m= w2/m2 // w1/1000
how did it come?
The correct expression of molality is [(w2 / M2.) / w1 ] x 1000
m is known as molality of solute. It is defined as number of moles of solute in 1 kg of solvent.
Let us suppose that w2 g of solute with M2 g/mol of molar mass is dissolved in w1 g, of solvent.
Number of moles of solute = w2 / M2.
Thus, Molality, m = (w2 / M2.) / w1 in grams.
Since molality is moles/kg, therefore, we need to convert mass of solvent from g to kg.
So, m = [(w2 / M2.) / w1 in kg] x 1000
Hope its clear now.