A certain weak base B has a base-ionization constant K_b of 6.6 × 10^-4 at 25°C.If strong acid is added to a solution of B,at what pH will [B] = [BH⁺]? A)8.5 B)10.8 C)7.0 D)3.2 E)5.5

Question

Quizplus · Accepted Answer

The equation for the ionization of the weak base B is:

B + H2O ↔ BH+ + OH-

The equilibrium constant for this reaction is the base-ionization constant, which has a value of 6.6 × 10-4 at 25°C. We can use this equilibrium constant to find the pH at which [B] = [BH+].

Let x be the concentration of [BH+] (and [OH-] by conservation of charge), then the concentration of [B] is also x. The concentration of [H+] is initially zero (as we are starting with a weak base in water), but as we add strong acid, the concentration of [H+] will increase. Let [H+] be y.

The equation for the reaction between strong acid and the weak base is:

H+ + B ↔ BH+

The equilibrium constant for this reaction is:

Ka = [BH+][H+] / [B]

We can write the acid dissociation constant for the strong acid as:

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

where [A-] and [HA] are the concentrations of the conjugate base and acid, respectively.

Since we are adding strong acid, we can assume that initially [A-] = 0 and [HA] = y (the concentration of the strong acid added). Therefore:

Ka' = [H+]y / y = [H+]

Substituting this into the expression for Ka gives:

Ka = x( [H+] / 6.6 × 10-4 ) = [H+] ( x / 6.6 × 10-4 )

At equilibrium, we have:

[H+] + [OH-] = Kw / [H+] = 1.0 × 10-14 / [H+]

where Kw is the ion-product constant of water.

Substituting this and x = [BH+] = [B] into the expression for Ka gives:

[H+] = 6.6 × 10-4 / x

Substituting this and the equation for [OH-] into the equation for Kw:

6.6 × 10-4 / x × x / (1.0 × 10-14 / 6.6 × 10-4 x) = 1.0 × 10-14

x2 = Kw / Ka = 1.52 × 10-11

x = [BH+] = [B] = sqrt(1.52 × 10-11) = 3.9 × 10-6

Therefore, pOH = -log[OH-] = -log(3.9 × 10-6) = 5.4

pH = pKw - pOH = 14.0 - 5.4 = 8.6

So the best choice is B (rounded to one decimal place).

A Certain Weak Base B Has a Base-Ionization Constant Kb

A Certain Weak Base B Has a Base-Ionization Constant K_b