Picric acid has been used in the leather industry and in etching copper. However, its laboratory use has been restricted because it dehydrates on standing and can become shock sensitive. It has an acid dissociation constant of 0.42. What is the [H₃O⁺] for a 0.20 M solution of picric acid?

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Quizplus · Accepted Answer

The acid dissociation constant (Ka) for picric acid can be written as: Ka = [HSO4-][H+]/[H2SO4] Since picric acid is a triprotic acid, we need to consider all three dissociations: C6H3N3O7 + H2O ⇌ C6H2N3O7- + H3O+ Ka1 = [C6H2N3O7-][H3O+]/[C6H3N3O7] = 0.42 C6H2N3O7- + H2O ⇌ C6H1N3O7 2- + H3O+ Ka2 = [C6H1N3O7 2-][H3O+]/[C6H2N3O7-] C6H1N3O7 2- + H2O ⇌ C6N3O7 3- + H3O+ Ka3 = [C6N3O7 3-][H3O+]/[C6H1N3O7 2-] The concentration of H3O+ can be assumed to be negligible, so we can simplify the expressions to: Ka1 = [HSO4-][H+]/[H2SO4] = 0.42 Ka2 = [SO42-][H+]/[HSO4-] Ka3 = [C6N3O7 3-][H+]/[C6H1N3O7 2-] We can use these expressions to set up an ICE table: C6H3N3O7 + H2O ⇌ C6H2N3O7- + H3O+ I 0.20 M 0 M 0 M C -x +x +x E 0.20-x x x Ka1 = [HSO4-][H+]/[H2SO4] = 0.42 x^2/(0.20-x) = 0.42 x^2 = 0.084-0.42x x^2+0.42x-0.084 = 0 Using the quadratic formula, we can solve for x: x = 0.15 M (rounded to two significant figures) Therefore, [HSO4-] = [C6H1N3O7 2-] = [C6N3O7 3-] = 0.15 M The concentration of H+ can be calculated using Ka2: Ka2 = [SO42-][H+]/[HSO4-] 0.42 = x^2/(0.15) x = 0.29 M (rounded to two significant figures) Therefore, [H+] = 0.29 M The concentration of [C6H2N3O7-] can be calculated as the difference between the initial concentration and the concentration of [HSO4-]: [C6H2N3O7-] = 0.20 - 0.15 = 0.05 M Therefore, the concentration of [H₃O⁺] for a 0.20 M solution of picric acid is 0.15 M.

Picric Acid Has Been Used in the Leather Industry and in Etching