Question

Calculate the concentration of all species in a 0.520 M solution of H2SO3. The acid ionization constants for the acid are Ka1=1.6×10−2 and Ka2=6.4×10−8.

Answer 1

H₂SO₃ is diprotic acid dissociate as

H₂SO₃ + H₂O   H₃O⁺  + HSO₃^-

HSO₃^- + H₂O   H₃O⁺  + SO₃^2-

Ka₁ = [H₃O⁺ ] [HSO₃^- ] /  [H₂SO₃ ]

Ka₁ of H₂SO₃ = 1.6 X 10^-2  

[H₃O⁺ ] = [HSO₃^- ] = x

then Ka₁ = x²  / [H₂SO₃]

x² = Ka₁ X [HSO₄^- ] = 1.6 X 10^-2 X0.520 = 0.00832

x = 0.0912 M

[H₃O⁺ ] = [HSO₃^- ] = x = 0.0912 M

Ka₂ = [H₃O⁺ ] [SO₃^2- ] /  [HSO₃^- ]

Ka₂ of HSO₃^- = 6.4 X 10^-8  

[H₃O⁺ ] = [SO₃^2- ] = x

then Ka₂ = x²  / [HSO₃^-]

x² = Ka₁ X [HSO₃^- ] = 6.4 X 10^-8 X0.0912 = 5.838 X 10^-9

x = 7.64 X10^-5 M

[H₃O⁺ ] = [SO₃^2- ] = x = 7.64 X10^-5 M

Total [H₃O⁺ ] = 0.0912 + 7.64 X10^-5 = 0.0912764 M

[HSO₃^-] = 0.0912 - 7.64 X10^-5 = 0.0911236 M

[SO₃^2- ] = 7.64 X10^-5  M

[H₂SO₃] = 0.520 - 0.0912 = 0.4288 M