 Molality

In chemistry, the molality, b (or m), of a solvent/solute combination is defined as the amount of solute, n_{solute}, divided by the mass of the solvent, m_{solvent} (not the mass of the solution)^{[1]}:
If a mixture contains more than one solute or solvent, each solvent/solute combination in the mixture is defined in this same way.
Contents
Origin
The earliest such defintion of the intensive property molality and of its adjectival unit, the nowdeprecated molal (formerly, a variant of molar, describing a solution of unit molar concentration), appear to have been coined by G.N. Lewis and M. Randall in their 1923 publication of Thermodynamics and the Free Energies of Chemical Substances. ^{[2]} Though the two words are subject to being confused with one another, the molality and molarity of a weak aqueous solution happen to be nearly the same, as one kilogram of water (the solvent) occupies 1 liter of volume at room temperature and the small amount of solute would have little effect on the volume.
Unit
The SI unit for molality is mol/kg.
A solution with a molality of 3 mol/kg is often described as "3 molal" or "3 m". However, following the SI system of units, the National Institute of Standards and Technology, the United States authority on measurement, considers the term "molal" and the unit symbol "m" to be obsolete, and suggests mol/kg or a related unit of the SI^{[3]}. This recommendation has not been universally implemented in academia yet.
Example
Dissolving 1.0 mol of table salt (NaCl) in 2.0 kg of water constitutes a solution with a molality of m(NaCl) = 0.50 mol/kg. Adding and dissolving sugar to the solution does not change the molality of NaCl.
Properties
Like other massbased measures, the determination of molality only requires a good scale, because masses of both solvent and solute can be obtained by weighing, and molality is independent of physical conditions like temperature and pressure, providing advantages over molar concentration.
In a dilute aqueous solution near room temperature and standard atmospheric pressure, the numerical values of molarity (in mol/L) and molality (in mol/kg) are very similar because 1 L of solution contains about 1 kg of solvent under these conditions.
Unlike all the other compositional properties listed in "Relation" section (below), molality depends on our choice of the substance we call “solvent” in an arbitrary mixture. If there is only one pure liquid substance in a mixture, the choice is clear, but not all solutions are this clearcut: in an alcoholwater solution, either one could be called the solvent; in an alloy, or solid solution, there is no clear choice and all constituents may be treated alike. In such situations, mass or mole fraction is the preferred compositional specification.
Relation to other Compositional Properties
In what follows, the solvent may be given the same treatment as the other constituents of the solution, such that the molality of the solvent of an nsolute solution, say b_{0}, is found to be nothing more than the reciprocal of its molar mass, M_{0}:
Mass fraction
The conversions to and from the mass fraction, w, of the solute in a singlesolute solution are
where b is the molality and M is the molar mass of the solute.
More generally, for an nsolute/onesolvent solution, letting b_{i} and w_{i} be, respectively, the molality and mass fraction of the ith solute,
where M_{i} is the molar mass of the ith solute, and w_{0} is the mass fraction of the solvent, which is expressible both as a function of the molalities as well as a function of the other mass fractions,
Mole fraction
The conversions to and from the mole fraction, x, of the solute in a singlesolute solution are
where M_{0} is the molar mass of the solvent.
More generally, for an nsolute/onesolvent solution, letting x_{i} be the mole fraction of the ith solute,
where x_{0} is the mole fraction of the solvent, expressible both as a function of the molalities as well as a function of the other mole fractions:
Molar concentration (Molarity)
The conversions to and from the molar concentration, c, for onesolute solutions are
where ρ is the mass density of the solution, b is the molality, and M is the molar mass.
For solutions with n solutes, the conversions are
where c_{0} is expressible both as a function of the molalities as well as a function of the molarities:
Mass concentration
The conversions to and from the mass concentration, ρ_{solute}, of an singlesolute solution are
where ρ is the mass density of the solution, b is the molality, and M is the molar mass of the solute.
For the general nsolute solution, the mass concentration of the ith solute, ρ_{i}, is related to its molality, b_{i}, as follows:
where the mass density of the solvent, ρ_{0}, is expressible both as a function of the molalities as well as a function of the mass concentrations:
Equal Ratios
Alternatively, we may use just the last two equations given for the compositional property of the solvent in each of the preceding sections, together with the relationships given below, to derive the remainder of properties in that set:
where i & j are subscripts representing all the constituents, the n solutes plus the solvent.
Example of Conversion
An acid mixture consists of 0.76/0.04/0.20 mass fractions of (70%HNO_{3})/(49%HF)/(H_{2}O), where the percentages refer to mass fractions of the bottled acids carrying a balance of also H_{2}O. We start by determining the mass fractions of the constituents:
The approximate molar masses in kg/mol are
Let us first derive the molality of the solvent, in mol/kg,
and use that to derive all the others by use of the equal ratios:
Actually, b_{H2O} cancels out, because it is not needed. In this case, there is a more direct equation: we use it to derive the molality of HF:
The mole fractions may be derived from this result:
References
 ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "molality".
 ^ www.OED.com. Oxford University Press. 2011.
 ^ "NIST Guide to SI Units". http://physics.nist.gov/Pubs/SP811/sec11.html. Retrieved 20071217.
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and related quantitiesMolar concentration · Mass concentration · Number concentration · Volume concentration · Normality · Percentage solution · Molality · Mole fraction · Mass fraction · Mixing ratioSolubility Solubility equilibrium · Total dissolved solids · Solvation · Solvation shell · Enthalpy of solution · Lattice energy · Raoult's law · Henry's law · Solubility table (data) · Solubility chartSolvent Categories: Analytical chemistry
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molality — n. (Chem.) A measure of concentaration of substances in mixtures, 1 molal being the concentration of a solution containing 1 mole of solute per 1000 grams of solvent. Compare {molar}. [WordNet 1.5] … The Collaborative International Dictionary of English
molality — Moles of solute per kilogram of solvent; the molarity is equal to mρ/(1 + mM), where m is the m., ρ is the density of the solution, and M is the molar mass of the solute. Cf.:molarity. * * * mo·lal·i·ty (mo lalґĭ te) the number of moles of a … Medical dictionary
molality — molialumas statusas T sritis Standartizacija ir metrologija apibrėžtis Ištirpusios medžiagos molekulių molių skaičius 1 kg tirpiklio. atitikmenys: angl. molality; molar concentration vok. Kilogramm Molalität, f; molale Konzentration, f; Molalität … Penkiakalbis aiškinamasis metrologijos terminų žodynas
molality — molialumas statusas T sritis chemija apibrėžtis Ištirpusios medžiagos molių kiekis 1 kg tirpiklio. atitikmenys: angl. molal concentration; molality rus. моляльная концентрация; моляльность ryšiai: sinonimas – molialinė koncentracija … Chemijos terminų aiškinamasis žodynas
molality — molialumas statusas T sritis fizika atitikmenys: angl. molal concentration; molality vok. Kilogramm Molalität, f; molale Konzentration, f; Molalität, f rus. моляльная концентрация, f; моляльность, f pranc. concentration molale, f; molalité, f … Fizikos terminų žodynas
molality — noun see molal … New Collegiate Dictionary
molality — /moh lal i tee/, n., pl. molalities. Chem. the number of moles of solute per kilogram of solvent. [1920 25; MOLAL + ITY] * * * … Universalium
molality — noun the concentration of a substance in solution, expressed as the number of moles of solute per kilogram of solvent Syn: molal concentration … Wiktionary
molality — n. number of moles of solute per kilogram of solvent (Chemistry) … English contemporary dictionary
molality — mo·lal·i·ty … English syllables