Acids & Bases Chemistry Math Question 3

Question

If the concentration of an acid in solution is 1.8 times larger than the concentration of its conjugate base, and the pH of the solution is 2.5, what is the pK_a of the acid?

Answer 1

Let the acid be HA and the conjugate base = A-

HA ===> H+ + A-

Ka = [H+][A-][HA]

From pH = 2.5, we can find [H+] = [A-]:

[H+] = [A-] = 1x10^-2.5 = 3.16x10^-3 M

Since HA is 1.8 times [A-], we can calculate the [HA] to be (1.8)(3.16x10-3) = 5.69x10-3 M

Ka = (3.16x10-3)(3.16x10-3) / 5.69x10-3

Ka = 1.75x10^-3

pKa = -log Ka = 2.76