What is the molar solubility of AgI in 0.20 M NaCN? (a) 6.2 x 10^-4 M (b) 1.0 x 10^-1 M (c) 7.6 x 10^-2 M (d) 2.1 x 10^-3 M

Verified step by step guidance

1. First, write the balanced chemical equation for the dissolution of AgI in NaCN. AgI(s) will dissociate into Ag+ and I- ions. The Ag+ ions will then react with the CN- ions from NaCN to form Ag(CN)2- complex ions. The overall reaction is: AgI(s) + 2CN- (aq) -> Ag(CN)2- (aq) + I- (aq)
2. Next, write the expression for the solubility product constant (Ksp) for AgI and the formation constant (Kf) for the complex ion Ag(CN)2-. The Ksp expression for AgI is [Ag+][I-] and the Kf expression for Ag(CN)2- is [Ag(CN)2-]/[Ag+][CN-]^2. The Ksp for AgI is 8.5 x 10^-17 and the Kf for Ag(CN)2- is 1.0 x 10^21.
3. Since the Ag+ ions are completely consumed in the formation of the complex ion, the concentration of Ag+ ions is equal to the molar solubility of AgI. Let's denote this as 's'. The concentration of CN- ions is 0.20 M. The concentration of Ag(CN)2- ions is also 's' because one Ag+ ion reacts with two CN- ions to form one Ag(CN)2- ion.
4. Substitute these concentrations into the Kf expression and solve for 's'. The equation becomes: Kf = [s]/[s][0.20]^2. Simplify this equation to find 's'.
5. Finally, substitute the value of 's' into the Ksp expression and solve for [I-]. The equation becomes: Ksp = [s][I-]. Since [s] is equal to [I-], the equation simplifies to: Ksp = [s]^2. Solve this equation to find the molar solubility of AgI in 0.20 M NaCN.

Key Concepts

Molar Solubility

Molar solubility refers to the maximum concentration of a solute that can dissolve in a solvent at a given temperature, typically expressed in moles per liter (M). It is a crucial concept in understanding how substances interact in solution, particularly in the context of equilibrium and saturation.

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 this case, the presence of NaCN introduces CN⁻ ions, which shifts the equilibrium of AgI dissolution, thereby reducing its molar solubility due to Le Chatelier's principle.

Equilibrium Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It quantifies the extent to which a compound can dissolve in water, and is calculated from the concentrations of the ions in a saturated solution. For AgI, Ksp can be used to determine its molar solubility in the presence of other ions.