Sulfuric acid is a diprotic acid.What is the pH of a 0.200 M H₂SO₄ solution? (The pK_a of the hydrogen sulfate ion is 1.92.)

Question

Quizplus · Accepted Answer

The correct answer is A because the pH of a 0.200 M H2SO4 solution can be calculated using the following equation: pH = -log[H+], where [H+] is the molar concentration of hydrogen ions in the solution. The hydrogen sulfate ion (HSO4-) is a weak acid with a pKa of 1.92, which means that it will only partially dissociate in water. The equilibrium constant for the dissociation of HSO4- is Ka = [H+][SO42-]/[HSO4-], where [H+], [SO42-], and [HSO4-] are the molar concentrations of hydrogen ions, sulfate ions, and hydrogen sulfate ions, respectively. Using the pKa and the equilibrium constant, we can calculate the concentration of hydrogen ions in the solution: pKa = -logKa = -log([H+][SO42-]/[HSO4-]) = 1.92, so Ka = 10^-1.92 = 1.22 x 10^-2. Substituting this value into the equilibrium constant equation, we get: 1.22 x 10^-2 = [H+][SO42-]/[HSO4-]. Since the initial concentration of H2SO4 is 0.200 M, the initial concentration of HSO4- is also 0.200 M. Assuming that x is the concentration of hydrogen ions that dissociate from HSO4-, we have: 1.22 x 10^-2 = x^2/0.200 - x, which can be rearranged to: x^2 + 1.22 x 10^-2x - 2.44 x 10^-4 = 0. Solving for x using the quadratic formula, we get: x = [H+] = 1.11 x 10^-2 M. Substituting this value into the pH equation, we get: pH = -log(1.11 x 10^-2) = 0.68.

Sulfuric Acid Is a Diprotic Acid