By reacting a soluble zinc salt such as zinc sulphate with a solution of sodium carbonate. The products are zinc carbonate (which is insoluble and forms a white precipitate) and sodium sulphate which is very soluble and so remains in solution;-
Using Ion-Exchange Resins: you can do the Separation of Cations.
Every metal is adsorbed at certain pH range and property can be used as the basis for separation. For example, zinc can be adsorbed from 2 M of acidic solution but not magnesium and aluminium. Therefore, if a solution containing Zn and Mg being introduced to column, only Zn will be adsorbed. Mg is thus separated from Zn which can then be eluted with dilute nitric acid. The amount of separated Mgand Zn can be determined through EDTA titration
Both magnesium and zinc carbonates are poorly soluble in aqueous solution. I shall thus consider that (initially) they are mixed and predominantly not dissolved. You may consider to selectively dissolve the zinc carbonate; either in ammonia aq. sol. (as ammonium zinc carbonate), or with hot dil. aq. lactic acid (as zinc lactate). Alternatively, H2SO4 (aq) could be added, to generate soluble magnesium and zinc sulphates. These salts could be separated by selective cation-exchange.