Acid pKa of heart medicine

Question

A new potential heart medicine, code-named X-281, is being tested by a pharmaceutical company, Pharma-pill. As a research technician at Pharma-pill, you are told that X-281 is a monoprotic weak acid, but because of security concerns, the actual chemical formula must remain top secret. The company is interested in the drug's K_a value because only the dissociated form of the chemical is active in preventing cholesterol buildup In arteries.

To find the pK_a of X-281, you prepare a 0.075 M test solution of X-281 at 25. degrees C. The pH of the solution is determined to be2.70. What is the pK_a of X-281?

Answer 1

Let the monoprotic acid be represented as HA

HA <==> H⁺ + A^-

Ka = [H⁺][A^-] / [HA]

From the pH, we can obtain the [H⁺] and [A^-]

pH = 2.70

pH = -log [H⁺], therefore

[H⁺] = 1x10^-2.70 = 1.995x10^-3 M

Substituting this back into the Ka expression, we have ...

Ka = [1.995x10^-3 M][1.995x10^-3 M] / .075 - 1.995x10^-3 M

Ka = 3.98x10^-6 / 0.0730

Ka = 5.45x10^-5

pKa = -log Ka = -log 5.45x10^-5

pKa = 4.26

Answer 2