An aqueous basic solution has a concentration of 0.050 M and K_b is 4.4 × 10^-4.What is the concentration of hydroxide ion in this solution (M)? A)2.2 × 10^-5 B)4.5 × 10^-3 C)2.9 × 10^-3 D)4.7 × 10^-3 E)0.050

Question

Quizplus · Accepted Answer

The concentration of hydroxide ion (OH-) can be found using the equilibrium constant expression for the ionization of water:

Kw = [H+][OH-] = 1.0 × 10^-14

In a basic solution, [OH-] > [H+]. We can assume that the contribution of [H+] from the autoionization of water is negligible compared to the concentration of OH- from the base.

The Kb expression is:

Kb = Kw/Ka

Since the base is not given, we can assume it is the conjugate base of a weak acid, and use the Kb expression.

B + H2O ⇌ BH+ + OH- 
Kb = [BH+][OH-]/[B]

Under equilibrium conditions, [BH+] ≈ 0 since the acid is weak, so Kb ≈ [OH-]^2/[B].

Substituting the given values,

4.4 × 10^-4 = x^2/(0.050 - x)

Since x is much smaller than 0.050, we can make the approximation

Kb ≈ [OH-]^2/0.050

Solving for [OH-] gives

[OH-] = sqrt(Kb*0.050) = 4.5 × 10^-3 M

Therefore, the correct answer is B.

An Aqueous Basic Solution Has a Concentration of 0