The solubility of [latex]PbI_{2}(s)[/latex] in water at 25°C is [latex]0.59\ g\cdot L^{−1}[/latex]. Calculate the value of [latex]K_{sp}[/latex] for [latex]PbI_{2}(s)[/latex].

Question 22.3: The solubility of PbI2(s) in water at 25°C is 0.59 g∙L^−1. C......

The solubility of $PbI_{2}(s)$ in water at 25°C is $0.59\ g\cdot L^{−1}$ . Calculate the value of $K_{sp}$ for $PbI_{2}(s)$ .

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The solubility of $PbI_{2}(s)$ in moles per liter is

s = (0.59\ g·L^{–1})\left(\frac{1\ mol\ PbI_{2}}{461.0\ g\ PbI_{2}} \right) = 0.0013\ M

The chemical equation for the solubility equilibrium is

PbI_{2}(s) ⇋ Pb^{2+}(aq) + 2\ I^−(aq)

The solubility s is related to $[Pb^{2+}]$ and $[I^-]$ by

$[Pb^{2+}] = s$ and $[I^-] = 2s$

Therefore,

K_{sp} = [Pb^{2+}] [I^−]^2 = (s)(2s)^2 = 4s^3 = 4(0.0013\ M)^3 = 8.8 × 10^{−9}\ M^3

The value of $K_{sp}$ calculated here differs somewhat from that in Table 22.1 because the solubility-product constant for a species assumes the formation of simple ions from that species, such as $Pb^{2+}(aq)$ and $I^-(aq)$ in the case of $PbI_{2}(s)$ . In actuality the chemistry that occurs in solution can be more complex than this and so the actual experimentally determined solubility of a species can differ somewhat from the value determined from its solubilityproduct constant. Nevertheless, calculations involving solubility and $K_{sp}$ are often reasonably accurate and allow us to make useful predictions about the solubility of ionic species.

