The Ksp for lead carbonate, PbC0_3, is 1.5 times 10^-13. What is the solubility

Question

The Ksp for lead carbonate, PbC0_3, is 1.5 times 10^-13. What is the solubility of PbC03 in water? Lead is highly toxic and it is desirable to remove it from drinking water. If lake water containing lead is treated with Na_2C0_3 such that the concentration of CO_3^-2 is 0.1 M, PbC0_3(s) will be formed and can be filtered out. What is tip solubility of PbC0_3(s) in a solution of 0.1 M CO^-2 3 If, instead of adding Na2C03 the treatment facility buffered the water to a pH = 10.0, the formation of Pb(OH)2(s) will form. Ksp = 2.8/x 10^-16. What is the Pb^+2 concentration in a solution of pH = 10.0?

Explanation / Answer

a)

PbCO3 ===> Pb2+ + CO32-

Ksp = [Pb2+][CO32-] = 1.5 x 10^-13

The molar solubility of PbCO3 = [Pb2+]

Let [Pb2+] = x = [CO32-] , and (x)^2 = 1.5 x 10^-13

x^2 = 1.5 x 10^-13

x = 3.87 x 10^-7 = molar solubility

b) PbCO3 <===> Pb2+ + CO32-
    Ksp = 1.5 x 10^-13 =(x) ( x+0.1)^2
    x is small compared to 0.1 so we assume (x + 0.1) = 0.1
    1.5 x 10^-13 = (x) ( 0.1)^2
     x = 1.5 x 10^-11 M

c) pH = 10 = -log[H+]

             log[H+] = -10

             [H+] = 1x10-10

                   Hence [OH-] = 1x10-4 M

              Pb(OH)2 = Pb2+ + 2OH-

             2.8x10-16 = [Pb2+][OH-]^2 = [x][1x10-4]^2

              X = 2.8 x 10-8

                   

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