Would alcohols having longer alkyl groups be completely soluble in water?
Both methanol and ethanol are infinitely miscible with water. Propanol has limited solubility. The longer the alkyl chain, the less should be the aqueous solubility. Why? Well, the longer the chain the less water like the solvent, and the more dispersion forces between alkyl chains. As a physical scientist you should look up a table of alcoholic solubilities in water.