Problem 16 - Chemistry An Atoms First Approach

Question

Is the conjugate base of a weak acid a strong base? Explain. Explain why \(\mathrm{Cl}^{-}\) does not affect the \(\mathrm{pH}\) of an aqueous solution.

Step-by-Step Solution

Answer

Typically, the conjugate base of a weak acid is a strong base, as a low acid dissociation constant (Ka) value for the weak acid results in a high base dissociation constant (Kb) value for the conjugate base, according to the relationship \(K_{a} \times K_{b} = K_{w}\). However, Cl- ions do not affect the pH of an aqueous solution because they are the conjugate base of a strong acid (HCl), which has a very large Ka value. This leads to a very low Kb value for Cl-, meaning it will not readily react with water molecules or bind with H+ ions, and therefore, does not significantly affect the pH.

Step 1: 1. Definitions of weak acid and conjugate base

A weak acid is an acid that does not completely ionize in an aqueous solution, meaning that it only partially donates its protons (H+ ions) to the solution. The equilibrium constant for the ionization reaction of a weak acid (HA) is called the acid dissociation constant (Ka). HA (aqueous) + H2O (liquid) ⇌ H3O+ (aqueous) + A- (aqueous) A conjugate base is the species that remains after an acid has donated a proton. In the case of the above reaction, A- is the conjugate base of acid HA.

Step 2: 2. Determining if the conjugate base is strong or not

To decide whether a conjugate base of a weak acid is strong or not, we should consider the base dissociation constant (Kb) for the reaction: A- (aqueous) + H2O (liquid) ⇌ HA (aqueous) + OH- (aqueous) A strong base tends to have a high Kb value, meaning that it will quickly bind with H+ ions. On the other hand, a weak base has a lower Kb value, meaning it will not bind as efficiently. In the case of the conjugate base A-, if the weak acid HA has a low Ka value, it means that the dissociation into A- and H+ ions is difficult. As the relationship between Ka and Kb is given by: \(K_{a} \times K_{b} = K_{w}\) where Kw is the ion product constant for water (\(K_{w} \approx 1\times10^{-14}\) at 25°C), a low Ka value results in a high Kb value for the conjugate base, A-. So typically, the conjugate base of a weak acid is a strong base.

Step 3: 3. Explaining why Cl- ions do not affect the pH

Now, we want to explain why Cl- ions do not affect the pH of an aqueous solution. Cl- ions are the conjugate base of hydrochloric acid (HCl), which is a strong acid. This means that HCl fully dissociates into H+ and Cl- ions in water: HCl (aqueous) + H2O (liquid) → H3O+ (aqueous) + Cl- (aqueous) Because HCl is a strong acid, it has a very large Ka value. According to the relationship between Ka and Kb mentioned above, this means that the conjugate base, Cl-, will have a very low Kb value. Therefore, Cl- will not readily react with H2O to form OH- ions or bind with H+ ions to form HCl. Consequently, Cl- ions do not significantly affect the pH of an aqueous solution.