It depends. The solvents need to be immiscible. Acetone, unfortunately, tends to be miscible with most solvents. Your compound needs to "partition" in one solvent while the impurities should partition in another solvent.
Solvent pairs include:
water/ethyl acetate
water/dichloromethane
water/ether
hexane/methanol
hexane/acetonitrile
(hexane can be substituted with petroleum ether or other hydrocarbons)
If you desired compound is an alkaloid, you can partition it into acidic water from dichloromethane. Make the aqueous solution basic, and partition again with dichloromethane. You may find your compound in the DCM layer.
There are other solvent systems beyond what I listed for partitioning.
yes you can use a separatory funnel to purify a mixture instead of column chromatography, particularly if the components have different solubilities in immiscible solvents like acetone and water. The process involves dissolving the mixture in an organic solvent, adding water or an aqueous solution, shaking to allow partitioning between the layers, separating the layers, and repeating the extraction to improve the purification. This solvent extraction technique can be an effective alternative to column chromatography, especially for small-scale purifications where the components have sufficiently different solubilities in the chosen solvents.
You can use a separatory funnel for purification if your purification solvents are immiscible with acetone, allowing for distinct phase separation. If the solvents are not immiscible, column chromatography would be a more effective method for purification.