Calculate the molar solubility of AgI in:(a) Pure Water(b) 0.10 M NaCN: Kf for [Ag(CN)2]- is 3.0 x 10^20

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Step 1: Determine the solubility product constant (K_sp) for AgI. The dissolution of AgI in water can be represented as: AgI(s) ⇌ Ag⁺(aq) + I^-(aq). Look up the K_sp value for AgI in a chemistry reference.

Step 2: Calculate the molar solubility of AgI in pure water. Let the molar solubility be 's'. Then, [Ag⁺] = s and [I^-] = s. Use the expression K_sp = [Ag⁺][I^-] to solve for 's'.

Step 3: For part (b), consider the complexation of Ag⁺ with CN^-. The formation of the complex [Ag(CN)₂]^- can be represented as: Ag⁺(aq) + 2 CN^-(aq) ⇌ [Ag(CN)₂]^-(aq). Use the given formation constant (K_f) to express the equilibrium condition.

Step 4: Set up the equilibrium expressions for the dissolution of AgI and the formation of the complex ion. Assume the initial concentration of CN^- is 0.10 M. Use the K_sp and K_f values to write the overall equilibrium expression for the system.

Step 5: Solve the equilibrium expression to find the molar solubility of AgI in 0.10 M NaCN. This involves substituting the expressions for the concentrations of Ag⁺, I^-, and [Ag(CN)₂]^- into the equilibrium equations and solving for the solubility.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Solubility

Molar solubility refers to the maximum amount of a solute that can dissolve in a given volume of solvent at equilibrium, expressed in moles per liter (M). It is a crucial concept in understanding how solutes interact with solvents and is influenced by factors such as temperature and the presence of other ions in solution.

Common Ion Effect

The common ion effect describes the decrease in solubility of a salt when a common ion is added to the solution. In the case of AgI, the presence of NaCN introduces CN⁻ ions, which can shift the equilibrium and reduce the solubility of AgI due to the formation of complex ions, thereby affecting the molar solubility.

Formation Constant (Kf)

The formation constant (Kf) quantifies the stability of a complex ion in solution. For the complex ion [Ag(CN)2]⁻, a high Kf value (3.0 x 10^20) indicates that the complex is very stable, which significantly influences the solubility of AgI in the presence of CN⁻ ions, as it drives the equilibrium towards the formation of the complex and reduces the concentration of free Ag⁺ ions.

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Write a balanced net ionic equation for each of the follow-ing dissolution reactions, and use the appropriate Ksp and Kf values in Appendix C to calculate the equilibrium constant for each.(a) AgI in aqueous NaCN to form [Ag(CN)2]-

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