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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 : [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.
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
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.
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.
where ν is the number of ions produced from the dissociation of one molecule of the dissolved salt, b is the molality of the salt dissolved in water, φ is the osmotic coefficient of water, and the constant 55.51 represents the molality of water. In the above equation, the activity of a solvent (here water) is represented as inversely ...
List of orders of magnitude for molar concentration; Factor (Molarity) SI prefix Value Item 10 −24: yM 1.66 yM: 1 elementary entity per litre [1]: 8.5 yM: airborne bacteria in the upper troposphere (5100/m 3) [2]