Calculate buffer pH with Henderson-Hasselbalch.
The Henderson-Hasselbalch equation says a buffer's pH is set by its pKa plus the logarithm of the base-to-acid ratio. Because the term is logarithmic, the pH is remarkably insensitive to dilution — halving both concentrations leaves the ratio and therefore the pH unchanged. A buffer works best when that ratio is near 1, which puts the pH at the pKa; beyond a ten-to-one ratio in either direction the buffer is nearly exhausted.
Henderson-Hasselbalch
pH = pKa + log10([conjugate base] / [weak acid]); pOH = 14 - pH
Because only the ratio of the two species appears in the equation. Diluting the buffer tenfold divides both concentrations by ten, leaving the ratio unchanged — although the buffer capacity, the amount of acid or base it can absorb, does fall proportionally.
Approximately pKa plus or minus 1 pH unit, which corresponds to base-to-acid ratios between 1:10 and 10:1. Outside that range one component is nearly depleted and small additions of acid or base swing the pH sharply.
At very dilute concentrations below roughly 0.001 M, where water's own ionisation matters, and at high ionic strength where activity coefficients diverge from concentrations. It also assumes the weak acid dissociates only slightly, which fails for pKa values below about 2.