The solubility of any compound is given by the enthalpy change in the solution. The solubility of any ionic compounds in water is given by the ionization constant at equilibrium; here it refers to the non-changement in the ionization constant of water. The ionization constant for acids and bases in water is especially sought out by finding the equilibrium constant for a particular temperature which is the concentration of the products to the reactants at equilibrium when the substance is not completely dissolved, likely in the case of non-polar solvents. In case of complete dissolution, it is more obvious that the ionization constant is the product of the reactants, i.e. the conjugate acids and bases as the compound is no more in the pure form and it's dissociated into ions. But in all these processes, the ionization constant of water (Kw) always remains constant. This is in accordance with the very famous Le Chatelier's principle. As the change in the equilibrium of the system (here water as neutral) by adding of a solute will shift the reaction to such a direction as to counter effect the changes caused by the added substance, although the Kw does not change, the concentration of H+ and OH- do change as there is a shift in the direction of reaction as well as more H+ and OH- ions from other compounds:
In solubility of any compound, the solution enthalpy, as previously mentioned, depends upon the enthalpy change, which again depends upon the enthalpy or the energy required to break one mole of any ionic compound into its gaseous state ions, more familiar lattice enthalpy, but not only the lattice enthalpy can give information about solubility but also how much energy it is then required to dissolve the ions in the solvent (if water) and then the hydration enthalpy. The hydration enthalpy is negative, which means it is exothermic in nature. On adding these enthalpies, the enthalpy of solution is figured out:
This also tells if the enthalpy of solvation (hydration enthalpy) is less than the lattice enthalpy, then the compound will not dissolve sufficiently. Therefore, it becomes essential for any polar or non-polar compound that its hydration enthalpy must be big enough to compensate for the lattice enthalpy which is endothermic.
In the equilibrium process of solubility of a compound, the rate of forward reaction (the ions formed) must be equal to the rate of formation of the solid/compound back. This is generally a case with the saturated solution when no more solute dissolves as the system attains equilibrium. The solute ions will form, collide, and react again to form the solute back, a dynamic equilibrium state is attained, so the overall concentration of the pure solute does not change. And the equilibrium constant at this equilibrium condition is called solubility product constant, which is the product of the concentration of the products and equal to the molar solubility of the solute/compound.
The values of Ksp constant are and for BaSO4 and AgCN, respectively. What will be the concentration of the ions dissociated and which one is sparingly soluble?