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If we value a 20 mL solution of 0.25 M acetic acid with a 0.1M solution of NaOH

The end point of the titration is reached when 50 mL of NaOH is added from the burette. At this point, the pH of the solution is 8.81

Since the pH at the end point is 8.81, phenolphthalein, whose pKa is 9.7, has been used as an indicator.

I need to calculate the error associated with using this indicator, because as the turn does not exactly coincide with the pH at the end point, there must be some error.

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    $\begingroup$ Phenolphthalein is a fine indicator for this titration, but the answer you seek depends on just how well the titration was done. At the titration end point, the phenolphthalein should be the faintest pink you can see, as distinct from the colorless solutions, and it fades quickly because of carbon dioxide dissolving in the swirled solution. So, if the end point was really pink, the end point error would be larger than it would otherwise have been. Practice helps a great deal. $\endgroup$
    – Ed V
    Apr 8, 2020 at 20:04
  • $\begingroup$ Also, have a look at this nice answer by @MaxW : chemistry.stackexchange.com/a/88650/79678. $\endgroup$
    – Ed V
    Apr 8, 2020 at 20:14
  • $\begingroup$ The error is not related to the choice of the indicator. It is related to the number of drops, needed to be sure that you have obtained the equivalent point. $\endgroup$
    – Maurice
    Apr 8, 2020 at 20:35
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    $\begingroup$ @Maurice - RE: "The error is not related to the choice of the indicator." -- That is not true. There is a definite bias in the analysis due to the difference between the pH at the equivalence point and the pH at which the indicator is noticed to change. It would be very unusual for the two pH values to be equal. $\endgroup$
    – MaxW
    Apr 8, 2020 at 20:40
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    $\begingroup$ @MaxW. You are right. I have not been precise enough. I should have said that when titrating acetic acid with NaOH using phenolphtalein as an indicator, the main error is not related to the choice of the indicator. It is in the doubt about plus or minus one drop of NaOH added $\endgroup$
    – Maurice
    Apr 8, 2020 at 20:53

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For future titration practices, you should never use the buret until the end. Most high quality burets (Class A) are limited to 50 mL (max) or even 25 mL. If it is a made up exercise by a teacher, they should not promote this approach either. You will have far more error from the incorrect volume measurements rather than the choice of your indicator. Also be careful with reporting concentrations: 0.1 M NaOH is not the same as 0.10 M NaOH.

Anyway, one cannot determine the indicator error from the given data. Practically, you would plot a pH titration curve on a graph paper. Determine the equivalence point (= the true point at which the titration is stoichiometrically complete) from the graph. Lets say, you get 40.56 mL (last digit estimated). With an indicator you get an end-point at 40.60 mL. The end-point is the point where the indicator "hints" you the end of the titration. Now the excess concentration of acetic acid calculated via the end-point is your indicator error.

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