Question

A very old and tired , grey haired AP Chem instructor wanted to determine the Ka of an unlabelled monoprotic acid in his stockroom. He dissolved an unknown amount of acid in an unknown amount of water and proceeded to titrate the sample with a solution of NaOH of unknown molarity. After adding 10.0 ml of NaOH, he uttered that famous first order expletive “Oh, Michigan State”. He stopped and measured the pH of the solution at that point and found pH= 5.0. He continued to add NaOH until he realized he didn’t add phenolphthalein to the solution. He added 3 drops and the solution remained colorless. He continued the titration and found the equivalence point to be 32.22 ml of the NaOH solution. Can our intrepid hero calculate the Ka? Hint: he can. So calculate the Ka. Show all of your work.