Relation Between Molarity (M) and Molality (m)

$$\frac{1}{m} = \frac{d}{M} - \frac{M_B}{1000} \quad \implies \quad m = \frac{1000 \cdot M}{1000 \cdot d - M \cdot M_B}$$

Concept: Converts molarity (volume-based, temperature-dependent) into molality (mass-based, temperature-independent) using the density of the solution.

Notation:

• m = Molality ($$\text{mol kg}^{-1}$$)
• M = Molarity ($$\text{mol L}^{-1}$$)
• $$d$$ = Density of solution ($$\text{g mL}^{-1}$$)
• $$M_B$$ = Molar mass of solute ($$\text{g mol}^{-1}$$)