What is the pH of the solution at this point in the titration?

Question

Two drops of a phenolphthalein indicator solution are added to a 30.0 mL solution of 0.12 M hydrofluoric acid. The solution is titrated with 0.097 M sodium hydroxide until a faint pink color is visible. The pKa of HF is 3.46.

Answer 1

The faint pink color should occur at the equivalence point which means when the moles of base (NaOH) equals the moles of acid (HF). And because NaF is the salt of a weak acid and a strong base, the pH will be basic (>7)

moles HF = 30.0 ml x 1 L/1000 ml x 0.12 mole/L = 0.0036 mol

Now we need the volume of NaOH to provide 0.0036 moles NaOH....

(x L)(0.097 mol/L) = 0.0036 moles and x = 0.0371 L = 37.1 mls

Total final volume = 30.0 mls + 37.1 mls = 67.1 mls = 0.0671 L

We did all of this so that we can find the final concentration of the NaF that is formed based on the following:

HF + NaOH ==> H₂O + NaF

0.0036 mol NaF / 0.0671 L = 0.0537 M

Now we must look at the hydrolysis of the salt, NaF, or simply F^-...

F^- + H₂O ==> HF + OH^-

Kb = [HF][OH^-] / [F^-] and since pKa = 3.46 the pKb must be 14 - 3.46 = 10.54 and then Kb = 2.88x10^-11

2.88x10^-11 = (x)(x) / 0.0537

x² = 1.55x10^-12

x = 1.24x10^-6 M = [OH^-]

pOH = -log 1.24x10^-6 = 5.90

pH = 14 - pOH

pH = 8.1 (note our prediction of a basic pH is correct)