How high can molality be?
The maximum molality is 52.8 m.
One litre of pure water has a mass of 1 kg. Since the molar mass of water is 18.02 g/mol, the molality of pure water is 55.49 mol/kg or 55.49 m.
In a solution, the solvent must be the major component. That means we would need to have less than 1000 g of solute in 1 kg of water. Not many substances are this soluble. The only compound that comes close is NH₃, which has a solubility of 900 g/kg water.
If we mixed 900 g of NH₃ (molar mass = 17.03 g/mol) with 1000 g of water, we would have a 52.8 m solution of NH₃. This is therefore the maximum practical molality for aqueous solutions.