One of the buffer systems used to control the pH of blood involves the equilibrium between H₂PO₄^– and H₂PO₄^2–. The pK_a for H₂PO₄^2– is 7.21.
a. Write the Henderson-Hasselbalch equation for this buffer system.

Verified step by step guidance

1. Step 1: Recall the Henderson–Hasselbalch equation, which is used to calculate the pH of a buffer system. The general form of the equation is: $\mathrm{pH}=\mathrm{pK}$_a+log([A^-][HA]), where [A⁻] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.
2. Step 2: Identify the components of the buffer system in the problem. The weak acid is H₂PO₄⁻, and the conjugate base is HPO₄²⁻.
3. Step 3: Substitute the given pKₐ value (7.21) and the buffer components into the Henderson–Hasselbalch equation. The equation becomes: $\mathrm{pH}=7.21+\log (\frac{\mathrm{[HPO}}{}$₄^2-][H₂PO₄^-]).
4. Step 4: Understand that this equation allows you to calculate the pH of the buffer system if the concentrations of HPO₄²⁻ and H₂PO₄⁻ are known.
5. Step 5: Note that the logarithmic term in the equation represents the ratio of the conjugate base concentration to the weak acid concentration. This ratio determines how the buffer resists changes in pH when acids or bases are added.

Key Concepts

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation is a mathematical formula used to relate the pH of a solution to the concentration of an acid and its conjugate base. It is expressed as pH = pKa + log([A⁻]/[HA]), where pKa is the acid dissociation constant, [A⁻] is the concentration of the conjugate base, and [HA] is the concentration of the acid. This equation is essential for understanding buffer systems in biological contexts, such as blood pH regulation.

Buffer Systems

Buffer systems are solutions that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, which work together to neutralize added acids or bases. In the context of blood, the phosphate buffer system, involving H₂PO₄⁻ and H₂PO₄²⁻, plays a crucial role in maintaining physiological pH levels, which is vital for proper cellular function.

pKa and Acid-Base Equilibrium

pKa is a measure of the strength of an acid in solution, specifically the pH at which half of the acid is dissociated into its conjugate base. It indicates the tendency of an acid to donate protons (H⁺) in a solution. Understanding pKa is crucial for applying the Henderson–Hasselbalch equation, as it helps predict how changes in the concentrations of the acid and base will affect the overall pH of the buffer system.