Textbook Question
Calculate the minimum pH needed to precipitate Mn1OH22 so completely that the concentration of Mn2 +1aq2 is less than 1 mg per liter [1 part per billion (ppb)].
Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 73
A solution contains 2.0 * 10^-4 M Ag^+ (aq) and 1.5 * 10^-3 M Pb^2+ (aq). If NaI is added, will AgI (Ksp = 8.3 * 10^-17) or PbI2 (Ksp = 7.9 * 10^-9) precipitate first? Specify the concentration of I^- (aq) needed to begin precipitation.
Verified step by step guidance1
Step 1: Identify the relevant solubility product constants (Ksp) for AgI and PbI2. AgI has a Ksp of 8.3 \times 10^{-17}, and PbI2 has a Ksp of 7.9 \times 10^{-9}.
Step 2: Write the equilibrium expressions for the precipitation reactions. For AgI, the reaction is Ag^+ + I^- \rightleftharpoons AgI(s), and the Ksp expression is Ksp_{AgI} = [Ag^+][I^-]. For PbI2, the reaction is Pb^{2+} + 2I^- \rightleftharpoons PbI2(s), and the Ksp expression is Ksp_{PbI2} = [Pb^{2+}][I^-]^2.
Step 3: Calculate the concentration of I^- needed to begin precipitation for each compound. For AgI, rearrange the Ksp expression to find [I^-] = \frac{Ksp_{AgI}}{[Ag^+]}. For PbI2, rearrange the Ksp expression to find [I^-] = \sqrt{\frac{Ksp_{PbI2}}{[Pb^{2+}]}}.
Step 4: Substitute the given concentrations of Ag^+ and Pb^{2+} into the respective equations. Use [Ag^+] = 2.0 \times 10^{-4} M and [Pb^{2+}] = 1.5 \times 10^{-3} M to find the required [I^-] for each compound.
Step 5: Compare the calculated [I^-] values for AgI and PbI2. The compound with the lower [I^-] value will precipitate first, as it requires a lower concentration of I^- to reach its Ksp.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solubility Product Constant (Ksp)
The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of ionic compounds. It represents the maximum concentration of ions in a saturated solution at a given temperature. For a salt, Ksp is calculated from the concentrations of its constituent ions, and a precipitate will form when the product of the ion concentrations exceeds the Ksp value.
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Solubility Product Constant
Precipitation Reaction
A precipitation reaction occurs when two soluble salts react in solution to form an insoluble compound, or precipitate. The formation of a precipitate is driven by the decrease in solubility of the product ions when their concentrations exceed the Ksp. In this scenario, the order of precipitation depends on the Ksp values of the potential precipitates and the concentrations of the ions involved.
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Ionic Concentration and Precipitation Threshold
To determine when a precipitate will form, one must calculate the critical concentration of the anion (I^-) required to exceed the Ksp for each potential precipitate. This involves rearranging the Ksp expression to solve for the concentration of I^- that will lead to the formation of AgI or PbI2. The lower the required concentration of I^-, the more likely that compound will precipitate first.
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Related Practice
Textbook Question
Suppose that a 10-mL sample of a solution is to be tested for I- ion by addition of 1 drop (0.2 mL) of 0.10 M Pb1NO322. What is the minimum number of grams of I- that must be present for PbI21s2 to form?
Textbook Question
A solution of Na2SO4 is added dropwise to a solution that is 0.010 M in Ba2+(aq) and 0.010 M in Sr2+(aq). (a) What concentration of SO42- is necessary to begin precipitation? (Neglect volume changes. BaSO4: Ksp = 1.1⨉10-10; SrSO4: Ksp = 3.2⨉10-7.)
Textbook Question
A solution of Na2SO4 is added dropwise to a solution that is 0.010 M in Ba2+(aq) and 0.010 M in Sr2+(aq). (b) Which cation precipitates first?
Textbook Question
A solution of Na2SO4 is added dropwise to a solution that is 0.010 M in Ba2+(aq) and 0.010 M in Sr2+(aq). (c) What is the concentration of SO42-(aq) when the second cation begins to precipitate?