What is the Henderson–Hasselbalch equation to calculate the ratio of HCO3- and H2CO3 in blood with a pH of 7.40, given that the value of Ka for carbonic acid at body temperature (37 degrees Celsius) is 7.9 x 10^-7?

Verified step by step guidance

1. Identify the Henderson–Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the base form (HCO3-) and \([\text{HA}]\) is the concentration of the acid form (H2CO3).
2. Calculate the pKa from the given Ka value using the formula \( \text{pKa} = -\log(\text{Ka}) \).
3. Substitute the given pH value (7.40) and the calculated pKa into the Henderson–Hasselbalch equation.
4. Rearrange the equation to solve for the ratio \( \frac{[\text{HCO}_3^-]}{[\text{H}_2\text{CO}_3]} \).
5. Use the properties of logarithms to express the ratio in terms of powers of 10, if needed, to simplify the interpretation of the result.

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 negative logarithm of the acid dissociation constant (Ka). This equation is particularly useful in biochemistry for understanding buffer systems in biological fluids.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, indicating how well it donates protons (H+) to water. A lower Ka value signifies a weaker acid, while a higher value indicates a stronger acid. For carbonic acid, with a Ka of 7.9 x 10^-7 at body temperature, this value helps determine the equilibrium concentrations of HCO3- and H2CO3 in blood at a specific pH.

Buffer Systems in Blood

Buffer systems in blood, primarily involving bicarbonate (HCO3-) and carbonic acid (H2CO3), help maintain a stable pH in the physiological range. These buffers resist changes in pH by neutralizing excess acids or bases. The Henderson–Hasselbalch equation is essential for calculating the ratio of these components, which is crucial for understanding acid-base balance in the body, especially at a pH of 7.40.