Problem 14 - Chemistry The Molecular Science

Question

Many natural processes can be studied in the laboratory but only in an environment of controlled \(\mathrm{pH}\). Which of these combinations is the best to buffer the \(\mathrm{pH}\) at approximately 7 ? Explain your choice. (a) \(\mathrm{H}_{3} \mathrm{PO}_{4} / \mathrm{NaH}_{2} \mathrm{PO}_{4}\) (b) \(\mathrm{NaH}_{2} \mathrm{PO}_{4} / \mathrm{Na}_{2} \mathrm{HPO}_{4}\) (c) \(\mathrm{Na}_{2} \mathrm{HPO}_{4} / \mathrm{Na}_{3} \mathrm{PO}_{4}\)

Step-by-Step Solution

Answer

Choose (b) \( \mathrm{NaH}_{2}\mathrm{PO}_{4} / \mathrm{Na}_{2}\mathrm{HPO}_{4} \); it works around pH 7.

Step 1: Understanding Buffer Systems

Buffers resist changes in pH when small amounts of acids or bases are added. The best buffering occurs around the pKa value of the weak acid in the buffer system.

Step 2: Identify pKa Values

The buffer (a) \( \mathrm{H}_{3}\mathrm{PO}_{4} / \mathrm{NaH}_{2}\mathrm{PO}_{4} \) has a pKa near 2.1.(b) \( \mathrm{NaH}_{2}\mathrm{PO}_{4} / \mathrm{Na}_{2}\mathrm{HPO}_{4} \) has a pKa near 7.2.(c) \( \mathrm{Na}_{2}\mathrm{HPO}_{4} / \mathrm{Na}_{3}\mathrm{PO}_{4} \) has a pKa near 12.4.

Step 3: Choose the Best Buffer System

We want a buffer system that works around pH 7, which is close to the pKa of 7.2. Therefore, the best choice is (b) \( \mathrm{NaH}_{2}\mathrm{PO}_{4} / \mathrm{Na}_{2}\mathrm{HPO}_{4} \).

Key Concepts

Buffer Capacity

Buffer capacity refers to the ability of a buffer solution to resist changes in pH when small amounts of an acid or base are added. It's a measure of how well the buffer maintains the pH level. The buffer capacity is determined by two main factors. Firstly, the concentration of the buffering agents; higher concentrations mean a greater capacity to neutralize added acids or bases. Secondly, the pH of the solution in relation to the pKa of the acid present in the buffer system. The closer the pH is to the pKa value, the better the buffer capacity. In practice, this means that a buffer system is most effective in a pH range that is within one unit of its pKa. If the pH moves too far from the pKa, the buffer capacity drops, and the solution's pH can change significantly with the addition of acids or bases.

pKa Values

pKa values are a key concept in understanding buffer systems. The pKa of a compound is the pH at which the acid form of the compound is in equilibrium with its base form. It is a measure of the strength of an acid; lower pKa values indicate stronger acids that dissociate more in solution. The significance of pKa values in buffer systems lies in their relationship with pH. A buffer is most effective when the pH of the solution is approximately equal to the pKa of the acid. This is because at pKa, there are equal amounts of the acid and its conjugate base present. As seen in the choices, the best buffer option is one that has a pKa close to the desired pH of 7, such as choice (b) with a pKa of 7.2, ensuring optimal buffering capacity at that pH level.

Phosphate Buffer System

The phosphate buffer system is a common buffer used to regulate the pH in biological and chemical processes. This system involves a series of phosphate salts which can donate or accept protons, thereby stabilizing pH changes. In the context of the exercise, the phosphate buffer involving

• (H₂PO₄⁻)/HPO₄²⁻
• (NaH₂PO₄/Na₂HPO₄)

with a pKa of 7.2 is particularly useful as it works well around pH 7, a neutral pH that is common in biological systems. This buffer operates by converting between its dihydrogen phosphate ( H₂PO₄⁻ ) and hydrogen phosphate ( HPO₄²⁻ ) forms, thereby resisting changes in pH. This transformation helps maintain a stable environment, crucial for enzyme activities and metabolic processes. Using the right composition of phosphate salts allows the system to neutralize added acids or bases effectively, thus preserving the desired pH.