KI(aq) is slowly added to a solution with [Pb^2+]=...

$\mathrm{KI}(\mathrm{aq})$ is slowly added to a solution with $\left[\mathrm{Pb}^{2+}\right]=$ $\left[\mathrm{Ag}^{+}\right]=0.10 \mathrm{M} .$ For $\mathrm{PbI}_{2}, K_{\mathrm{sp}}=7.1 \times 10^{-9} ;$ for $\mathrm{AgI}$ $K_{\mathrm{sp}}=8.5 \times 10^{-17}$ (a) Which precipitate should form first, $\mathrm{PbI}_{2}$ or AgI? (b) What $\left[\mathrm{I}^{-}\right]$ is required for the second cation to begin to precipitate? (c) What concentration of the first cation to precipitate remains in solution at the point at which the second cation begins to precipitate? (d) $\operatorname{Can} \mathrm{Pb}^{2+}(\mathrm{aq})$ and $\mathrm{Ag}^{+}(\mathrm{aq})$ be effectively sepa- rated by fractional precipitation of their iodides?

$\mathrm{KI}(\mathrm{aq})$ is slowly added to a solution with $\left[\mathrm{Pb}^{2+}\right]=$ $\left[\mathrm{Ag}^{+}\right]=0.10 \mathrm{M} .$ For $\mathrm{PbI}_{2}, K_{\mathrm{sp}}=7.1 \times 10^{-9} ;$ for $\mathrm{AgI}$
$K_{\mathrm{sp}}=8.5 \times 10^{-17}$
(a) Which precipitate should form first, $\mathrm{PbI}_{2}$ or AgI? (b) What $\left[\mathrm{I}^{-}\right]$ is required for the second cation to begin to precipitate?
(c) What concentration of the first cation to precipitate remains in solution at the point at which the second cation begins to precipitate?
(d) $\operatorname{Can} \mathrm{Pb}^{2+}(\mathrm{aq})$ and $\mathrm{Ag}^{+}(\mathrm{aq})$ be effectively sepa-
rated by fractional precipitation of their iodides?

Key Concepts

Common Ion Effect

The common ion effect refers to the phenomenon where the addition of an ion already present in the equilibrium shifts the solubility of a salt, usually resulting in decreased solubility. In the context of precipitation, adding a common ion can suppress the dissolution of a salt, thus influencing the precise point at which precipitation occurs and aiding in selective precipitation techniques.

Ion Product and Precipitation Threshold

The ion product is the multiplied concentration of the ions in solution, each raised to the power of its coefficient in the salt's chemical equation. This product is compared with the Ksp to determine if the solution is supersaturated. Only when the ion product meets or exceeds the Ksp will a saturated solution transition into precipitation, defining the threshold at which a compound begins to form as a solid.

Fractional (Selective) Precipitation

Fractional precipitation is a separation technique that leverages the differences in solubility of various salts to selectively precipitate one ion from solution while others remain dissolved. By gradually adding a precipitating agent, typically forming a common ion, one can control the order and extent of precipitation, ultimately facilitating the separation of ions based on their respective Ksp values.

Solubility Product (Ksp) and Precipitation Equilibrium

The solubility product constant (Ksp) characterizes the equilibrium that exists when a sparingly soluble salt dissolves in water, representing the product of the ion concentrations at saturation. When the ion product (the actual product of the ion concentrations in solution) exceeds the Ksp, the solution becomes supersaturated and precipitation occurs. This concept is essential for predicting when and which salt will begin to precipitate under varying ionic conditions.

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