So I came across a question on the equation of the pH curve, and I wanted to know how the user here arrived at the matter balance equation. Any help would be appreciated!
Here is the question:
The reason behind the steep rise in pH in the acid base titration curve
Nicolau already outlined it quite clearly in his answer.
Notice that after mixing the solutions, the number of moles of species containing $\ce{A}$ ($\ce{HA}$ or $\ce{A−}$) is simply $n_A = C_A V_A$
so you have $n_{\ce{HA}} + n_{\ce{A-}} = C_A V_A$
We will assume that volumes are additive (total volume $V_T = V_A + V_B$)
and given that $[\ce{HA}] = n_{\ce{HA}}/V_T$ and $[\ce{A-}] = n_{\ce{A-}}/V_T$ it should be fairly clear that
$$[\ce{HA}] + [\ce{A-}] = \frac{C_A V_A}{V_A + V_B}$$
as desired.
