What happens to the red blood cell in CaCl₂ solution?
The reason why the cell would shrink more in CaCl2 solution is because it has a higher van't Hoff factor i.e. total number of dissociated ionic species per solute molecule (it is 2 for NaCl whereas it is 3 for CaCl2). 

(Nonionic solutes do not dissociate and will therefore have a van't Hoff factor of 1)

Osmotic pressure (and other colligative properties) are proportional to van't Hoff factor. Therefore osmotic pressure in CaCl2 solution will be 3/2 times of that in an equimolar NaCl solution.

Note that the ionic chemical potential is not what drives osmosis; it is the differential concentration of water (or any other solvent) that drives it.