Question

What is the hydroxide-ion concentration in a 0.20 M solution of Na₂CO₃? For carbonic acid, K_a1 = 4.2

Answer 1

When Na2CO3 is dissolved in water, it is completely dissociated. Hence

C = [CO₃^2- ] = 0.20M

Ka1 = 4.2 x 10^-7

Ka2 = 4.8 x 10^-11

Na2CO3 is a salt of weak acid H2CO3 and strong base NaOH, and when it is hydrolysed the following reaction occurs

   CO₃^2-             +      H2O ------------> HCO₃^-      +     OH-

C(1 - alpha)                                    Cx(alpha)         Cx(alpha)          

Hydrolysis constant Kh for the above hydrolysis reaction can be calculated as

Kh = K x[H2O] = [ HCO₃^- ]x[ OH-] / [CO₃^2-]

Multiplying and dividing numerator and denominator by [H+] we get

Kh = K x[H2O] = [ HCO₃^- ]x[ OH-]x[H+] /[H+]x [CO₃^2-] = Kw / Ka2

=> Kh = Kw / Ka2 = (1.0 x 10^-14 ) /(4.8 x 10^-11 )

Degree of dissociation, alpha = underroot (Kh /C) = Underroot[Kw / (Ka2 xC)]

Now [OH-] can be calculated as

[OH-]   =  C x alpha = C x Underroot[Kw / (Ka2 xC)] = Underroot[CxKw /Ka2]

=> [OH-] = Underroot[(0.2x1.0 x 10^-14 ) /(4.8 x 10^-11 )] = 6.45x10^-3 M (answer)