(i) the presence of functional groups, for instance, alcohol, carboxyl, carbonyl, or amino, all of which would promote water solubility....
and (ii) the absence of an exceptionally large hydrocarbyl chain.
So were we to consider the water solubility or #RCH_2OH#, we would expect some water solubility. And indeed we do. #"Ethanol"#, #H_3C-CH_2OH#, and #"methanol"#, #H_3C-OH#, are infinitely miscible in water. Methanol is even insoluble in hexanes. Extend the hydrocarbyl tail, and you detract from the water solubility.
Of course, we have only dealt with alcoholic solubility. Carboxylic acids, #RCO_2H#, and amines, #R_3N# would likewise exhibit some considerable solubility in water. Depending on their composition, primary, versus secondary, versus tertiary, they should also show some differential solubility in water. And in the limit of long hydrocarbyl tail length, they should become increasingly LESS soluble.
Are you happy with this?