What is the Molarity to Molality Calculator?
This tool converts molarity (moles of solute per litre of solution, mol/L) into molality (moles of solute per kilogram of solvent, mol/kg). The two concentration units differ because molarity is based on the total volume of solution while molality is based only on the mass of the solvent. Converting between them requires knowing the solution's density and the molar mass of the dissolved solute.
How to use it
Enter the molarity (M) in mol/L, the measured density of the solution (ρ) in g/mL, and the molar mass (MW) of the solute in g/mol. The calculator returns the molality in mol/kg along with the mass of solvent contained in one litre of solution.
The formula explained
Consider 1 litre (1000 mL) of solution. Its total mass is \(1000\cdot\rho\) grams. It contains \(M\) moles of solute, whose mass is \(M\cdot MW\) grams. The solvent mass is therefore \((1000\cdot\rho - M\cdot MW)\) grams \(= (1000\cdot\rho - M\cdot MW)/1000\) kg. Molality is moles of solute divided by kilograms of solvent:
$$m = \frac{1000 \cdot \text{M (mol/L)}}{1000 \cdot \text{$\rho$ (g/mL)} - \text{M} \cdot \text{MW (g/mol)}}$$
Worked example
A 1 mol/L NaCl solution (MW = 58.44 g/mol) has a density of 1.05 g/mL. The solvent mass is $$(1000\times1.05 - 1\times58.44)/1000 = 0.99156 \text{ kg}.$$ Molality $$= 1 / 0.99156 \approx 1.0085 \text{ mol/kg}.$$ Because some solution mass is solute, molality is slightly larger than molarity.
FAQ
Why are molarity and molality different? Molarity uses solution volume (temperature dependent), while molality uses solvent mass (temperature independent), so they only match in very dilute aqueous solutions.
What density should I use? Use the measured density of the whole solution, not the pure solvent.
Can the result be negative or undefined? If \(M\cdot MW\) exceeds \(1000\cdot\rho\) the inputs are physically inconsistent; double-check the molar mass and density.
