Problem 13 - Chemistry: An Atoms-Focused Approach

Question

Identify a suitable buffer system to maintain a pH of 3.0 in an aqueous solution.

Step-by-Step Solution

Answer

Answer: The citrate buffer system is suitable for maintaining a pH of 3.0 in an aqueous solution, as it has a pKa value close to the desired pH (pKa1 = 3.13) and the ratio of the conjugate base concentration to the weak acid concentration is approximately 0.74, which is close to 1.

Step 1: Understand the Buffer System and Relationship with pH

A buffer system is made up of a weak acid (HA) and its conjugate base (A-) or a weak base and its conjugate acid. The relationship between pH, pKa, and the concentrations of the weak acid (HA) and its conjugate base (A-) is given by the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]) Where: pH is the pH of the buffer solution pKa is the negative logarithm of the acid dissociation constant (Ka) of the weak acid (HA) [A-] is the concentration of the conjugate base (A-) [HA] is the concentration of the weak acid (HA) We are interested in finding a weak acid and its conjugate base with a pKa value close to the desired pH (3.0) to create an effective buffer system.

Step 2: Research Common Buffer Systems with pKa Values Near 3.0

It is essential to know some common buffer systems and their pKa values. Some buffer systems used in laboratory practice are citrate, phosphate, tris, and acetate buffer systems. The pKa values for these systems are: 1. Citrate buffer system: pKa1 = 3.13, pKa2 = 4.76, pKa3 = 6.40 2. Phosphate buffer system: pKa1 = 2.15, pKa2 = 7.20, pKa3 = 12.3 3. Tris buffer system: pKa = 8.07 4. Acetate buffer system: pKa = 4.76 From the given pKa values, the citrate buffer system seems to have the closest pKa value (pKa1 = 3.13) to the desired pH (3.0).

Step 3: Confirm the Citrate Buffer System as the Suitable Buffer System

To confirm that the citrate buffer system is suitable for maintaining a pH of 3.0, we can plug the pKa1 value of 3.13 from citrate into the Henderson-Hasselbalch equation and check if the ratio of the conjugate base concentration ([A-]) to the weak acid concentration ([HA]) results in an appropriate buffer system. Using the Henderson-Hasselbalch equation: 3.0 = 3.13 + log([A-]/[HA]) We know from the equation above that if the ratio ([A-]/[HA]) is around 1, it should maintain the pH close to 3.0. Solving the equation for the ratio: log([A-]/[HA]) = 3.0 - 3.13 log([A-]/[HA]) = -0.13 Taking the antilog (inverse log) of both sides: [A-]/[HA] = 10^(-0.13) ≈ 0.74 Since the ratio ([A-]/[HA]) is close to 1, the citrate buffer system is appropriate for maintaining a pH of 3.0 in an aqueous solution.