Question 2
What is the solubility of AgCl in 10 M NH3? The Kf of Ag(NH3)2+ from AgCl(s) in aqueous NH3 is 0.0031, which is for the balanced reaction shown below.
AgCl(s) + 2 NH3(aq) → Ag(NH3)2+(aq) + Cl-(aq)
Is the answer 0.557 M?
I don't get that answer. Are you sure you have typed in the correct values? I think that 0.0031 is closer to the Knet for the reaction and not Kf for the formation of the complex. I think that number is very much higher; i.e., something like 10^7 or so. If I use 0.0031 for the Keq for the reaction I obtained 0.5 M for the solubility; I expect that 0.0031 is the Keq for the dissolution and that is Ksp*Kf.
1.8E-10*1.7E7 = 0.0031
To determine the solubility of AgCl in 10 M NH3, we can use the concept of the solubility product constant (Ksp) and the given information about the formation constant (Kf) for Ag(NH3)2+.
1. Write down the balanced equation for the reaction:
AgCl(s) + 2 NH3(aq) → Ag(NH3)2+(aq) + Cl-(aq)
2. Write the expression for the solubility product constant (Ksp) for AgCl:
Ksp = [Ag+][Cl-]
3. Use the given formation constant (Kf) for Ag(NH3)2+ to write the expression for the equilibrium constant (Keq) for the reaction:
Keq = [Ag(NH3)2+][Cl-] / [AgCl]
4. Since the reaction is at equilibrium, the concentrations of the products (Ag(NH3)2+ and Cl-) and the reactant (AgCl) will be related by the equilibrium constant (Keq):
Keq = [Ag(NH3)2+][Cl-] / [AgCl]
5. In 10 M NH3, we can assume that the concentration of NH3 remains constant. Therefore, we can write the expression for the equilibrium constant in terms of the formation constant (Kf) and the concentration of NH3:
Keq = [Ag(NH3)2+][Cl-] / [AgCl] = Kf * [NH3]^2
6. Substituting the given value for Kf and the concentration of NH3, solve for the solubility of AgCl:
Kf = 0.0031
[NH3] = 10 M
Keq = 0.0031 * (10 M)^2
Keq = 0.0031 * 100 M^2
Keq = 0.31 M^2
7. Rearrange the equation to solve for the solubility of AgCl:
[AgCl] = (Kf * [NH3]^2) / Keq
[AgCl] = (0.0031 * (10 M)^2) / 0.31 M^2
[AgCl] = 0.031 M / 0.31
[AgCl] = 0.1 M
Therefore, the solubility of AgCl in 10 M NH3 is 0.1 M (not 0.557 M).