relation between molarity and molality

Molarity/Molality = (moles of solute/volume of solution) × (mass of solvent/moles of solute)
           = mass of solvent (in kg)/volume of solution (in litre)
           = mass of solvent (in grams)/volume of solution = W/V  
Let the density of the solution be d.   Unit= g mL−1 
Mass of solution = V × d 
Mass of solute = number of moles × molecular mass of solute 
          = n mA
Mass of solvent, W = mass of solution – mass of solute 
          = V × d – n × mA 
Thus,  Molaity/Molality (M/m) = V×d–n×mA/V
  Molaity (m) = molarity×V/V×d–n×mA 
                    =molaity/d–n/V×mA 
                  m =molaity/d–molaity×mA 
where wZ, wBare masses of solvent and solute respectively xAand xBare mole fractions of solvent and solute respectively mAis molecular mass of solvent.

Thanks
Bharat Bajaj
Askiitians faculty

Hi