How do we use #K_"sp"# values for solubility calculations....?

Question

Wyatt Adkins · Accepted Answer

Well, for a start write the solubility expression, and then do a bit of work...

Let's take a sparingly soluble salt, #PbCl_2#, for which #K_(sp)=5.89xx10^(−5)# at #25# #""^@C#. We can write the solubility expression as follows: #PbCl_2(s) rightleftharpoons Pb^(2+) + 2Cl^-# #K_(sp)=5.89xx10^(−5)=[Pb^(2+)][Cl^-]^2#, and if we represent the #"solubility of lead chloride"# under these conditions as #S#, then #K_(sp)=5.89xx10^(−5)=Sxx2S^2=4S^3#. We could usually solve this for #S# fairly easily. Now that's the solubility product. However, there are scenarios when the ion product is greater than #K_(sp)#, i.e. if we did the reaction in a salt solution, where #[Cl^-]# was artificially high. Because this ion product #># #K_"sp"#, #"lead chloride"# would precipitate from solution until the ion product #-=K_"sp"#. Such a process is normally called #"salting out"#, and if the metal were precious, say a salt of gold, or rhodium, or iridium, we would want to #"salt out"# the metal species so as maximize recovery of the metal. See https://tutor.hix.ai for another treatment of the problem.

Cameron Andrews · Answer

undefined To use Ksp values for solubility calculations, you first write the balanced chemical equation for the dissolution of the compound in water. Then, you write the equilibrium expression using the concentrations of the ions in solution and the Ksp value. Finally, you use the Ksp value and the concentrations of the ions to calculate the solubility of the compound in water.