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.

According to the Brønsted-Lowry theory, an acid is a proton donor, and a base is a proton acceptor. When an acid donates a proton, it forms its conjugate base, while when a base accepts a proton, it forms its conjugate acid. In this case, we are considering the conjugate base of a weak acid. A weak acid is one that does not fully ionize in aqueous solution, so it only partially donates its proton(s). These acids have low acid dissociation constants (\(K_a\)). Correspondingly, the conjugate base formed when a weak acid loses a proton has a low tendency to accept protons. Actually, the conjugate base's tendency to accept protons is rated using a base dissociation constant (\(K_b\)). It is essential to understand that if the conjugate acid is weak, with a low \(K_a\), then the conjugate base will generally have a low \(K_b\), which means it will not accept protons easily (it will not be a strong base). So the conjugate base of a weak acid is typically a weak base.

To understand why Cl- does not affect the pH of a solution, let's consider its conjugate acid, which is HCl (hydrochloric acid). HCl is a strong acid, meaning it almost completely ionizes when dissolved in water. Because it donates protons so readily, its \(K_a\) is very high. Now let's analyze Cl-. When looking at a base that is the conjugate of a strong acid, we can consider the relationship between \(K_a\) and \(K_b\). These are related through the formula: \[K_a \times K_b = K_w\] Where \(K_w\) is the ion-product constant for water (\(1.0 \times 10^{-14}\) at 25°C). If the \(K_a\) of a strong acid is very high, the conjugate base's \(K_b\) will be very low, making it extremely weak. Therefore, Cl- will not readily accept protons from water and will not contribute hydroxide ions (OH-) or hydroxonium ions (H3O+) to the solution. In other words, the presence of Cl- will not significantly change the concentration of H3O+ or OH- ions, and hence the pH of the solution remains almost unaffected. In conclusion: 1. The conjugate base of a weak acid is usually a weak base, not a strong one. 2. Cl- does not affect the pH of an aqueous solution because its conjugate acid, HCl, is a strong acid, making Cl- an extremely weak base with no significant proton-accepting capacity.