What is Kb of this base?

Question

An unknown weak base with a concentration of 0.170 M has a pH of 9.56. What is the Kb of this base?

Answer 1

Bronsted-Lowry Base equation B + H₂O ⇒ BH⁺ + OH^- and K_B = [BH⁺][OH^-]/[B] at equilibrium (Think NH₃ = B)

Assuming that the base is weak but stronger than water, we can assume the amount of production of BH⁺ = OH^- and the concetration of OH^- is obtained from the 10^-pOH = 10^-(14-pH) = 3.63 x 10^-5M (That swamps the 10^-7M in pure water (3% error))

K_B = (3.63 x 10^-5M)²/(.17M) (the denominator should be .17-[OH-], but that only affects the 6th sig fig, so it is negligible)

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