Re: How does a buffer work and how can I prove it?

You have described the titration curve for a strong acid and base.  pH 
rises slowly with the amount of added base until the vicinity of the 
equivalence point is reached, where it rises sharply.  In this region, a 
drop or 2 of added base will change the pH by 4 or 5 units.

This is because before the equivalence point, the acid is in excess so the 
pH corresponds to the amount of free acid.  Near the equivalence point, 
the pH increases more rapidly if the acid is stronger and increases less 
rapidly if the acid is weaker.  After the equivalence point, base is in 
excess so the curve reflects the amount of base.

Buffer solutions, though contain substantial amounts of both a weak acid 
and a salt of that acid (or a weak base and a salt of that base).  The 
experiment that you did was titration of a strong acid with a strong 
base.  Buffers have the remarkable property of having a pH that remains 
unchanged by addition of small amounts of acid or base or by dilution.

For more, see "Modern University Chemistry" by Norbert T. Porile, p. 271-
282.

-Bonnie