Determine the pH

Question

Determine the pH of 9.00E-3 M of sodium hydrogen sulfate and 1.01E-3 M of diethylamine.

Answer 1

Sodium hydrogen sulfate = NaHSO4

NaHSO4 ==> Na+ + HSO4-

HSO₄^- + H₂O ==> H₃O⁺ + SO₄^2- Ka = 1.0x10^-2

Ka = 1.0x10^-2 = [H₃O⁺][SO₄^2-] / [HSO₄^-]

1x10^-2 = (x)(x) / 9.00x10^-3 - x

9.00x10^-5 - 1x10^-2x = x²

x² + 1x10^-2x - 9x10^-5 = 0 (solve using quadratic equation)

x = 0.00572 M = [H3O⁺]

pH = -log 0.00572 = 2.24

Diethylamine = HN(C₂H₅)₂

HN(C2H5)2 + H2O ==> H2N(C2H5)2 + OH-

Look up the Kb for diethylamine. I found 6.9x10^-4, you may find a different value.

Kb = 6.9x10^-4 = [H2N(C2H5)₂] [OH-] / [ HN(C2H5)₂]

6.9x10^-4 = (x)(x) / 1.01x10^-3 - x

6.97x10^-7 - 6.9x10^-4x = x²

x² + 6.9x10^-4x - 6.97x10^-7 = 0 solve using quadratic

x = 0.000558 M = [OH-]

pOH = -log 0.000558 = 3.25

pH = 14 - 3.25 = 10.7