Question #118039
4. Solubility products for a series of iodides are:

AgI Ksp = 8.3 x 10-17
PbI2 Ksp = 7.1 x 10-9
BiI3 Ksp = 8.1 x 10-19

List these three compounds in order of decreasing (from highest to lowest) molar solubility in:
a. Water
b. 0.10 M NaI
1
Expert's answer
2020-05-27T13:35:13-0400

The molar solubility is related to KSP in the following way:

S0=(KSPxxyy)1/(x+y)S_0 =(\frac{K_{SP}}{x^xy^y})^{1/(x+y)} ,

where x and y are the number of cations and anions to which the iodide dissociate, respectively. Therefore, the molar solubilities of AgI, PbI2 and BiI3 in water are:

AgI: x=1, y=1, S0=(8.310171)(1/2)=9.1109S_0 = (\frac{8.3·10^{-17}}{1})^{(1/2)} = 9.1·10^{-9} M,

PbI2: x=1, y=2, S0=(7.11094)(1/3)=1.2103S_0 = (\frac{7.1·10^{-9}}{4})^{(1/3)} = 1.2·10^{-3} M,

BiI3: x=1, y=3, S0=(8.1101927)(1/4)=1.3105S_0 = (\frac{8.1·10^{-19}}{27})^{(1/4)} = 1.3·10^{-5} M.

The list of these three compounds in order of decreasing (from highest to lowest) molar solubility in water is:

PbI2>BiI3>AgI.

In 0.10 M NaI, a common ion is present: I-. The concentration of sodium iodide must be taken in account:

KSP=[Me]x(0.1+[Me])yK_{SP} = [Me]^x(0.1+[Me])^y , or (as all x=1) :

KSP=[Me](0.1+[Me])yK_{SP} = [Me]·(0.1+[Me])^y

and the molar solubility equals [Me]. Solving the equation above for each KSP, we obtain:

AgI: y=1: [Me]<<0.1, [Me] = 8.3·10-16 M

PbI2: y=2: [Me]<<0.1, [Me] = 7.1·10-7 M

BiI3: y=3: [Me]<<0.1, [Me] =8.1·10-16 M.

Therefore, the list of these three compounds in order of decreasing (from highest to lowest) molar solubility in 0.10 M NaI is:

PbI2>AgI<BiI3.

Answer: water: PbI2>BiI3>AgI; 0.10 M NaI: PbI2>AgI<BiI3.


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