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The term molality is formed in analogy to molarity which is the molar concentration of a solution. The earliest known use of the intensive property molality and of its adjectival unit, the now-deprecated molal, appears to have been published by G. N. Lewis and M. Randall in the 1923 publication of Thermodynamics and the Free Energies of Chemical Substances. [3]
Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. [1] For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c {\displaystyle c} : [ 2 ]
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
Here K f is the cryoscopic constant (equal to 1.86 °C kg/mol for the freezing point of water), i is the van 't Hoff factor, and m the molality (in mol/kg). This predicts the melting of ice by road salt. In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze.
The molar ionic strength, I, of a solution is a function of the concentration of all ions present in that solution. [3]= = where one half is because we are including both cations and anions, c i is the molar concentration of ion i (M, mol/L), z i is the charge number of that ion, and the sum is taken over all ions in the solution.
Change in volume with increasing ethanol fraction. The molar volume of a substance i is defined as its molar mass divided by its density ρ i 0: , = For an ideal mixture containing N components, the molar volume of the mixture is the weighted sum of the molar volumes of its individual components.
The apparent (molal) volume of a solute can be expressed as a function of the molality b of that solute (and of the densities of the solution and solvent). The volume of solution per mole of solute is
b is the molality of the solution. Through cryoscopy, a known constant can be used to calculate an unknown molar mass. The term "cryoscopy" means "freezing measurement" in Greek. Freezing point depression is a colligative property, so ΔT depends only on the number of solute particles dissolved, not the nature of those particles.