What is the H₃O⁺ concentration in 0.0055 M Ba(OH)₂(aq)at 25 °C? (K_w = 1.01 × 10^-14)?

Question

Quizplus · Accepted Answer

The balanced equation for the dissociation of Ba(OH)S1U1B12S1U1B0(aq) is:

Ba(OH)S1U1B12S1U1B0(aq) -> BaS1U1B2S1U1B0S1S1P0(aq) + 2OH-S1U1B1-(aq)

Kw = [H+S1U1B1(aq)][OH-S1U1B1(aq)] = 1.01 × 10S1U1P1-14S1S1P0

From the balanced equation, we see that the concentration of H+S1U1B1(aq) is twice the concentration of BaS1U1B2S1U1B0S1S1P0(aq), so:

[H+S1U1B1(aq)] = 2[BaS1U1B2S1U1B0S1S1P0(aq)]

Substituting this into the expression for Kw, we get:

Kw = 4[BaS1U1B2S1U1B0S1S1P0(aq)][OH-S1U1B1(aq)]

At equilibrium, the initial concentration of BaS1U1B2S1U1B0S1S1P0(aq) will decrease by an amount equal to the concentration of OH-S1U1B1(aq), and the concentration of H+S1U1B1(aq) will increase by the same amount. Let x be the concentration of OH-S1U1B1(aq) at equilibrium. Then:

[BaS1U1B2S1U1B0S1S1P0(aq)] = 0.0055 - x
[H+S1U1B1(aq)] = 2(0.0055 - x)

Substituting these expressions into the equation for Kw, we get:

1.01 × 10S1U1P1-14S1S1P0 = 4(0.0055 - x)(x)

Solving for x, we get:

x = 9.1 × 10S1U1P1-14S1S1P0

Therefore, the concentration of OH-S1U1B1(aq) at equilibrium is 9.1 × 10S1U1P1-14S1S1P0 M. Since the initial concentration of H+S1U1B1(aq) is negligible compared to the equilibrium concentration, we can assume that the concentration of H+S1U1B1(aq) is equal to 2(0.0055 - x) = 1.1 × 10S1U1P1-2S1S1P0 M. The concentration of BaS1U1B2S1U1B0S1S1P0(aq) at equilibrium is equal to 0.0055 - x = 0.0055 - 9.1 × 10S1U1P1-14S1S1P0 = 0.0055 M.

Therefore, the concentration of HS1U1B13S1U1B0OS1U1P1+S1S1P0 at equilibrium is equal to the concentration of H+S1U1B1(aq) plus the concentration of HS1U1B13S1U1B0OS1U1P1-S1U1B0 formed by the reaction of OH-S1U1B1(aq) with the initial concentration of HS1U1B13S1U1B0OS1U1P1+S1S1P0:

[HS1U1B13S1U1B0OS1U1P1+S1S1P0] = [H+S1U1B1(aq)] + [HS1U1B13S1U1B0OS1U1P1-S1U1B0]
[HS1U1B13S1U1B0OS1U1P1-S1U1B0] = x

Substituting the values of x and [H+S1U1B1(aq)], we get:

[HS1U1B13S1U1B0OS1U1P1+S1S1P0] = (1.1 × 10S1U1P1-2S1S1P0) + (9.1 × 10S1U1P1-14S1S1P0) = 1.0 × 10S1U1P1-13S1S1P0

Therefore, the answer is choice C, 9.1 × 10S1U1P1-13S1S1P0 M.

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