Converting Between Molarity and Molality

Converting a solution's molarity to molality means using the solution's density to find the mass of one liter of solution, subtracting the mass of the dissolved solute to isolate the mass of solvent, then dividing the known moles of solute by that solvent mass in kilograms.

A 0.556 M glucose solution with density 1.04 g/mL contains 0.556 mol glucose per liter. One liter of solution has a mass of 1040 g; subtracting the glucose's own mass, about 100 g, leaves 940 g of water. Dividing 0.556 mol by 0.940 kg gives a molality of about 0.591 m.