Kₐ: Calculate from pH

Question

In the laboratory, a general chemistry student measured the pH of a 0.533 M aqueous solution of acetylsalicylic acid (aspirin), HC₉H₇O₄ to be 1.883.

Use the information she obtained to determine the K_a for this acid.

K_a(experiment) = 

Answer 1

Let the weak acid, aspirin, be represented by HA.

HA ==> H⁺ + A^-

Ka = [H⁺][A^-] / [HA]

We can find the [H⁺] from the given pH. This will then also be the [A^-]

From pH = 1.883, the [H⁺] = 1x10^-1.883 = 1.31x10^-2 M = [H⁺] = [A^-]

Ka = (1.31x10^-2 )(1.31x10^-2 ) / 0.533

Ka = 3.22x10^-4