The expression relating mole fraction of solute (χ2) and molarity (M) of the solution is: (where d is the density of the solution in g L-1 and Mw1 and Mw2 are the molar masses of solvent and solute, respectively

Let the volume of solution =1 L Weight of solution = I x d = d g Number of moles of solute (n2) in 1 L solution = M ∴W2Mw2=MW2 (weight of solute) =M×Mw2W1 (weight of solvent) = Weight of solution − Weight of solute  =d−M×Mw2Number of moles of solvent (n1)=W1Mw1=d−M×Mw2Mw1∴χ2=n2n1+n2=Md−M×Mw2Mw1+M=M×Mw1MMw1−Mw2+dw