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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]
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.
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.
Theoretical chemistry requires quantities from core physics, such as time, volume, temperature, and pressure.But the highly quantitative nature of physical chemistry, in a more specialized way than core physics, uses molar amounts of substance rather than simply counting numbers; this leads to the specialized definitions in this article.
However, most chemical literature traditionally uses mol/dm 3, which is the same as mol/L. This traditional unit is often called a molar and denoted by the letter M, for example: 1 mol/m 3 = 10 −3 mol/dm 3 = 10 −3 mol/L = 10 −3 M = 1 mM = 1 mmol/L. The SI prefix "mega" (symbol M) has the same symbol. However, the prefix is never used ...
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: = = Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K ...