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Molarity is the measure of concentration of a solution in terms of moles solute per liter of solution. Molality is a measure of concentration in terms of moles solute per kg of solvent. In practical terms, dilute solutions in water will have the same value of molarity and molality since the density of water is 1 g/mL, thus 1 liter of water will weigh 1 kg. But as the concentration of the solution increases, the volume of the solute will start to become appreciable and will start to take a measurable amount of space that would otherwise be taken by the water. Whereas in the case of molality, the denominator is always the mass of the solvent (not solvent plus solute) so it will remain unchanged regardless of the concentration.
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