# Best pH indicator for titration

Which substance is best suited as a pH indicator for titration of $$\pu{15 mL}$$ of $$\pu{0.1 M}$$ ascorbic acid $$(K_\mathrm{a} = \pu{7.9E-5})$$ with $$\pu{1.0 M}$$ sodium hydroxide solution? Using the image below to find the best suited substance. My progress:

$$\mathrm{p}K_\mathrm{a} = -\log (\pu{7.9E-5}) = 4.102,$$

then

$$\mathrm{pH} = 4.102 + \log\frac{\pu{0.1 M}}{\pu{1.0 M}} = 3.102$$

I am quite sure this is wrong, but don't know what I should do.

• Your calculation does not make sense. If you want to titrate a solution of a weak acid with a strong base like NaOH, you should choose an indicateur whose pKa is approximately half-way between the pKa of your weak acid and the pH of you basic solution. For your ascorbic acid solution, whose pKa is $4.1$, titrated by NaOH whose pH is $14$, the average is pH = $9$. Phenolphtalein is the best choice, because its color changes between $8.2$ and $9.5$ Dec 13, 2020 at 17:44
• thanks so much for the answer, what about if we would titrate a solution of a strong acid with a weak base, how would I choose the best suited indicator? Dec 13, 2020 at 19:21
• Usually this titration is made in the other way. The basic solution is in a beaker where the strong acid is added drop by drop from a burette. Anyhow, you choose the indicator by calculating the average of the pH of the strong acid and of the pKa of the weak base (14 - pKb of this base). Dec 13, 2020 at 20:10
• @Maurice Usually? You cannot titrate by adding the weak base/acid. You'd need to know the concentrations beforehand, for startes, and the curve would be so shallow you cannot make out anything. Not to mention the complications by huge concentration change.
– Karl
Dec 14, 2020 at 10:17
• @Karl. So you would replace "usually" by "always" in my last comment. I agree with you. I simply did'nt want to criticize the author too abruptly. Dec 14, 2020 at 11:05

For titration of weak acids by strong bases, usable are generally indicators with transition from less to more intense colour in mild pH range. Typical, available and frequently used one is phenolphthalein with range 8.2-10.0.

To take it more analytically, you can find pH of the point of equivalence as pH of solution of weak base with $$\mathrm{p}K_\mathrm{b}=14-\mathrm{p}K_\mathrm{a}$$.

We can justify two simplifying assumptions $$c \gg [\ce{OH-}] \gg [\ce{H+}]$$

$$\mathrm{pOH} =0.5(\mathrm{p}K_\mathrm{b} - \log {c})$$

$$\mathrm{pH} =14 - 0.5(14 - \mathrm{p}K_\mathrm{a} - \log {c})$$

$$\mathrm{pH} =7 + 0.5(\mathrm{p}K_\mathrm{a} + \log {c})$$

$$\mathrm{pH} =9.05 + 0.5 \log{0.1}=8.65$$

Then choose the indicator with the range the equivalence point about falls into. Phenolphthalein will be ideal.

• Thanks for adding the answer :) Dec 24, 2021 at 17:15