D38.6 Henderson-Hasselbalch Equation

However, an equation we derived earlier

can be used to significantly simplify this calculation.

First, let’s use the initial concentrations rather than the equilibrium concentrations:

Here, “x” is the change in concentrations as the solution reaches equilibrium, and [HA]₀ and [A⁻]₀ are the initial concentrations of the weak acid and the weak base used to prepare the buffer solution.

When the approximation that “x is at least 100 times smaller than [HA]₀ and [A⁻]₀” is valid, we have the Henderson-Hasselbalch equation:

which is a more straightforward way to calculate the pH of a buffer solution when given the K_a and the initial concentrations, or it can be used to determine the ratio of initial concentrations of weak acid and weak base needed to achieve a desired buffer pH.

The Henderson-Hasselbalch equation applies only to buffer solutions in which the ratio is between 0.1 and 10. If enough strong acid or strong base is added to the buffer solution so that the weak-base-to-weak-acid ratio falls outside of this range, the the solution is no longer a buffer solution and its pH will begin to change significantly. The approximation that x is at least 100 times smaller than [HA]₀ and [A⁻]₀ is no longer valid, and hence you cannot use the Henderson-Hasselbalch equation anymore.