The relation between molarity and molality is:
Consider,
- W to be the mass of the given solute
- W’ to be the weight of the solvent
- V to be the volume of the solution
- m to be the molality
- M to be the molarity
- M’ to be the molar mass of the solute
Molarity, M = \(frac{W}{M’}times frac{1000}{V}\) (equ.1)
Molality, m = \(frac{W}{M’}times frac{1000}{W’}\) (equ.2)
Density, d = \(frac{M}{V}=frac{W+W’}{V}\)
From equ.1
\(V=frac{Wtimes 1000}{MM’}\) (equ.3)From equ.2
\(W’=frac{Wtimes 1000}{mM’}\)Therefore,
w+W’ = W + \(frac{Wtimes 1000}{mM’}\) \(frac{1000}{M’}[frac{mM’}{1000m}+frac{1}{m}]W'\) (equ.4)
Dividing equ.4 by equ.3,
\(frac{d}{M}=frac{1}{m}+frac{M’}{1000}\) \(frac{1}{m}=frac{d}{M}-frac{M’}{1000}\) \(m=frac{Mtimes 1000}{(dtimes 1000)-M(M’)}\)Therefore, above is the relation between molality and molarity.
