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Ch.17 - Additional Aspects of Aqueous Equilibria
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.17 - Additional Aspects of Aqueous EquilibriaProblem 67
Chapter 17, Problem 67

Use values of Ksp for AgI and Kf for [Ag(CN)2]- to (a) calculate the molar solubility of AgI in pure water. (b) calculate the equilibrium constant for the reaction AgI(s) + 2 CN⁻(aq) ⇌ [Ag(CN)2]⁻(aq) + I⁻(aq). (c) determine the molar solubility of AgI in a 0.100 M NaCN solution.

Verified step by step guidance
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Step 1: Identify the relevant equilibrium expressions. For AgI, the solubility product (K_{sp}) is given by the expression: K_{sp} = [Ag^+][I^-]. For the complex ion formation, the formation constant (K_f) is given by: K_f = \(\frac{[Ag(CN)_2^-]}{[Ag^+][CN^-]^2}\).
Step 2: Calculate the molar solubility of AgI in pure water. Assume the solubility of AgI is 's' mol/L. Then, [Ag^+] = s and [I^-] = s. Substitute these into the K_{sp} expression to solve for 's'.
Step 3: Write the overall reaction for the dissolution of AgI in the presence of CN^-: AgI(s) + 2 CN^- \(\rightleftharpoons\) [Ag(CN)_2]^- + I^-. The equilibrium constant for this reaction (K_{overall}) can be found by multiplying K_{sp} and K_f.
Step 4: Calculate the molar solubility of AgI in a 0.100 M NaCN solution. Assume the solubility of AgI is 's' mol/L. In this case, [CN^-] is approximately 0.100 M. Use the expression for K_{overall} to solve for 's', considering the initial concentration of CN^-.
Step 5: Set up the equilibrium expression for the reaction in the NaCN solution: K_{overall} = \(\frac{[Ag(CN)_2^-][I^-]}{[CN^-]^2}\). Substitute the known values and solve for the molar solubility 's'.

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 sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For AgI, Ksp can be used to determine its molar solubility in water by setting up the equilibrium expression based on its dissociation into Ag⁺ and I⁻ ions.
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Formation Constant (Kf)

The formation constant (Kf) quantifies the stability of a complex ion in solution, representing the equilibrium between the complex and its constituent ions. For the complex ion [Ag(CN)2]⁻, Kf indicates how readily Ag⁺ ions react with CN⁻ ions to form the complex. This value is crucial for calculating the equilibrium constant for the reaction involving AgI and CN⁻, as it reflects the extent to which the complex forms in solution.
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Equilibrium Constants and Reaction Quotients

Equilibrium constants (K) relate the concentrations of products and reactants at equilibrium for a given reaction. The reaction quotient (Q) is similar but can be calculated at any point in the reaction. By using Ksp and Kf, one can derive the equilibrium constant for the reaction involving AgI and CN⁻, allowing for the determination of how the presence of CN⁻ affects the solubility of AgI in solution.
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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?

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Textbook Question

Calculate the solubility of Mn(OH)2 in grams per liter when buffered at pH (a) 7.0 (b) 9.5 (c) 11.8.

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Textbook Question

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid: (a) MnS (b) PbF2 (c) AuCl3 (e) CuBr (d) Hg2C2O4.

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