For example, if I am using 1-10 uM of solute so that buffer solution should be 1mM, 100 mM or 1M (or it doesn’t matter).
it seems that solutes salting out at higher buffer concentration.
The buffering capacity of buffer (resistance of pH change when H+ or OH- is added) is proportional to the concentration of the buffer. When pH = pKa (buffers containing an equal quantity of acid and its salt) the capacity is maximum. More simply, if about 10% (relative to the buffer concentration) of OH- or H+ is added to the solution, the change is less than 0.05 pH units (for 1% it is about 0.004 units, etc.). Remember that pH = pKa - log(AH/A-). So a factor of 10 relative to a solute (the species which brings H+ or OH- to the solution) seems to be a minimum, but depends on the tolerance of your process to pH changes. Note that the buffer capacity decreases when the condition pH = pKa is no longer fulfilled.
The Henderson Hasselbalch equation : pH= Pk + log (A-/HA) allows you to determine
the change of ph for any ratio. Of course this is solution chemistry.If you exceed the solubility of the salt then you are in a more complex system.
To complete the Joaquim answer and mine, you can evaluate the pH change (as I did) from the Henderson Hasselbalch equation : pH = pKa + log(A-/HA) (similar to the one I gave) by calculating log (A-/HA) for (A-/HA) ratios slightly different from 1 (0.9 or 1.1 for a buffer excess of 10, 0.99 or 1.01, for a buffer excess of 100, etc). This is what I did in my answer. When you are not exactly at pH = pKa the change may be evaluated by calculating -for example- a pH change when log(A-/HA) change from 1.1 to 1.2 (more basic side) or 0.9 to 0.8 (acidic side).
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