What is the hydronium-ion concentration in a solution resulting from mixing 133 mL of 0.100 M HCN and 80 mL of 0.100 M KOH at 25°C? K_a for HCN = 4.9 × 10^-10 at 25°C. A)3.5 × 10^-6 M B)7.0 × 10^-6 M C)2.7 × 10^-13 M D)3.2 × 10^-10 M E)1.0 × 10^-13 M

Question

Quizplus · Accepted Answer

The balanced chemical equation for the reaction between HCN and KOH is:

HCN + KOH → H2O + KCN

From the equation, we can see that the same number of moles of HCN and KOH react to form water and KCN.

First, we need to calculate the number of moles of HCN and KOH in the solution:

moles HCN = 0.133 L * 0.100 mol/L = 0.0133 mol
moles KOH = 0.080 L * 0.100 mol/L = 0.0080 mol

Since the same number of moles of HCN and KOH react, the limiting reactant is KOH (it has fewer moles). Thus, all the KOH will be consumed by the reaction, and 0.0080 mol of HCN will also react.

The initial concentration of HCN was 0.100 M, but only 0.0080 mol of HCN remained after the reaction, so the concentration of HCN in the final solution is:

[HCN] = 0.0080 mol / (0.133 L + 0.080 L) = 3.2 × 10^-2 M

Next, we need to calculate the concentration of hydronium ions (H3O+) in the solution. The reaction between HCN and KOH produces CN- (cyanide) ions, which can react with water to form HCN and OH- (hydroxide) ions through a reversible reaction:

CN- + H2O ⇌ HCN + OH-

The equilibrium constant for this reaction is Kw/Ka, where Kw is the ion product constant of water (1.0 × 10^-14 at 25°C) and Ka is the acid dissociation constant of HCN (4.9 × 10^-10 at 25°C). Thus:

Kw/Ka = (1.0 × 10^-14) / (4.9 × 10^-10) = 2.04 × 10^-5

At equilibrium, the product of the concentrations of HCN and OH- ions is equal to this constant:

[HCN][OH-] = Kw/Ka = 2.04 × 10^-5

We know that the initial concentration of OH- ions is zero, and that some HCN has reacted to form OH- ions. So we can use the equilibrium expression to calculate the concentration of H3O+ ions (since [H3O+][OH-] = Kw):

[H3O+] = Kw / [OH-] = Kw / (Kw/Ka/[HCN]) = Ka/[HCN] = 4.9 × 10^-10 / 3.2 × 10^-2 = 1.5 × 10^-8 M

Therefore, the hydronium-ion concentration in the solution is 1.5 × 10^-8 M.

The best choice is D because it correctly calculates the concentration of hydronium ions in the solution.

What Is the Hydronium-Ion Concentration in a Solution Resulting from Mixing