Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of
molarity
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
which is based on a specified
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
of solution.
A commonly used unit for molality in
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
is
mol/
kg. A solution of concentration 1 mol/kg is also sometimes denoted as ''1 molal''. The unit ''mol/kg'' requires that molar mass be expressed in ''kg/mol'', instead of the usual ''g/mol'' or ''kg/kmol''.
Definition
The molality (''b''), of a
solution
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Soluti ...
is defined as the
amount of substance
In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
(in
mole
Mole (or Molé) may refer to:
Animals
* Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America
* Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
s) of solute, ''n''
solute, divided by the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
(in
kg) of the
solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
, ''m''
solvent:
:
In the case of solutions with more than one solvent, molality can be defined for the mixed solvent considered as a pure pseudo-solvent. Instead of mole solute per kilogram solvent as in the binary case, units are defined as mole solute per kilogram mixed solvent.
Origin
The term ''molality'' is formed in analogy to ''molarity'' which is the
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
of a solution. The earliest known use of the
intensive property
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is on ...
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.''
Though the two terms are subject to being confused with one another, the molality and molarity of a dilute
aqueous solution
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be re ...
are nearly the same, as one kilogram of water (solvent) occupies the volume of 1 liter at room temperature and a small amount of solute has little effect on the volume.
Unit
The
SI unit for molality is moles per kilogram of solvent.
A solution with a molality of 3 mol/kg is often described as "3 molal", "3 m" or "3 ''m''". However, following the SI system of units, the
National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
, the
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
authority on
measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
, considers the term "molal" and the unit symbol "m" to be obsolete, and suggests mol/kg or a related unit of the SI.
Usage considerations
Advantages
The primary advantage of using molality as a measure of concentration is that molality only depends on the masses of solute and solvent, which are unaffected by variations in temperature and pressure. In contrast, solutions prepared volumetrically (e.g.
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
or
mass concentration) are likely to change as temperature and pressure change. In many applications, this is a significant advantage because the mass, or the amount, of a substance is often more important than its volume (e.g. in a
limiting reagent
The limiting reagent (or limiting reactant or limiting agent) in a chemical reaction is a reactant that is totally consumed when the chemical reaction is completed. The amount of product formed is limited by this reagent, since the reaction canno ...
problem).
Another advantage of molality is the fact that the molality of one solute in a 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 clear-cut: in an alcohol–water solution, either one could be called the solvent; in an alloy, or
solid solution
A solid solution, a term popularly used for metals, is a homogenous mixture of two different kinds of atoms in solid state and have a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word ...
, 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 quantities
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 ''b''
0, is found to be nothing more than the reciprocal of its molar mass, ''M''
0 (expressed as kg/mol):
:
For the solutes the expression of molalities is similar:
:
The expressions linking molalities to mass fractions and mass concentrations contain the molar masses of the solutes ''M''
i:
:
Similarly the equalities below are obtained from the definitions of the molalities and of the other compositional quantities.
The mole fraction of solvent can be obtained from the definition by dividing the numerator and denominator to the amount of solvent n
0:
:
Then the sum of ratios of the other mole amounts to the amount of solvent is substituted with expressions from below containing molalities:
:
:
giving the result
:
Mass fraction
The conversions to and from the
mass fraction, ''w
1'', of the solute in a single-solute solution are
:
where ''b
1'' is the molality and ''M
1'' is the
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, p ...
of the solute.
More generally, for an ''n''-solute/one-solvent solution, letting ''b
i'' and ''w
i'' be, respectively, the molality and mass fraction of the ''i''-th solute,
:
where ''M
i'' is the molar mass of the ''i''th 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,
:
Substitution gives:
:
Mole fraction
The conversions to and from the
mole fraction
In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
, ''x
1'' mole fraction of the solute in a single-solute solution are
:
where ''M''
0 is the molar mass of the solvent.
More generally, for an ''n''-solute/one-solvent solution, letting ''x
i'' be the mole fraction of the ''i''th 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:
:
Substitution gives:
:
Molar concentration (molarity)
The conversions to and from the
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
, ''c
1'', for one-solute solutions are
:
where ''ρ'' is the
mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
of the solution, ''b
1'' is the molality, and ''M
1'' is the molar mass (in kg/mol) 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 other molarities:
:
Substitution gives:
:
Mass concentration
The conversions to and from the
mass concentration, ''ρ''
solute, of a single-solute solution are
:
or
:
where ''ρ'' is the mass density of the solution, ''b
1'' is the molality, and ''M
1'' is the molar mass of the
solute
In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
.
