Question

Choice of Weak Acid for a Buffer Determine whether each weak acid would best buffer at \(\mathrm{pH} 3.0\), at \(\mathrm{pH} 5.0\), or at \(\mathrm{pH} 9.0\) : a. formic acid \(\left(p K_{\mathrm{x}}=3.8\right)\); b. acetic acid \(\left(p K_{a}=4.76\right)\); c. ammonium \(\left(\mathrm{p} K_{\mathrm{n}}-9.25\right) ;\) d. boric acid \(\left(\mathrm{p} K_{\mathrm{a}}=9.24\right)\); e. chloroscetic acid \(\left(\mathrm{p} K_{\mathrm{z}}=2.87\right)\); f. hycdrazoic acid \(\left(p K_{a}=4.6\right)\). Briefly justify your answer.

Short answer

Formic and chloroscetic acids buffer at pH 3.0; acetic and hydrazoic acids at pH 5.0; ammonium and boric acids at pH 9.0.

Step-by-step solution

Understand the Role of pK_a in Buffering

A weak acid is most effective as a buffer at a pH close to its pK_a value. It can buffer pH changes most effectively within a range of about ±1 pH unit from its pK_a.

Analyze Each Acid's pK_a with Respect to Given pH Values

Compare each acid's pK_a with the target pH values (3.0, 5.0, and 9.0) to determine which pH it is most suitable to buffer.- Formic acid (\(pK_a = 3.8\)): Ideal for buffering around\(pH 3.8\), hence suitable for \(pH = 3.0\).- Acetic acid (\(pK_a = 4.76\)): Ideal for \(pH ≈ 4.76\), closest to \(pH = 5.0\).- Ammonium (\(pK_n = 9.25\)): Ideal for \(pH ≈ 9.25\), suitable for \(pH = 9.0\).- Boric acid (\(pK_a = 9.24\)): Also suitable for\(pH ≈ 9.0\), similar to ammonium.- Chloroscetic acid (\(pK_z = 2.87\)): Ideal for \(pH ≈ 2.87\), closest to \(pH = 3.0\).- Hydrazoic acid (\(pK_a = 4.6\)): Best at around\(pH = 4.6\), suitable for \(pH = 5.0\).

Match Acids to Ideal Buffering pH

List each weak acid with its most appropriate buffering pH based on the analysis:- Formic acid: Buffers best at \(pH 3.0\).- Acetic acid: Buffers best at \(pH 5.0\).- Ammonium: Buffers best at \(pH 9.0\).- Boric acid: Also buffers best at \(pH 9.0\).- Chloroscetic acid: Best suited for \(pH 3.0\).- Hydrazoic acid: Best for \(pH 5.0\).This distribution ensures the acids are used near their effective pK_a range.

Key concepts

pKa

In chemistry, the term "pKa" is a vital concept when discussing buffer solutions. It represents the acid dissociation constant, which is a quantitative measure of the strength of an acid in the solution. The formula to express it is:\[pK_a = -\log_{10}(K_a)\]Where \(K_a\) is the equilibrium constant of the acid dissociation reaction. The importance of pKa lies in its ability to help us predict the pH at which an acid can easily donate or accept protons, making it essential for buffer solutions. A buffer is most effective when the pH of the solution is close to the pKa of the weak acid or weak base it contains. This is because at this pH, the concentrations of the acid and its conjugate base are comparable and can neutralize added acids or bases. For example, formic acid with a pKa of 3.8 is ideal for buffering a pH close to its pKa, making it suitable for environments like pH 3.0.

Weak Acids

A weak acid is characterized by its partial dissociation in a solution, unlike strong acids which dissociate completely. This partial dissociation is expressed by their equilibrium constant (\(K_a\)) and their pKa value which tends to be higher than that of strong acids. Weak acids are integral to buffer solutions because they can resist changes in pH when small amounts of acids or bases are added. This property is due to the presence of both the weak acid and its conjugate base in the solution, which can react to neutralize additions of H\(^+\) ions or OH\(^-\) ions.Here's why weak acids are chosen for buffer systems:

• They help resist drastic pH changes, maintaining a stable environment.
• They can maintain a near-constant pH over a range of conditions.
• Their nearly equal amounts of weak acid and conjugate base make them efficient at neutralizing added substances.

pH Selection

Choosing the appropriate pH for a buffer solution involves aligning the solution's pH as closely as possible to the pKa of the buffering agent used. This choice is crucial because a buffer can effectively resist changes in pH within a range of approximately ±1 unit around its pKa. For instance, if targeting a pH environment of 5.0, acetic acid with a pKa of 4.76 would be ideal. When selecting the pH, consider:

• Analyze the compatibility of the buffer's pKa with the intended pH environment.
• Ensure the buffer can resist changes effectively within the required pH range.
• Use the Henderson-Hasselbalch equation to adjust the buffer system according to needs:\[pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)\]

This equation helps determine the necessary ratio of acid and conjugate base needed in the buffer solution to achieve the desired pH.

Buffer Capacity

Buffer capacity refers to the ability of a buffer solution to maintain its pH when an acid or base is added. It's a measure of the buffer's resistance to changes in pH. The buffer capacity depends on the concentrations of both the weak acid and its conjugate base present in the solution. Generally, higher concentrations equate to greater buffer capacity because more of the acid-base pair can neutralize added acids or bases. However, it is crucial to note: - The capacity is highest when the pH is equal to the pKa. - It decreases as the pH moves away from the pKa. - Large amounts of added acid or base can exceed the buffer capacity, causing a significant shift in pH. Choosing the right buffer capacity ensures that the solution remains consistently at the target pH, particularly in biological and chemical processes where precise pH control is necessary.