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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.

What are your thoughts?

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    $\begingroup$ 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. $\endgroup$ – orthocresol Jun 14 '16 at 1:24
  • $\begingroup$ I'm curious though, is 2) really true? If you add H+ to a buffer system will all the H+ react with A-? $\endgroup$ – user2879934 Jun 14 '16 at 1:26
  • $\begingroup$ Your reasoning is right, buffers can't keep pH exactly the same. $\endgroup$ – Ivan Neretin Jun 14 '16 at 7:35
  • $\begingroup$ It is not an all or nothing thing. Not ALL of the H+ will react but it does not invalidate your proof. $\endgroup$ – orthocresol Jun 14 '16 at 10:25
  • $\begingroup$ But when doing buffer pH change problems we assume that all the H+ reacts ... Is that just to simplify the problem? $\endgroup$ – user2879934 Jun 14 '16 at 13:07
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A buffer is a solution that can resist pH change upon the addition of an acidic or basic components. It is able to neutralize small amounts of added acid or base, thus maintaining the pH of the solution relatively stable.

Buffers do not maintain exact same pH, but keep it relatively stable i.e. close to the original value. log(ratio) << pKa, therefore, pH changes will be minimal, unless substantial amount of acid has been added to the solution.

For instance, when the ratio between the conjugate base/acid is equal to 1, the pH = pKa.

If the ratio between the two is 0.10, the pH drops by 1 unit from pKa since log (0.10) = -1.

If a ratio increases to a value of 10, then the pH increases by 1 unit since log (10) = 1.

As you can see, changing ratio by 10 times, affects pH value only by 1 unit.

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