If the pOH of a borax solution is 4.55, what is the H₃O⁺ concentration in the borax solution? A)4.6 M B)3.5 × 10^-9 M C)3.5 × 10^-10 M D)3.5 × 10^-11 M E)9.4 M

Question

Quizplus · Accepted Answer

First, we need to use the relationship between pH, pOH, and the concentration of H+ and OH- ions: pH + pOH = 14 Then, we can use the fact that borax (Na2B4O7) undergoes hydrolysis in water, producing OH- ions: Na2B4O7 + 7 H2O -> 2 Na+ + 4 B(OH)3 + 2 OH- Since the reaction produces two OH- ions for every one borax molecule, we can set up an equilibrium expression for the hydrolysis reaction: Kb = [B(OH)3][OH-]^2 / [Na2B4O7] where Kb is the base dissociation constant for borax. We can rearrange this expression to solve for [OH-], since that is what the question is asking for: [OH-] = sqrt(Kb [Na2B4O7] / [B(OH)3]) Now we need to relate Kb to the pOH value given in the problem. Since pOH = -log[OH-], we can rearrange this expression to solve for [OH-]: [OH-] = 10^-pOH Substituting this in for [OH-] in the first equation above, we get: pH + (-log[OH-]) = 14 pH + pOH = 14 pH = 14 - pOH pH = 9.45 Now we can use the fact that pH = pKa + log([A-]/[HA]) for the weak acid dissociation of B(OH)3: B(OH)3 + H2O -> H3O+ + B(OH)4- Ka = [H3O+][B(OH)4-] / [B(OH)3] pKa = -log(Ka) Using the fact that pKa + pKb = 14, we can find pKa: pKa = 14 - pKb Now we can use the Henderson-Hasselbalch equation to solve for [B(OH)4-] / [B(OH)3], since we know the pH and pKa: pH = pKa + log([B(OH)4-] / [B(OH)3]) 9.45 = (14 - pKb) + log([B(OH)4-] / [B(OH)3]) log([B(OH)4-] / [B(OH)3]) = -4.55 + pKb Taking antilogs of both sides, we get: [B(OH)4-] / [B(OH)3] = 10^-4.55 * 10^pKb Substituting in the expression for [OH-] and rearranging, we get: [B(OH)4-] / [Na2B4O7] = Kb / [OH-] [B(OH)4-] / [Na2B4O7] = Kb / (10^-4.55) [B(OH)4-] / [Na2B4O7] = 3.50 x 10^-10 Since each borax molecule produces one B(OH)4- ion in the hydrolysis reaction, we can multiply the above ratio by the number of borax molecules in solution to get the concentration of B(OH)4- ions: [B(OH)4-] = 3.50 x 10^-10 [Na2B4O7] [B(OH)4-] = 3.50 x 10^-10 (0.1 M) # assuming a 0.1 M borax solution [B(OH)4-] = 3.50 x 10^-11 M Finally, since the H₃O⁺ ion is just a hydrated form of B(OH)4-, we can assume that its concentration is the same as [B(OH)4-]: [HSBOOS+P-] = [B(OH)4-] = 3.50 x 10^-11 M Therefore, the best answer is C, 3.5 x 10^-10 M.

If the POH of a Borax Solution Is 4