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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]
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.
In thermodynamics, the ebullioscopic constant K b relates molality b to boiling point elevation. [1] It is the ratio of the latter to the former: = i is the van 't Hoff factor, the number of particles the solute splits into or forms when dissolved. b is the molality of the solution.
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 c is the colligative molality, calculated by taking dissociation into account since the boiling point elevation is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as b c = b solute · i, where b solute is the molality of the solution. [3]
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process.
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 : [2]
For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. This is true for ideal solutions only, as occasionally ion pairing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle.