Find Ka using pH?

Question

Aspirin (acetylsalicylic acid, C9H8O4) is a weak monoprotic acid. To determine its acid-dissociation constant, we dissolved 2.00g of aspirin in 0.600L of water and measured the pH. What was the Ka value calculated by the student if the pH of the solution was 2.62 ?

Answer 1

so what you have here is a weak acid dissociation.
HA <--> (H+) + (A-)
Ka = [H+][A-] / [HA]
pH = -log[H+]

so set up a table that lists the initial concentration of HA, H, and A, the change in the concentration, and the equilibrium concentrations. initially you only have HA and the concentration is the moles of HA found from the mass divided by the volume.

using the pH determine the concentration of H+. this concentration is equal to the change in concentration. from stoichiometry you know that for every mole of H+ there is there is a mole of A- so you know the equilibrium concentrations of H and A. the equilibrium concentration of HA is the initial concentration minus the change in concentration. so you now have all you need to find Ka