Acids & Bases Chemistry Math Question 6

Question

An aqueous solution containing 0.24 M of unknown base has a measured pH equal to 8.39. What is the value of pK_b for the unknown base?

Answer 1

Let the unknown base be B

In aqueous solution, you have...

B + H₂O ==>BH⁺ + OH^-

From the pH of 8.39, we can now find the [OH-] which will also be [BH⁺]:

pH = 8.39

pOH = 14 - 8.39 = 5.61

[OH-] = 1x10^5.61 = 2.45x10^-6 M = [ BH⁺]

And we know that Kb = [BH⁺][OH-]/[B], so we can now solve for Kb:

Kb = (2.45x10^-6)(2.45x10^-6)/0.24

Kb = 2.5x10^-11

pKb = -log Kb

pKb = -log 2.5x10^-11 = 10.6