How to Calculate Molality From Molarity & Density

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Molality and molarity are measures of a solution's concentration. Both describe concentration in terms of the number of moles of a solute in a solution. One mole is the number of atoms in 12 grams of carbon-12. Molality describes how concentrated a solution is by specifying the number of moles per unit mass of the solvent. Molarity, by contrast, describes the concentration by specifying the moles per unit volume of the entire solution.

  • Calculate the solute's molecular mass by multiplying each of its elements' relative atomic masses by the number of atoms of the element in each molecule. For a list of atomic masses, see the first link in "Resources." Each molecule of sodium hydroxide, for instance, contains one atom of sodium, which has an relative mass of 23; one atom of oxygen, which has a relative mass of 16; and one atom of hydrogen, which has a relative mass of 1 -- (1 x 23) + (1 x 16) + (1 x 1) = 40.

  • Multiply this relative molecular mass by the solution's molarity. If, for example, the solution has a molarity of 1.5 -- 40 x 1.5 = 60. This is the mass of solute, measured in grams, in one liter of solution.

  • Subtract this answer from the solution's density. With a density, for instance, of 1,050 grams per liter --1,050 - 60 = 990. This is the mass of solvent, measured in grams, in one liter of solution.

  • Divide this answer by 1,000 to convert it to kilograms: 990 / 1,000 = 0.99kg.

  • Divide the solution's molarity by this mass -- 1.5 / 0.99 = 1.52. This is the solution's molality, measured in moles per kilogram.

Tips & Warnings

  • Molarity and molality are always close to each other at room temperature.

References

  • Photo Credit Ablestock.com/AbleStock.com/Getty Images
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