To solve these types of problems, we need to use the solubility product constant (Ksp) expressions and also take into consideration the common ion effect. In each question, the solubility product expression will be dependent on the chemical equation for the dissolution process.
1) The solubility product constant for AgSCN is given by Ksp = [Ag+][SCN-]. If μ (ionic strength) is provided, it can be included in the equation as an activity correction factor. You would substitute these concentrations into your Ksp expression and solve for unknowns.
2) Repeat the above process for PbI2, La(IO3)3, and MgNH4PO4, each having its own unique solubility equilibrium.
3) To find the molar solubility of Zn(OH)2 in various solutions, we first need to balance the dissolution equation for Zn(OH)2, which gives us Zn(OH)2 (s) ⇌ Zn2+ + 2OH-. Then you need to calculate the concentrations of Zn2+ and OH- ions for each situation. These concentrations can be used in the solubility product expression Ksp = [Zn2+][OH-]^2 to determine the molar solubility for each scenario.
4) For calculating the solubility of compounds in a Mg(ClO4)2 solution, you follow a similar method as before but factor in the extra magnesium ions that are introduced from the Mg(ClO4)2. Remember to use the appropriate Ksp expressions for each compound.
5) Lastly, you calculate the solubility of compounds in a Ba(NO3)2 solution. Similar to the Mg(ClO4)2 solution calculations, remember to account for the extra ions introduced by the Ba(NO3)2.
In all of these calculations, you also need to consider any common ions present in each solution because they will affect the overall solubility. Make sure to keep track of all ions and assign correct stoichiometric coefficients when balancing your chemical equations.
Finding the exact results without numerical values of each Ksp, it would be difficult to provide a detailed, step-by-step solution. Nevertheless, the above steps should give a general guide to solve these types of problems.