For the general ''n''-solute solution, the mass concentration of the ''i''th 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 other mass concentrations:
:
Substitution gives:
:
Equal ratios
Alternatively, one 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 0.76, 0.04, and 0.20 mass fractions of 70% HNO
3, 49% HF, and H
2O, where the percentages refer to mass fractions of the bottled acids carrying a balance of H
2O. 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
Osmolality is a variation of molality that takes into account only solutes that contribute to a solution's
osmotic pressure
Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.
It is also defined as the measure of the tendency of a solution to take in a pure ...
. It is measured in
osmole
Osmotic concentration, formerly known as osmolarity, is the measure of solute concentration, defined as the number of osmoles (Osm) of solute per litre (L) of solution (osmol/L or Osm/L). The osmolarity of a solution is usually expressed as Osm/L ...
s of the solute per
kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
of water. This unit is frequently used in
medical laboratory
A medical laboratory or clinical laboratory is a laboratory where tests are conducted out on clinical specimens to obtain information about the health of a patient to aid in diagnosis, treatment, and prevention of disease. Clinical Medical labor ...
results in place of
osmolarity
Osmotic concentration, formerly known as osmolarity, is the measure of solute concentration, defined as the number of osmoles (Osm) of solute per litre (L) of solution (osmol/L or Osm/L). The osmolarity of a solution is usually expressed as Osm/L ...
, because it can be measured simply by depression of the freezing point of a solution, or
cryoscopy
Freezing-point depression is a drop in the minimum temperature at which a substance freezes, caused when a smaller amount of another, non- volatile substance is added. Examples include adding salt into water (used in ice cream makers and for ...
(see also:
osmostat The osmostat is the regulatory center in the hypothalamus that controls the osmolality of the extracellular fluid. The area in the anterior region of the hypothalamus contains the osmoreceptors, cells that control osmolality via the secretion of a ...
and
colligative properties
In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number r ...
).
Relation to apparent (molar) properties
Molality appears in the expression of the
apparent (molar) volume of a solute as a function of the molality ''b'' of that solute (and density of the solution and solvent):
:
:
For multicomponent systems the relation is slightly modified by the sum of molalities of solutes. Also a total molality and a mean apparent molar volume can be defined for the solutes together and also a mean
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, p ...
of the solutes as if they were a single solute. In this case the first equality from above is modified with the mean molar mass M of the pseudosolute instead of the molar mass of the single solute:
:
,
:
, y
i,j being ratios involving molalities of solutes i,j and the total molality b
T.
The sum of products molalities - apparent molar volumes of solutes in their binary solutions equals the product between the sum of molalities of solutes and apparent molar volume in ternary or multicomponent solution.
:
,
Relation to apparent molar properties and activity coefficients
For concentrated ionic solutions the activity coefficient of the electrolyte is split into electric and statistical components.
The statistical part includes molality b,
hydration index number h, the number of ions from the dissociation and the ratio r
a between the
apparent molar volume of the electrolyte and the molar volume of water.
Concentrated solution statistical part of the activity coefficient is:
:
Molalities of a ternary or multicomponent solution
The molalities of solutes b
1, b
2 in a ternary solution obtained by mixing two binary aqueous solutions with different solutes (say a sugar and a salt or two different salts) are different than the initial molalities of the solutes b
ii in their binary solutions.
The content of solvent in mass fractions w
01 and w
02 from each solution of masses m
s1 and m
s2 to be mixed as a function of initial molalities is calculated. Then the amount (mol) of solute from each binary solution is divided by the sum of masses of water after mixing:
Mass fractions of each solute in the initial solutions w
11 and w
22
are expressed as a function of the initial molalities b
11, b
22 :
These expressions of mass fractions are substituted in the final molalitaties.
The results for a ternary solution can be extended to a multicomponent solution (with more than two solutes).
From the molalities of the binary solutions
The molalities of the solutes in a ternary solution can be expressed also from molalities in the binary solutions and their masses:
The binary solution molalities are:
The masses of the solutes determined from the molalities of the solutes and the masses of water can be substituted in the expressions of the masses of solutions:
Similarly for the mass of the second solution:
From here one can obtain the masses of water to be summed in the denominator of the molalitities of the solutes in the ternary solutions.
Thus the ternary molalities are:
See also
*
Molarity
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
References
{{Chemical solutions
Chemical properties
es:Concentración#Molalidad