J.R. S. answered 08/12/21
Ph.D. University Professor with 10+ years Tutoring Experience
This appears to be a problem dealing with solubility and Ksp. It appears they are asking you to find the concentration of Pb2+ and Cl- in the presence of the common ion Cl- which is present in the form of MgCl2. The way the question is written, it isn't clear what is meant by "Show that changes in the initial concentrations:"
PbCl2(s) <==> Pb2+(aq) + 2Cl-(aq) ... this is the dissolution equilibria
Ksp = 1.6x10-5 = [Pb2+][Cl-]2
The [Cl-] can be taken as 2 x 0.631 M = 1.26 M since MgCl2 ==> Mg2+ + 2Cl-
1.6x10-5 = [Pb2+][1.26]2
1.6x10-5 = 1.59 [Pb2+]
[Pb2+] = 1.0x10-5 M
[Mg2+] = 0.631 M
[Cl-] = 2 x 0.631 M = 1.26 M