Question

A very old and tired , grey haired AP Chem instructor wanted to determine the K_a 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 turned dark pink. Now he was really irritated and dropped an “Oh, Ohio State” on the situation. At this point he had added 34.68 ml of NaOH. He thought for a moment and then carefully began to add the unknown acid back to the titration mixture. He added back 2.62 ml of the unknown acid which caused the solution to become colorless. Can our intrepid hero calculate the K_a ? Hint : he can. So calculate the K_a Show all of your work.

this is due tomorrow morning so i'd reaaly apperciate an answer now

Answer 1

Yes he can, first adding the 2.62 mL extra of acid, means that the equivalence point is reached at the following volume:

34.68 - 2.62 = 32.06 mL this is the volume of the equivalence point, and we need to find the pKa. so, let's reason for a moment:

I figure at 10 mL, where the pH = 5, at that point some of the "base"(the anion) has been formed so you should be able to use the Henderson-Hasselbalch equation and calculate pKa.
pH = pKa + log(base)/(acid)
5.0 = pKa + log (base)/(acid)
At 10 mL it seems to me that the base formed is 10/32.06.

How much of the acid is left at this point? It has neutralized 10 mL so it has another 22.06 mL to go so that fraction is 22.06/32.06.

Substitute into the HH equation and solve for pKa.

5 = pKa + log (10/32.06 / 22.06/32.06)

5 - log (10/22.06) = pKa

pKa = 5.3436

Ka = 10^(-5.3436)

Ka = 4-53x10^-6

This should be the correct value. Hope this helps, and tell me in a comment if there's something you need to be fixed.