Core-shell nanoparticles can be synthesized by partial exchange of the cation of the core nanoparticles by a second cation of the desired shell compound. Process time and cation concentration can be varied to control the thickness of the shell. A mathematical model is presented that describes the process of ion-exchange from preformed spherical nanoparticles. The overall process consists of diffusion of the cation from the solution to the core - nanoparticle surface, then solid-state diffusion of the cation across the shell, and finally the cation exchange reaction. We find that the second step of diffusion in the shell is rate-controlling. Our model compares well with the available experimental data of CdS-PbS core-shell nanoparticle formation at various [Ph2+]/[Cd2+] molar ratios and at different process times. The model can be useful for a priori specification of experimental conditions required for a desired shell thickness.