Question

The stepwise formation constants for the complexes Pb(OH)+ (aq) and Pb(OH)2(aq) from Pb2+ (aq) are 2.0 × 10^6 and 4.0 × 10^4 , respectively.

The reactions forming these complexes are:

Pb2+(aq) + OH(aq) <--> PbOH+ (aq)

PbOH+ (aq) + OH(aq) <--> Pb(OH)2 (aq)

Calculate the pKa1 and pKa2 values for deprotonation of the aquo complexes of lead (II), and determine the fractional concentration of the two most important species at pH 7.0.

Please use the alpha for the fractional compositions!

Answer 1

$Pb(OH)_{2}\rightleftharpoons Pb(OH)^{+}+OH^{-}\: \: \: \: \: \: \: \: \: K_{b1}$?

$Pb(OH)^{+}\rightleftharpoons Pb^{2+}+OH^{-}\: \: \: \: \: \: \: \: K_{b2}$

$K_{b1}=\frac{1}{K_{f1}}=\frac{1}{2\times10^{6}}$

$K_{b1}=5\times10^{-7}$

$pK_{b1}=-log(5\times10^{-7})$

$pK_{b1}=6.301$

$pK_{a1}=14-6.301$

$pK_{a1}=7.699$

$K_{b2}=\frac{1}{K_{f2}}=\frac{1}{4\times10^{4}}$

$K_{b2}=2.5\times10^{-5}$

$pK_{b2}=-log(2.5\times10^{-5})$

$pK_{b2}=4.602$

$pK_{a2}=14-4.602$

$pK_{a2}=9.398$