Many students are familiar with the ICE (Initial, Change, Equilbrium) Table when calculating the pH of a weak acid (or weak base) solution. The Henderson-Hasselbach equation will also enable you to calculate the pH of a weak acid (or weak base solution). In this post, I will derive the Henderson-Hasselbach equation from the equilibrium expression. In my next post, I will discuss the similarities and differences between using an ICE table versus using the Henderson-Hasselbach equation.
Our next steps are mathematical in nature. Multiply both sides by [HF] and then divide both sides by [F-] to get by itself.
The next step is to take the negative logarithm of both sides.
For the remainder of the post, I am just going to work with the yellow highlighted section of the above equation. We are going to simplify the equation and get to a value. By our laws of logarithms, when two values are multiplied, it is the same as distributing the log to both values and taking the sum. See below.
A little more manipulation and we can rearrange the part of the equation highlighted in blue. Here you will see me using the exponent rule
Now a logarithm rule:
After these manipulations we can return to our yellow highlighted equation. Our final step is to simplify our expression so that we are using pH and .
And voila! The Henderson-Hasselbach equation derived from the equilibrium expression of hydrofluoric acid.