In chemistry, the molality, b, of a solution is defined as the amount of substance of solute,
, divided by the mass of the solvent, :
Origin The earliest such definition of the intensive
property molality and of its adjectival unit, the now-deprecated molal, 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. 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 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. This recommendation has not
been universally implemented in academia yet. Usage considerations
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 mass-based nature of molality implies
that it can be readily converted into a mass ratio,
where the symbol M stands for molar mass, or into a mole ratio
The advantage of molality over other mass-based fractions is the fact that the molality of
one solute in a single-solvent solution is independent of the presence or absence of
other solutes. Problem areas:
Unlike all the other compositional properties listed in "Relation" section, 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 clear-cut: in an alcohol-water 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 n-solute solution, say b0, is found to be nothing more than the reciprocal
of its molar mass, M0:
Mass fraction The conversions to and from the mass fraction,
, of the solute in a single-solute solution are
where b is the molality and M is the molar mass of the solute.
More generally, for an n-solute/one-solvent solution, letting bi and wi be, respectively,
the molality and mass fraction of the i-th solute,
where Mi is the molar mass of the i-th solute, and w0 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 single-solute solution are
where M0 is the molar mass of the solvent. More generally, for an n-solute/one-solvent
solution, letting xi be the mole fraction of the i-th solute,
where x0 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 The conversions to and from the molar concentration,
c, for one-solute 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 c0 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,
ρsolute, of a single-solute 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 n-solute solution, the mass
concentration of the i-th solute, ρi, is related to its molality, bi, as follows:
where the mass concentration of the solvent, ρ0, 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 and j are subscripts representing all the constituents, the n solutes plus the
solvent. Example of conversion
An acid mixture consists of 0.760.20 mass fractions of / /(H2O), where the percentages
refer to mass fractions of the bottled acids carrying a balance of H2O. 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, bH2O 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 Osmolality is a variation of molality that
takes into account only 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. Relation to apparent properties
Molality appears in the expression of the apparent volume of a solute as a function
of the molality b of that solute:
For multicomponent systems the relation is slightly modified by the sum of molalities
of solutes.
References