Calculate the pOH of a solution that contains 3.9 × 10^-⁴ M H₃O⁺ at 25°C. A) 4.41 B) 3.41 C) 10.59 D) 9.59 E) 0.59

Question

Quizplus · Accepted Answer

First, we need to write the equation for the dissociation of H₃O⁺: H₃O⁺ → H⁺ + ₃O The equilibrium expression for this reaction is: Kb = ([H⁺][₃O])/[H₃O⁺] Since we want to find the pOH, we need to first find the pH. We can do this by using the fact that pKw = pH + pOH = 14 at 25°C. Therefore, if we know the pH, we can easily calculate the pOH. To find the pH, we need to use the fact that pH + pOH = 14 and the equilibrium expression for Kb. Since Kb = [H⁺][₃O]/[H₃O⁺], we can rearrange this equation to solve for [H⁺]: [H⁺] = Kb([H₃O⁺])/[₃O] Substituting the given values into this equation, we get: [H⁺] = (1.1 × 10⁻¹²)(3.9 × 10⁻¹⁴)/(3.9 × 10⁻¹⁴) [H⁺] = 1.1 × 10⁻¹² pH = -log([H⁺]) = -log(1.1 × 10⁻¹²) = 11.96 Finally, we can calculate the pOH: pOH = 14 - pH = 14 - 11.96 = 2.04 Since we want the pOH of a basic solution, we need to convert this to a concentration of hydroxide ions using the fact that pOH = -log([OH⁻]). Therefore, we get: [OH⁻] = 10⁻².⁰⁴ = 7.94 × 10⁻³ Now, we can calculate the pOH: pOH = -log([OH⁻]) = -log(7.94 × 10⁻³) = 2.41 We can convert this to a number with two decimal places: pOH = 2.41 ≈ 2.41 Since the question asks for the pOH to two decimal places, the answer is C: 10.59.

Calculate the POH of a Solution That Contains 3