[brotherwarren]

Hi, I am a UK high school teacher.  I am hoping to get some help answering a question:-

In a titration where a strong base is being added to a weak acid, a plot of the pH value against vol of base added shows an initial rapid change in pH, that becomes less rapid after a few cm3 of base have been added.   

I understand that the explanation for the slowing of the rate of pH change is usually stated as a buffer is being formed.  The first few drops of OH- are being added to a weak acid only, partially neutralising the acid produces a buffer that resists rapid pH change.   
[HA]  [H+] + [A-]
My question is, why does a pure weak acid solution not work as effectively as a buffer at preventing rapid pH change?  In my understanding a buffer resists pH change by shifting the dissociation equilibrium in the direction that replaces H+ ions that have been neutralised by the base.  If this is the case, wouldn't it follow that a weak acid, with large concentration of un-dissociated acid molecules in equilibrium with tiny amount of conjugate base should be able to shift to the right, replacing the H+ ions that have been removed? Why is it necessary to have a high(er) concentration of conjugate base ions in solution before the weak acid molecules are able to begin dissociating?

[AWK]

Buffer solutions work effectively within Bronsted acid to Bronsted base ratio from 1:10 to 10:1. Outside these limits more important are strong Bronsted acid or strong Bronsted base alone.

[Irlanur]

The most straight-forward way to explain this is probably purely physical/mathematical. This is logical, makes perfect sense and predicts everything we want to know about acid/base equilibria.

But I guess this is not what you are looking for.

Your reasoning probably goes somewhat like this:
-Let's say we have a pretty weak and concentrated acid. The pH is very low and most acid molecules are not dissociated.
-Now we add the base, some of the protons are "taken away". the pH rises.
-You would now think that the concentrated acid would give away its protons to counteract the pH change.
Here's the point: it doesn't.

Have a look at the following diagram:
http://pubs.sciepub.com/wjce/2/1/3/figure/2

Acetic Acid simply doesn't dissociate if the pH is too low, it will never provide it's additional protons if you are not close to the pKa value.

[brotherwarren]

Hi Irlanur,

thanks for the link,

try me with the mathematical explanation if you have time?

[Borek]

I am afraid it is not possible to simply answer the question "why". Quite often the only answer is "because that's what you get when you calculate" or "because that's the way it is". Sure, sometimes we can assign the observed effect to something specific, but more often than not we just trick ourselves into believing we know "why".

See these pages for more information related to the math involved:

http://www.titrations.info/acid-base-titration-curve-calculation (and links from there)

http://www.chembuddy.com/?left=pH-calculation&right=pH-buffer-capacity (in relation to the earlier AWK's post)

Note: these pages don't contain answer to "why". They show how to calculate the titration curve from the first principles, and the calculated curve has the property you have asked about.