Question

Without doing any calculations, determine if \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}, \mathrm{pH}>\mathrm{p} K_{\mathrm{a}},\) or \(\mathrm{pH}<\mathrm{p} K_{\mathrm{a}} .\) Assume that \(\mathrm{HA}\) is a weak monoprotic acid. a. 0.10 mol \(\mathrm{HA}\) and 0.050 \(\mathrm{mol}\) of \(\mathrm{A}^{-}\) in 1.0 \(\mathrm{L}\) of solution b. 0.10 \(\mathrm{mol} \mathrm{HA}\) and 0.150 \(\mathrm{mol}\) of \(\mathrm{A}^{-}\) in 1.0 \(\mathrm{L}\) of solution c. 0.10 mol \(\mathrm{HA}\) and 0.050 \(\mathrm{mol}\) of \(\mathrm{OH}^{-}\) in 1.0 \(\mathrm{L}\) of solution d. 0.10 \(\mathrm{mol} \mathrm{HA}\) and 0.075 \(\mathrm{mol}\) of \(\mathrm{OH}^{-}\) in 1.0 \(\mathrm{L}\) of solution

Short answer

a. pH < pKa, b. pH > pKa, c. pH < pKa, d. pH > pKa

Step-by-step solution

Understanding the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a relationship between pH, pKa, and the ratio of the concentrations of the conjugate base (A-) to the acid (HA): \[ \text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right) \]. If the ratio \(\frac{[A^-]}{[HA]}\) is equal to 1 (which means [A-] = [HA]), then pH = pKa. If the ratio is greater than 1 (more conjugate base than acid), pH is greater than pKa. If the ratio is less than 1 (more acid than conjugate base), then pH is less than pKa.

Case a: Evaluating the ratio \([A^-]/[HA]\)

For case (a), with 0.10 mol of HA and 0.050 mol of A- in 1.0 L solution, the ratio \([A^-]/[HA]\) is less than 1 (0.050/0.10 = 0.5). Since the ratio is less than 1, the pH will be less than the pKa.

Case b: Evaluating the ratio \([A^-]/[HA]\)

For case (b), with 0.10 mol of HA and 0.150 mol of A- in 1.0 L solution, the ratio \([A^-]/[HA]\) is greater than 1 (0.150/0.10 = 1.5). Therefore, the pH will be greater than the pKa.

Case c: Evaluating the effect of \(OH^-\) on \([A^-]/[HA]\) ratio

In case (c), 0.10 mol of HA will react with 0.050 mol of OH- to form additional 0.050 mol of A-. This will result in 0.10 mol of HA and 0.050 mol of A- in solution (as OH- will completely react with HA), leading to a ratio of \([A^-]/[HA]\) less than 1. Again, the pH will be less than pKa.

Case d: Evaluating the effect of \(OH^-\) on \([A^-]/[HA]\) ratio after complete reaction

In case (d), 0.10 mol of HA will react fully with 0.075 mol of OH-, forming an additional 0.075 mol of A-. After the reaction, there will be 0.025 mol of HA and 0.075 mol of A- in solution, making the ratio \([A^-]/[HA]\) equal to 3. Since this ratio is greater than 1, the pH will be greater than the pKa.

Key concepts

pH and pKa Relationship

The pH of a solution indicates its acidity or alkalinity, measured on a logarithmic scale where lower values mean higher acidity. On the other side, pKa is a constant that represents the acid dissociation equilibrium of a particular acid; it helps to understand the acid strength.

The Henderson-Hasselbalch equation formalizes the relationship between the pH and pKa. It tells us that if a solution has equal amounts of a weak acid and its conjugate base, the pH will equal the pKa of that acid. A solution with a higher concentration of the conjugate base than the weak acid will have a pH value higher than the pKa, while the opposite condition will result in a pH lower than the pKa.

This relationship is essential in determining the buffering range of a solution, a state where the solution can resist changes in pH upon the addition of small amounts of acid or base. Students must remember that the closer the pH is to the pKa, the more effective the solution is as a buffer.

Conjugate Acid-Base Pair

A conjugate acid-base pair consists of two substances that transform into each other by the loss or gain of a proton (hydrogen ion, H+). In any acid-base reaction, the acid donates a proton to the base, resulting in the formation of the conjugate base of the acid and the conjugate acid of the base.

In the context of the Henderson-Hasselbalch equation, the weak acid (HA) donates a proton to become the conjugate base (A-). This pair is critical when determining the pH of a solution, as their ratio is used in the equation. A good buffering solution is made when a weak acid is paired with its conjugate base in significant concentrations, allowing it to neutralize both added acids (H+) and bases (OH-).

For students to fully grasp the importance of this concept, it is helpful to understand how this pair functions in equilibrium reactions, and how their relative concentrations influence the overall pH of the system.

Acid-Base Titration

Acid-base titration is a laboratory technique used to determine the concentration of an unknown acid or base solution by reacting it with a solution of known concentration. During the titration, a pH indicator is often used, or pH measurements are taken to identify the endpoint at which equivalent amounts of acid and base have been mixed.

The significance of the Henderson-Hasselbalch equation in this context is its utility in predicting the pH at various points during the titration. Particularly during the buffering zone, close to the equivalence point, small additions of titrant lead to minimal changes in pH. Understanding the relationship between pH and pKa is also critical when choosing a suitable indicator for the titration that will change color at the desired pH range.

Students should visualize titration curves to better understand how the pH changes as an acidic or basic titrant is added to the solution, helping reinforce their concept of the buffering region and the equivalence point.

Weak Monoprotic Acid Behavior

Weak monoprotic acids, which are acids capable of donating a single proton per molecule, do not fully dissociate in water. Examples of their behavior can be examined through the lens of the Henderson-Hasselbalch equation, where the dissociation process produces the conjugate base and influences the pH of the solution.

When studying this behavior, it is essential to focus on the acid dissociation constant (Ka), which reflects the extent of acid dissociation. A lower Ka means a weaker acid, and a higher Ka means a stronger acid. The pKa, the negative logarithm of Ka, allows us to use the Henderson-Hasselbalch equation to determine the pH. If the solution's pH is lower than the weak acid's pKa, the acid form predominates; if higher, the conjugate base form is more predominant.

Understanding how different factors like the concentration of the acid and the presence of its conjugate base or a strong base (such as OH-) affect the pH is vital. Students should experiment with percentage dissociation and buffer capacity in various scenarios for a comprehensive understanding of weak monoprotic acid behavior.