I know that there already exist multiple questions concerning buffers and buffer capacities, but I would nevertheless like to clarify two things with your help:
Adding to a buffer $n$ moles of an acid of negligible volume or a solution of the same acid (also containing $n$ moles of the acid) both produce the same change in $pH$. Correct?
However there is a difference between the two, as the latter diminishes the buffer's capacity. How can I observe, from a mathematical standpoint, the decrease in the buffer capacity for the second approach; more precisely: Given,say an acidic buffer solution of volume $V_i$ with $HA$ being the weak acid and $A^-$, its conjugate base (with concentrations $c_a, c_b$ respectively), how does the buffer capacity change upon the addition of a solution of volume $V_s$, containing $n$ moles of a strong base?
Any help would be appreciated.