# Evaluate indicator choice (phenolphthalein)

A student wishes to find the concentration of a $$\pu{50 mL}$$ solution of acetic acid $$(K_\mathrm{a} = \pu{1.8e-5}).$$ He performs a titration using a solution of $$\pu{0.2 M}$$ sodium hydroxide. The student selects phenolphthalein as his indicator choice which has a $$K_\mathrm{a} = \pu{3.98e-10}.$$ Justify the student’s choice of indicator.

My attempt: I found the $$\mathrm{p}K_\mathrm{a}$$ of the indicator to be $$9.4$$ and the fact that the titration was weak acid + strong base meant the $$\mathrm{pH}$$ at equivalence would be around that too, so the indicator was justified. In saying this, my justification isn’t very mathematical.

1. $$99.9\%$$ of acetic acid is titrated at about
$$\mathrm{pH} = \mathrm{p}K_\mathrm{a} + \log{1000} = 7.75$$
2. $$100\%$$ of acetic acid is titrated at
$$\mathrm{pH} = 7 + \frac12 \cdot (\mathrm{p}K_\mathrm{a} + \log c) = 9.385 + \frac12 \log c$$
3. Phenolphthalein color transition is $$8.2-10.0.$$