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Question

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

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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.

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