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In chemistry, the molality, b (or m), of a solution is defined as the amount of substance (in mol) of solute, , divided by the mass (in kg) of the solvent, (not the mass of the solution):^{[1]}
The earliest such definition 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.
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.
Advantages:
Compared to molar concentration or mass concentration, the preparation of a solution of a given molality requires only a good scale: both solvent and solute need to be weighed, as opposed to measured volumetrically, which would be subject to variations in density due to the ambient conditions of temperature and pressure; this is an advantage because, in chemical compositions, the mass, or the amount, of a pure known substance is more relevant than its volume: a contained measured amount of substance may change in volume with ambient conditions, but its amount and mass are unvarying, and chemical reactions occur in proportions of mass, not volume. The massbased nature of molality implies that it can be readily converted into a mass ratio (or mass fraction, "w," ratio),
where the symbol M stands for molar mass, or into a mole ratio (or mole fraction, "x," ratio)
The advantage of molality over other massbased fractions is the fact that the molality of one solute in a singlesolvent solution is independent of the presence or absence of other solutes.
Problem areas:
Unlike all the other compositional properties listed in "Relation" section (below), molality depends on the choice of the substance to be called “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.
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}:
The conversions to and from the mass fraction, , 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,
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:
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 of the solute.
For solutions with n solutes, the conversions are
where the molar concentration of the solvent c_{0} is expressible both as a function of the molalities as well as a function of the molarities:
The conversions to and from the mass concentration, ρ_{solute}, of a 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 concentration of the solvent, ρ_{0}, is expressible both as a function of the molalities as well as a function of the mass concentrations:
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 and j are subscripts representing all the constituents, the n solutes plus the solvent.
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 H_{2}O. The first step is determining the mass fractions of the constituents:
The approximate molar masses in kg/mol are
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:
Osmolality is a variation of molality that only takes into account solutes that contribute to a solution's osmotic pressure. It is measured in osmoles of the solute per kilogram of water. This unit is frequently used in medical laboratory results in place of osmolarity, because it can be measured simply by depression of the freezing point of a solution, or cryoscopy (see also: osmostat and colligative properties).
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