Henderson hasselbalch equation

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henderson hasselbalch equation

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Henderson-Hasselbalch Equation

Answer: The Henderson-Hasselbalch equation is a fundamental formula in chemistry that relates the pH of a solution to the concentration of an acid and its conjugate base. It is particularly useful in the field of biochemistry for understanding buffer solutions. The equation is derived from the acid dissociation constant (K_a) and is expressed as:

\text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)

Where:

  • \text{pH} is the measure of the acidity or basicity of the solution.
  • \text{p}K_a is the negative base-10 logarithm of the acid dissociation constant (K_a) of the acid.
  • [\text{A}^-] is the concentration of the conjugate base.
  • [\text{HA}] is the concentration of the acid.

Derivation of the Henderson-Hasselbalch Equation

  1. Start with the acid dissociation reaction:

    \text{HA} \leftrightarrow \text{H}^+ + \text{A}^-

  2. Write the expression for the acid dissociation constant (K_a):

    K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}

  3. Rearrange to solve for [\text{H}^+]:

    [\text{H}^+] = \frac{K_a [\text{HA}]}{[\text{A}^-]}

  4. Take the negative logarithm of both sides:

    -\log [\text{H}^+] = -\log \left( \frac{K_a [\text{HA}]}{[\text{A}^-]} \right)

  5. Apply the properties of logarithms:

    \text{pH} = -\log K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)

  6. Recognize that -\log K_a = \text{p}K_a:

    \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)

Applications of the Henderson-Hasselbalch Equation

  1. Buffer Solutions:

    • The equation is essential for calculating the pH of buffer solutions, which are solutions that resist changes in pH upon the addition of small amounts of acid or base.
    • By knowing the concentrations of the acid and its conjugate base, one can determine the pH of the buffer solution.

  2. Biological Systems:

    • In biochemistry, the Henderson-Hasselbalch equation is used to understand the pH of blood and other bodily fluids, which is critical for maintaining proper physiological functions.
    • It is also used in enzyme kinetics and the study of metabolic pathways where pH plays a critical role.

  3. Pharmaceuticals:

    • The equation helps in the formulation of drugs, ensuring that they remain stable and effective at the desired pH.

Example Calculation

Suppose you have a buffer solution containing 0.1 M acetic acid (HA) and 0.1 M sodium acetate (A^-). The K_a of acetic acid is 1.8 \times 10^{-5}.

  1. Calculate \text{p}K_a:

    \text{p}K_a = -\log(1.8 \times 10^{-5}) \approx 4.74

  2. Use the Henderson-Hasselbalch equation:

    \text{pH} = 4.74 + \log \left( \frac{0.1}{0.1} \right)

  3. Simplify the log term:

    \log \left( \frac{0.1}{0.1} \right) = \log(1) = 0

  4. Calculate the pH:

    \text{pH} = 4.74 + 0 = 4.74

Therefore, the pH of the buffer solution is 4.74.

In conclusion, the Henderson-Hasselbalch equation is a versatile and powerful tool in chemistry and biochemistry for understanding the relationship between pH, acid and base concentrations, and the acid dissociation constant. It is widely used in various scientific and industrial applications to maintain and control pH levels.