関: M、molar、molar concentration、molarity

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concentration measured by the number of moles of solute per kilogram of solvent (同)molal concentration
the 13th letter of the Roman alphabet (同)m
pertaining to large units of behavior; "such molar problems of personality as the ego functions"--R.R. Hunt
grinding tooth with a broad crown; located behind the premolars (同)grinder
containing one mole of a substance; "molar weight"
designating a solution containing one mole of solute per liter of solution
of or pertaining to the grinding teeth in the back of a mammals mouth; "molar teeth"
concentration measured by the number of moles of solute per liter of solution (同)molar_concentration, M

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/07/05 10:00:38」(JST)

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Not to be confused with Molarity.

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]

Origin[edit]

The earliest such definition of the intensive property molality and of its adjectival unit, the now-deprecated 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[edit]

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.

Usage considerations[edit]

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 (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 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 (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, 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[edit]

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[edit]

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 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 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[edit]

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 x_i 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 (Molarity)[edit]

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[edit]

The conversions to and from the mass concentration, ρ_solute, of an 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, ρ_i, is related to its molality, b_i, 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[edit]

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[edit]

An acid mixture consists of 0.76/0.04/0.20 mass fractions of (70% HNO₃)/(49% HF)/(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:

$\begin{align} w_{HNO_3}&=0.70\times 0.76=0.532\\ w_{HF}&=0.49\times 0.04=0.0196\\ w_{H_2O}&=1-w_{HNO_3}-w_{HF}=0.448\\ \end{align}$

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:

$\frac{b_{HNO_3}}{b_{H_2O}}=\frac{w_{HNO_3}M_{H_2O}}{w_{H_2O}M_{HNO_3}} \ \therefore b_{HNO_3}=18.83.$

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:

$\begin{align} &x_{H_2O}=(1+M_{H_2O}(b_{HNO_3}+b_{HF}))^{-1}=0.726,\\ &\frac{x_{HNO_3}}{x_{H_2O}}=\frac{b_{HNO_3}}{b_{H_2O}}\ \therefore x_{HNO_3}=0.246,\\ &x_{HF}=1-x_{HNO_3}-x_{H_2O}=0.029. \end{align}$

Osmolality[edit]

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).

References[edit]

^ 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". Retrieved 2007-12-17.

English Journal

Glyoxal and Methylglyoxal Setschenow Salting Constants in Sulfate, Nitrate, and Chloride Solutions: Measurements and Gibbs Energies.

Waxman EM1,2, Elm J3,4, Kurtén T5, Mikkelsen KV3, Ziemann PJ1,2, Volkamer R1,2.
Environmental science & technology.Environ Sci Technol.2015 Oct 6;49(19):11500-8. doi: 10.1021/acs.est.5b02782. Epub 2015 Sep 22.
Knowledge about Setschenow salting constants, KS, the exponential dependence of Henry's Law coefficients on salt concentration, is of particular importance to predict secondary organic aerosol (SOA) formation from soluble species in atmospheric waters with high salt concentrations, such as aerosols.
PMID 26335375

Effect of Hydrophobic Chain Structure on Phase Transition and Domain Formation of Hybrid Alcohol Films Adsorbed at the Hexane/Water Interface.

Mitani K1, Imai Y2, Ina T3, Nitta K3, Tanida H3, Uruga T3, Matsubara H1, Aratono M1, Takiue T1,2.
The journal of physical chemistry. B.J Phys Chem B.2015 Sep 24;119(38):12436-45. doi: 10.1021/acs.jpcb.5b07632. Epub 2015 Sep 10.
The phase transition and domain formation of the adsorbed film of two kinds of hybrid alcohols (CF3(CF2)m-1(CH2)nOH, FmHnOH), 2-perfluorooctylethanol (F8H2OH) and 2-perfluorohexylhexanol (F6H6OH), as a mixture at the hexane/water interface was investigated by interfacial tensiometry and X-ray reflec
PMID 26308905

Separating chemical and excluded volume interactions of polyethylene glycols with native proteins: Comparison with PEG effects on DNA helix formation.

Shkel IA1,2, Knowles DB1, Record MT Jr1,2.
Biopolymers.Biopolymers.2015 Sep;103(9):517-27. doi: 10.1002/bip.22662.
Small and large PEGs greatly increase chemical potentials of globular proteins (μ2 ), thereby favoring precipitation, crystallization, and protein-protein interactions that reduce water-accessible protein surface and/or protein-PEG excluded volume. To determine individual contributions of PEG-prote
PMID 25924886

Japanese Journal

翻訳法、自由、道徳

Hart H. L. A.,加藤隆之 [訳]
青森法政論叢 (10), 61-78, 2009
NAID 40016818064

超臨界条件下における金雲母と2M塩化物水溶液間における2価金属イオンの同時分配実験

内田悦生,松本公平
岩石鉱物科学 35(4), 197-206, 2006-07-30
… KCl - (Ni2+,Mg2+,Co2+,Zn2+,Fe2+,Mn2+,Ca2+,Sr2+) Cl2 - H2O in the temperature range of 500 to 800 °C at 100 MPa, using the pressure vessel of a cold seal type. The partition coefficient KPN (Phl) for the ion exchange reaction between phlogopite (Phl) and aqueous chloride solution (aq) can be expressed as follows: KPN (Phl) = (X1/6K2Me6Al2Si6O20(OH)4 / X1/6K2Mg6Al2Si6O20(OH)4) Phl / (mMeCl20 / mMgCl20)aq where Me designates divalent metal ion, m: molality, and Xi: mole fraction of end-member i in biotite solid …
NAID 10017532471

糖水溶液中での氷結晶の融点(平成16年度第50回低温生物工学会研究報告)

清忠師,権田武彦
低温生物工学会誌 50(2), 93-95, 2004-12-30
… Above the molality to be estimated that no free water exist, melting point of ice crystal was lower than the formula of the molar depression of freezing point. …
NAID 110004799117

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リンク元	「モル濃度」「molar」「molarity」「molar concentration」「重量モル濃度」
拡張検索	「osmolality」「hyperosmolality」