.

Determine if Ka is greater or less than 1

Considering the acid equilibrium constant, Ka, which is defined as: Ka = \(\frac{[H_3O^+][A^-]}{[HA][H_2O]}\) Since water is a better base than A⁻ and HA is a strong acid, the reaction will have more dissociated HA into H3O+ and A⁻ ions. As a result, the [H3O+] and [A⁻] concentrations will be high, and [HA] will be relatively low. Therefore, Ka will be greater than 1 (for strong acids, Ka > 1). c. Ka > 1.

Key concepts

Acid-Base Reactions

Acid-base reactions are a cornerstone of chemistry that involve the transfer of protons (H⁺) between reactants. In the given exercise, we encounter such a reaction, where an acid (HA) donates a proton to water (H₂O), producing a hydronium ion (H₃O⁺) and the conjugate base (A⁻), according to the reversible reaction:

HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq)

The direction in which the equilibrium of this reaction lies is pivotal for understanding the acid's behavior. When water is a better base than the conjugate base A⁻, this implies that water has a higher affinity for protons. Thus, the equilibrium will shift to the right, favoring the production of H₃O⁺ and A⁻. This shift indicates that the reaction has a strong tendency to proceed in the forward direction when water acts as the base, a crucial concept for grasping the nature of the acid involved.

Acid Dissociation Constant (Ka)

Understanding Ka

The acid dissociation constant, Ka, quantifies the degree of dissociation of an acid in water, determining how well it releases its protons. It is defined by the equilibrium expression:

Ka = \(\frac{[H_3O^+][A^-]}{[HA][H_2O]}\)

The higher the Ka value, the more the acid dissociates to form protons and its conjugate base, and the stronger the acid is considered to be. In correlation with the exercise, if water is a better base than A⁻ and effectively takes up protons from HA, we would see larger concentrations of H₃O⁺ and A⁻ ions. Consequently, this would result in a larger Ka value (Ka > 1), indicative of a strong acid. Conversely, if Ka is less than 1, the acid is weak and does not dissociate significantly in water.

Strong and Weak Acids

Distinguishing Acid Strength

Acids are categorized as strong or weak based on their ability to dissociate in water. Strong acids, such as HCl, dissociate completely, providing an abundance of H⁺ ions, while weak acids only partially dissociate, leaving a majority of the acid molecules intact.

In the context of the exercise, since water is a better base than the conjugate base A⁻, HA tends to lose its proton more readily. This behavior is characteristic of strong acids—they're eager to part with their protons. Therefore, the implication here is that HA is a strong acid. Recognizing the strength of an acid is not only important for predicting the outcome of reactions but also for understanding the implications for acidity, pH levels, and the reactivity of compounds in various environments.