in NaCl, Na+ does not hydrolize but in Cr(NO3)3, Cr3+ hydrolizes to give H+, so when do we know which cation hydrolizes and which doesnt

A cation that is the salt of a strong base does not hydrolyze; therefore, Na^+, Li^+, K^+, Cs^+, Ba^+2, etc do not. NH4^+ (from NH3, a weak conjugate base) will, amine salts will (C6H6NH3^+ is the salt of aniline). Hydrated salts, such as Al(H2O)6 (+3 charge on ion), Cr(H2O)6(+3 charge on ion), react with water (hydrolyze) to form H3O^+ and the corresponding Al(H2O)5(OH)^+2. The bottom line is that NH4^+ and the corresponding amine salts are about the only ones that hydrolyze except for the highly hydrated ions.