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[Ag+]=1.8×10-9 Mopen bracket cap A g raised to the positive power close bracket equals 1.8 cross 10 to the negative 9 power M Step 3: Analyze the Results AgIcap A g cap I begins to precipitate when AgClcap A g cap C l will not start precipitating until is increased to . This gap allows for effective separation. 4. Why Copying the Answer Key Limits Your Success

"The range of ([Cl^-]) for successful separation is from (1.8\times10^-8 M) (start AgCl) to (0.041 M) (start PbCl_2)."

AgI has the smaller Kₛₚ value (approximately 8.5 × 10⁻¹⁷) compared to AgCl (approximately 1.8 × 10⁻¹⁰). A smaller Kₛₚ indicates lower solubility in water.

Fractional precipitation is a method used to separate two or more ions from a solution by adding a reagent that forms precipitates with each ion, one after another. The separation is possible because the solubilities of the resulting precipitates differ significantly, allowing one substance to precipitate almost completely before the second one begins to form.

[Ag⁺] = Kₛₚ(AgI) / [I⁻] = (8.5 × 10⁻¹⁷) / (0.10) = 8.5 × 10⁻¹⁶ M

8.5×10-17=[Ag+](0.10 M)8.5 cross 10 to the negative 17 power equals open bracket cap A g raised to the positive power close bracket open paren 0.10 M close paren

Most "Fractional Precipitation" POGIL activities use a mixture of 0.01 M (AgNO_3) and 0.01 M (Pb(NO_3)_2). A solution of 0.1 M HCl is added slowly.

A typical POGIL problem will provide a solution containing two ions—for example, . You are asked what happens when silver nitrate ( AgNO3AgNO sub 3 ) is slowly added.

The fundamental principle governing this process is the solubility product constant (Kₛₚ). When a common precipitating agent is added to a solution containing multiple ions, the compound with the lowest solubility (or more precisely, the one that requires the lowest concentration of the precipitating agent to exceed its Kₛₚ) will precipitate first. A table of Kₛₚ values is essential to determine which compounds to use to induce precipitation, and the Kₛₚ values must be sufficiently different to make this method practicable.