Acid-base titration » End point indicators
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Before proceeding with the end point detection discussion we should learn a little bit about the pH indicators behavior.
All pH indicators used for acid-base titration end point detection are weak acids or bases, with acidic form differing in color from the conjugate base. For now let's assume both forms have visible color - that doesn't have to be true, but we will discuss one color indicators separately. Indicator dissociation can be described by the reaction equation:
HInd ↔ H + + Ind -
Let's call its acid dissociation constant KInd :
This equation can be easily rearranged to important form, showing ratio of concentrations of both forms of the indicator:
Observed color of an indicator is a mixture of colors of both forms. At pH=pKInd both forms concentrations are identical (pH-pKInd =0, 10 0 = 1). When pH is one unit below pKInd. concentration of HInd is 10 times higher than concentration of Ind -. when pH is one unit above pKInd - concentration of HInd is 10 times smaller than concentration of Ind - .
If you will consult pH indicator table you will notice that in most cases it lists about 2 pH units distance between pure colors of an indicator. That's because for most hues sensitivity
of human eye is too low to differentiate between colors of solution containing less then 10% of one form of the indicator. Note that this is an individual thing and ranges reported by different researchers for different indicators can differ. It is also possible that particular indicator has more forms and more close dissociation steps, in which case color change can be observed over wider pH range.
As pH indicators are weak acids (or bases), they have to react with titrant - and they will modifiy titration result. Luckily amount of indicators used are so small, that in most cases they can be safely ignored. For example phenolphthalein is used as 0.5% ethanol solution. We usually add about 2-3 drops of this solution to titrated sample. Assuming 20 drops per millilter, density of the solution 0.8 g/mL and molar mass of phenolphthaleine of 318 g/mol, we can calculate amount of added weak acid to be about 2×10 -6 mole. As amount of titrated acids will be usuallly in the millimoles range, added micromoles of indicator can be safely ignored.
In the case of one color indicators we should take into account not only pKInd. but also total concentration of the indicator. Let's assume we have indicator HInd, dissociating according to the reaction
HInd ↔ H + + Ind -
and Ind - is the visible form. Sum of concentrations of both forms is
which is just a mass balance equation. Combining above equations we can write