Why is the shape of a pH titration like it is?

Could you account for me the shape of pH curves. I understand that pH=-log(H ions). Could you explain the shape of the curve and relate it to kinetics?

First - What we are plotting here, for a strong acid being titrated by a strong base, is the pH of the solution (= -log10[H+] ) against the volume of base added.

The shape is a sort of S - for a while it goes along more or less flat, then suddenly shoots up (the 'end point') and then flattens out. (It doesn't, of course, go back on itself like a real S).

Why? We know that acids contain H+ and bases OH- and when these are combined they more or less completely react to give water. In fact only one ten millionth of a mole of H+ and OH- are left in a neutral solution, whatever concentration of acid and base you start with. So if you start with an acidic solution it is going to have a pretty low pH (eg a 1 M solution of acid with have a pH of zero). When it is neutral the pH is 7, and when we have added lots of base the pH will be high (1 M base has a pH of 14). The shape comes from taking the log of the concentration. As base is added to the acid although the acid is reacted, as long as there is some left, the pH will stay low. Just after the end point, when all the acid is reacted and the first drop of excess base is added the pH will shoot up. (For example 0.2 mL 0f 0.1 M base in 10 mL of neutral solution will increase the pH from 7 to 11, ie a decrease of 10,000 in the concentration of H+).

An Excel spreadsheet (Office 97 or 2000) is available that has a calculator for strong acid/ strong base pH curves. There is also a graph of the actual H+ and OH- concentrations which shows they behave as you might expect - H+ goes down at a reasonable rate during the titration until it hits 'zero' at the end point. OH- remains at 'zero' until the end point when it starts to rise.

To download the Excel Spreadsheet, click here.

Finally - kinetics don't come into it. The reaction between H+ and OH- is hugely fast and all over as soon as you mix the solutions. What governs the shapes of the curves is thermodynamics - the science of energy changes.

(PS - what I have said works only for 'strong' acids and bases - ones that are completley dissociated into H+ and anion, or OH- and cation. For example: hydrochloric acid, sulfuric acid, nitric acid, sodium and potassium hydroxides. For weak acids (eg acetic acid, citric acid) and bases (ammonia) the curves are similar, but moved up a bit on the axis. They are also more complicated to calculate.)