A certain weak base B has a base-ionization constant K_b of 5.9 × 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

Let x be the concentration of [BH+] = [S1U1P1-] in the final solution.
Then the concentration of [B] = [S1U1B0]= [S1S1P0] = x.
The equation is:
KS1U1B1bS1U1B0/KS1U1P1S1S1B= [S1U1P1-]/[S1U1B0]
5.9 × 10S1U1P1-4S1S1P0/ x = x / x,
which simplifies to:
x² = 5.9 × 10S1U1P1-4S1S1P0,
taking the square root of both sides:
x = [BH+] = [S1U1P1-] = [B] = [S1S1P0]= ([B]₀ + [BH+]) / 2 = (x+x)/2
pH = -log([H+]) = -log([BH+]) = -log(x)
pH = -log(5.9 × 10S1U1P1-4S1S1P0) / 2 = 10.8.

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

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