One of the buffer systems used to control the pH of blood involves the equilibrium between H₂PO₄⁻ and H₂PO₄²⁻. The pKₐ for H₂PO₄²⁻ is 7.21. Write the Henderson–Hasselbalch equation for this buffer system.

Verified step by step guidance

1. Identify the components of the buffer system: the weak acid (H₂PO₄⁻) and its conjugate base (HPO₄²⁻).
2. Recall the Henderson–Hasselbalch equation: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the conjugate base and \([\text{HA}]\) is the concentration of the weak acid.
3. Substitute the given pKₐ value into the equation: \( \text{pH} = 7.21 + \log \left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^-]} \right) \).
4. Understand that this equation allows you to calculate the pH of the buffer solution based on the ratio of the concentrations of the conjugate base and the weak acid.
5. Recognize that this buffer system helps maintain the pH of blood by resisting changes in pH when small amounts of acid or base 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 particularly useful in buffer systems to determine the pH based on the ratio of the acid and its conjugate base.

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⁻, helps maintain a stable pH, which is crucial for physiological functions.

pKa and Acid-Base Equilibrium

pKa is a measure of the strength of an acid in solution, representing the pH at which half of the acid is dissociated into its conjugate base. It is a critical value in understanding acid-base equilibria, as it indicates the point at which the concentrations of the acid and its conjugate base are equal. In buffer systems, knowing the pKa allows for the prediction of how the system will respond to changes in pH, making it essential for calculating the pH using the Henderson–Hasselbalch equation.