TABLE 22.1 Solubility-product constants for various salts in water at 25°C
Bromates	$K_{sp}$	Cyanides	$K_{sp}$	Oxalates	$K_{sp}$
$AgBrO_{3}$	$5.4 × 10^{-5}\ M^{2}$	$AgCN$	$6.0 × 10^{-17}\ M^{2}$	$Ag_{2}C_{2}O_{4}$	$5.4 × 10^{-12}\ M^{3}$
$Ba(BrO_{3})_{2}$	$2.4 × 10^{-4}\ M^{3}$	$CuCN$	$3.5 × 10^{-20}\ M^{2}$	$CaC_{2}O_{4}$	$4 × 10^{-9}\ M^{2}$
$Pb(BrO_{3})_{2}$	$7.9 × 10^{-6}\ M^{3}$	$Hg_{2}(CN)_{2}{^*}$	$5 × 10^{-40}\ M^{3}$	$MgC_{2}O_{4}$	$7 × 10^{-7}\ M^{2}$
$TlBrO_{3}$	$1.1 × 10^{-4}\ M^{2}$	$Zn(CN)_{2}$	$3 × 10^{-16}\ M^{3}$	$SrC_{2}O_{4}$	$4 × 10^{-7}\ M^{2}$
Bromides	$K_{sp}$	Fluorides	$K_{sp}$	Sulfates	$K_{sp}$
$AgBr$	$5.4 × 10^{-13}\ M^{2}$	$BaF_{2}$	$1.8 × 10^{-7}\ M^{3}$	$Ag_{2}SO_{4}$	$1.2 × 10^{-5}\ M^{3}$
$CuBr$	$6.3 × 10^{-9}\ M^{2}$	$CaF_{2}$	$3.5 × 10^{-11}\ M^{3}$	$BaSO_{4}$	$1.1 × 10^{-10}\ M^{2}$
$Hg_{2}Br_{2}{^*}$	$6.4 × 10^{-23}\ M^{3}$	$LiF$	$1.8 × 10^{-3}\ M^{2}$	$CaSO_{4}$	$4.9 × 10^{-5}\ M^{2}$
$HgBr_{2}$	$6.2 × 10^{-20}\ M^{3}$	$MgF_{2}$	$5.2 × 10^{-11}\ M^{3}$	$Hg_{2}SO_{4}$	$6.5 × 10^{-7}\ M^{2}$
$PbBr_{2}$	$6.6 × 10^{-6}\ M^{3}$	$PbF_{2}$	$3.3 × 10^{-8}\ M^{3}$	$PbSO_{4}$	$2.5 × 10^{-8}\ M^{2}$
$TlBr$	$3.7 × 10^{-6}\ M^{2}$	$SrF_{2}$	$4.3 × 10^{-9}\ M^{3}$	$SrSO_{4}$	$3.4 × 10^{-7}\ M^{2}$
Carbonates	$K_{sp}$	Hydroxides	$K_{sp}$	Sulfides	$K_{sp}$
$Ag_{2}CO_{3}$	$8.5 × 10^{-12}\ M^{3}$	$Al(OH)_{3}$	$1.3 × 10^{-33}\ M^{4}$	$Ag_{2}S$	$8 × 10^{-51}\ M^{3}$
$BaCO_{3}$	$2.6 × 10^{-9}\ M^{2}$	$Ca(OH)_{2}$	$5.0 × 10^{-6}\ M^{3}$	$CdS$	$8.0 × 10^{-27}\ M^{2}$
$CaCO_{3}$	$3.4 × 10^{-9}\ M^{2}$	$Cd(OH)_{2}$	$7.2 × 10^{-15}\ M^{3}$	$CoS$	$5 × 10^{-22}\ M^{2}$
$CdCO_{3}$	$1.0 × 10^{-12}\ M^{2}$	$Co(OH)_{2}$	$5.9 × 10^{-15}\ M^{3}$	$CuS$	$6.3 × 10^{-36}\ M^{2}$
$CoCO_{3}$	$1.0 × 10^{-10}\ M^{2}$	$Cr(OH)_{3}$	$6.3 × 10^{-31}\ M^{4}$	$FeS$	$6.3 × 10^{-18}\ M^{2}$
$CuCO_{3}$	$1.4 × 10^{-10}\ M^{2}$	$Cu(OH)_{2}$	$2.2 × 10^{-20}\ M^{3}$	$HgS$	$4 × 10^{-53}\ M^{2}$
$FeCO_{3}$	$3.1 × 10^{-11}\ M^{2}$	$Fe(OH)_{2}$	$4.9 × 10^{-17}\ M^{3}$	$MnS$	$2.5 × 10^{-13}\ M^{2}$
$MgCO_{3}$	$6.8 × 10^{-6}\ M^{2}$	$Fe(OH)_{3}$	$2.8 × 10^{-39}\ M^{4}$	$NiS$	$1.3 × 10^{-25}\ M^{2}$
$MnCO_{3}$	$2.2 × 10^{-11}\ M^{2}$	$Mg(OH)_{2}$	$5.6 × 10^{-12}\ M^{3}$	$PbS$	$8.0 × 10^{-28}\ M^{2}$
$NiCO_{3}$	$1.4 × 10^{-7}\ M^{2}$	$Ni(OH)_{2}$	$5.5 × 10^{-16}\ M^{3}$	$SnS$	$1.0 × 10^{-25}\ M^{2}$
$PbCO_{3}$	$7.4 × 10^{-14}\ M^{2}$	$Pb(OH)_{2}$	$1.4 × 10^{-20}\ M^{3}$	$Tl_{2}S$	$6 × 10^{-22}\ M^{3}$
$SrCO_{3}$	$5.6 × 10^{-10}\ M^{2}$	$Sn(OH)_{2}$	$5.5 × 10^{-27}\ M^{3}$	$ZnS$	$1.6 × 10^{-24}\ M^{2}$
$ZnCO_{3}$	$1.5 × 10^{-10}\ M^{2}$	$Zn(OH)_{2}$	$1.0 × 10^{-15}\ M^{3}$
Chlorides	$K_{sp}$	Iodates	$K_{sp}$	Thiocyanates	$K_{sp}$
$AgCl$	$1.8 × 10^{-10}\ M^2$	$AgIO_{3}$	$3.2 × 10^{-8}\ M^2$	$AgSCN$	$1.0 × 10^{-12}\ M^2$
$CuCl$	$1.7× 10^{-7}\ M^2$	$Ba(IO_{3})_{2}$	$4.0 × 10^{-9}\ M^3$	$CuSCN$	$1.8 × 10^{-13}\ M^2$
$Hg_{2}Cl_{2}{^*}$	$1.4 × 10^{-18}\ M^3$	$Ca(IO_{3})_{2}$	$6.5 × 10^{-6}\ M^3$	$Cu(SCN)_{2}$	$4.0 × 10^{-14}\ M^3$
$PbCl_{2}$	$1.5 × 10^{-5}\ M^3$	$Cd(IO_{3})_{2}$	$2.5 × 10^{-8}\ M^3$	$Hg_{2}(SCN)_{2}{^*}$	$3.2 × 10^{-20}\ M^3$
$TlCl$	$1.9 × 10^{-4}\ M^2$	$Cu(IO_{3})_{2}$	$7.4 × 10^{-8}\ M^3$	$Hg(SCN)_{2}$	$2.8 × 10^{-20}\ M^3$
		$Pb(IO_{3})_{2}$	$3.7 × 10^{-13}\ M^3$	$TlSCN$	$1.6 × 10^{-4}\ M^2$
		$TlIO_{3}$	$3.1 × 10^{-6}\ M^2$
		$Zn(IO_{3})_{2}$	$3.9 × 10^{-6}\ M^3$
Chromates	$K_{sp}$	Iodides	$K_{sp}$
$Ag_{2}CrO_{4}$	$1.1 × 10^{-12}\ M^{3}$	$AgI$	$8.5 × 10^{-17}\ M^{2}$	* $Hg(I)$ exists as $Hg_{2}^{2+}(aq)$ in aqueous solution.
$BaCrO_{4}$	$1.2 × 10^{-10}\ M^{2}$	$CuI$	$1.3 × 10^{-12}\ M^{2}$
$CuCrO_{4}$	$3.6 × 10^{-6}\ M^{2}$	$Hg_{2}I_{2}{^*}$	$5.2 × 10^{-29}\ M^{3}$
$Hg_{2}CrO_{4}{^*}$	$2.0 × 10^{-9}\ M^{2}$	$HgI_{2}$	$2.9 × 10^{-29}\ M^{3}$
$PbCrO_{4}$	$2.8 × 10^{-13}\ M^{2}$	$PbI_{2}$	$9.8 × 10^{-9}\ M^{3}$
$Tl_{2}CrO_{4}$	$8.7 × 10^{-13}\ M^{3}$	$TlI$	$5.5 × 10^{-8}\ M^{2}$