Lakes and rivers are often contaminated with divalent lead (Pb\'), due to releas

Question

Lakes and rivers are often contaminated with divalent lead (Pb'), due to release from soils that were loaded with Pb prior to the widespread adoption of unleaded gasoline. The EPA has identified 0.015 mg L1 as the maximum allowable concentration of lead in drinking waters-higher levels are known to cause developmental issues in children A local Boulder lake has a measured Pb concentration of 10 M, which is well above the EPA limit. A restoration group has suggested adding blocks of limestone rock (CaCO) to the lake to safely control Pb levels by forming lead carbonates, which would then precipitate (a temporary measure until the lead in the sediments can be dealt with). The Boulder City Council will not pay for this without an assessment of the scheme. That's our job! The following reactions and K values will help us answer these questions: CaCO3 (s) Ca2+ (aq) + CO32-(aq) Ksp-10-8.4 = 10.13,1 24 a. The goal is to add so much limestone that the lake would be saturated with CaCOs. If we could assume that the [Ca2] and [CO,2] in the lake are derived only from limestone dissolution, and are approximately equal, what would the molar Ca2 concentration be in the lake? b. As we know, the current concentration of Pb2 in the lake is 10 M. Will this actually change if the limestone is added?

Explanation / Answer

a) Solubility product (Ksp) for the reaction involving dissociation of CaCO3 is 10-8.4, means [Ca2+].[CO32] = 10-8.4

The concentration of Ca2+ and CO32- is equal, so assuming it as x, we get:

x2 = 10-8.4

x = 0.63 x 10-4

Thus, [Ca2+] = 0.63 x 10-4 mol/l

Note that this is the concentration of CO32- as well.

b) Ksp for the reaction of Pb2+ and CO32- is 10-13.1, means

[Pb2+].[CO32-] = 10-13.1

[CO32-] = 10-13.1/ 10-5 = 7.94 x 10-9

The required concentration of CO32- for the formation of PbCO3 is 7.94 x 10-9 mol/l, and CO32- produced through dissociation of CaCO3 is 0.63 x 10-4 mol/l. So, the concentration of Pb will change (decrease) if the limestone is added, as CO3 will increase.

c) Let number of moles of Pb = X

So, 0.015 x 10-3/ X = 207.2 / 1

Thus, concentration of Pb specified by EPA in moles / litre is

X = 0.015 x 10-3 / 207.2 = 0.72 x 10-7 mol/l

d) Addition of 0.63 x 10-4 mol/l of CO3 through the limestone will produce:

10-13.1 / 0.63 x 10-4 = 1.26 x 10-9 mol/l of Pb

Thus, the blocks of limestone will reduce the levels of Pb to below the EPA limit i.e.0.72 x 10-7 mol/l

e) The volume of the lake is 2 x 109 liters. Assuming that 1 kg of water would need 1 kg of limestone, the cost of limestone would be $1060 x 2 x 109 / 1000 = $2.12 x 109

Thus, the minimum cost of the project would be $5000 + $2.12 x 109 = $2,120,005,000

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