I have a question about a calculation I was just trying to do. For some context, I am trying to calculate the pH of a solution of a weak acid in water. When the concentration of the weak acid is low enough, we need to consider the effect of ionization of the water itself (ie, autoprotolysis of water), since the order of magnitude of this ionization is the same as the order of magnitude of the ions due to the weak acid in this case of very low concentration.
There is a specific formula that can be used for this, which is shown below.
K_a is a constant that depends on the weak acid being considered, and K_w is a constant as well (for the autoprotolysis of water). I am interested in solving for the concentration of hydronium, given an initial concentration of the weak acid [HA]_initial.
I'd like to solve the equation for different values of [HA]_initial.