Molality and Molarity are linked to each other through density of solution. Beginning with the definition of molarity, a solution of molarity “M” means that 1 litre of solution contains “M” moles of solute. If the density of the solution is “d” in gm/cc, then

We need to calculate mass of solvent in kg to calculate molality(m) :

Hence, molality,

We should note that "density of solution (d)" and "strength of solution (S)" differ. Density of solution (d) is ratio of mass of solution (solute + solvent) in gm and volume of solution in cc. It has the unit of gm/cc. On the other hand, strength of solution (S) is ratio of mass of solute in gm and volume of solution in litre. It has the unit of gm/litre.

### Example 2

Problem : The density of 3M sodium thiosulphate (Na2S2O3) solution is 1.25 gm/cc. Calculate molality of

Solution : We can use the formula to calculate molality of the sodium thiosulphate :

Alternatively, we can proceed with the basic consideration in place of using formula Since molarity of solution is 3M, it means that 1 litre of solution contains 3 moles of sodium thiosulphate. We can use density to find the mass of the 1 litre solvent.

We are, however, required to calculate molality of ions. We see that one mole is equivalent to 2 moles of sodium ion and 1 mole of thiosulphate ion :

Hence,