# Proof of buffers inability to maintain exact same pH

I was wondering if the following is a legitimate proof of the statement above. Assume we have

HA -> A- + H+

where [HA] + [A-] is our buffer.

If we add a small amount of H+ one of two things will happen:

1) The H+ will not react with A- ...thereby raising the pH so we are done.

2) The H+ will react with A- ...converting to [HA]

looking at the HH equation we know that

pH = pKa + log(ratio)

since ratio_before != ratio_after

pH_after = pKa + log(ratio_after) and pH_before = pKa + log(ratio_before)

so therefore

pH_after - log(ratio_after) = pH_before -log(ratio_before)

Now assume pH_after == pH_before.... we get -log(ratio_after) = -log(ratio_before) which is a contradiction of above, so pH_after != pH_before.

• Not sure if I'm reading maths, programming, or chemistry... Anyway, yes. Buffers are not intended to maintain the exact same pH and indeed they cannot. They are designed to maintain the pH within a small range acceptable for whatever system you are studying. – orthocresol Jun 14 '16 at 1:24
• I'm curious though, is 2) really true? If you add H+ to a buffer system will all the H+ react with A-? – user2879934 Jun 14 '16 at 1:26
• Your reasoning is right, buffers can't keep pH exactly the same. – Ivan Neretin Jun 14 '16 at 7:35
• It is not an all or nothing thing. Not ALL of the H+ will react but it does not invalidate your proof. – orthocresol Jun 14 '16 at 10:25
• But when doing buffer pH change problems we assume that all the H+ reacts ... Is that just to simplify the problem? – user2879934 Jun 14 '16 at 13:07