# Molality

Physical size
Surname Molality
Formula symbol ${\ displaystyle b}$
Size and
unit system
unit dimension
SI mol · kg -1 N · M −1

The molality ( Symbols : b , partly m ) according to DIN 1310 a so-called content size , which is a physico-chemical quantity for quantitative description of the composition of solutions . Here is material amount of a solute to the mass of the solvent based .

## Definition and characteristics

The molality b i is defined as the quotient of the amount of substance n i of the considered solute i and the mass m j of the solvent (always below with j indicated, often find abbreviations such as L, LM, Lm, using Solvent):

${\ displaystyle b_ {i} = {\ frac {n_ {i}} {m_ {j}}}}$

Due to the possibility of confusion with the quantity “mass”, the alternative symbol m is not recommended for molality.

The " particles " on which the term “substance quantity” is based must be specified, if necessary; they can be material elementary objects such as atoms , molecules , ions or formula units (as in the NaCl example below).

The molarity should not be confused with the molarity , which is usually more important in laboratory practice , an outdated term for the content quantitymolar concentration ”, in which the molar amount n i of the dissolved substance i is related to the total volume V of the solution.

The reference to the mass m j of the solvent j differentiates the molality b i from the very similar content quantity “ specific partial substance amountq i , in which the substance amount n i of the considered dissolved substance i is related to the total mass m of the solution. Both content quantities have the same dimension and accordingly the same derived SI unit mol / kg .

Advantageously, the molality as well as the specific amount of partial substances - in contrast to the volume-related content variables ( concentrations such as the concentration of the amount of substance ; volume fraction ; volume ratio ) - is independent of temperature and pressure , since masses and amounts of substances, in contrast to volumes, vary with temperature or do not change the pressure, provided that no material conversion occurs. In addition, their use enables greater accuracy, since masses can be determined more precisely than volumes, and possible volume contractions (or dilation) do not have to be taken into account when preparing the solution. The content quantity molality finds u. a. Application in physical chemistry (e.g. in chemical thermodynamics or also in electrochemistry ).

The dimensionless normalized molality b / b ° is formed by dividing the molality b by the standard molality b ° = 1 mol / kg water.

## Relationships with other salary levels

The following table shows the relationships between the molality b i and the other content quantities defined in DIN 1310 in the form of size equations . The formula symbols M and ρ provided with an index stand for the molar mass or density (at the same pressure and temperature as in the solution) of the respective pure substance identified by the index . The index i generally designates the dissolved substance, the index j the solvent and the index k the solution.

Relationship between molality b i and other salary quantities
Masses - ... Amount of substance - ... Particle number - ... Volume - ...
... - share Mass fraction w Amount of substance fraction x Particle number fraction X Volume fraction φ
${\ displaystyle b_ {i} = {\ frac {w_ {i}} {w_ {j} \ cdot M_ {i}}}}$ ${\ displaystyle b_ {i} = {\ frac {x_ {i}} {x_ {j} \ cdot M_ {j}}}}$ ${\ displaystyle b_ {i} = {\ frac {X_ {i}} {X_ {j} \ cdot M_ {j}}}}$ ${\ displaystyle b_ {i} = {\ frac {\ varphi _ {i} \ cdot \ rho _ {i}} {\ varphi _ {j} \ cdot \ rho _ {j} \ cdot M_ {i}}} }$
… - concentration Mass concentration β Molar concentration c Particle number concentration C Volume concentration σ
${\ displaystyle b_ {i} = {\ frac {\ beta _ {i}} {\ beta _ {j} \ cdot M_ {i}}}}$ ${\ displaystyle b_ {i} = {\ frac {c_ {i}} {\ rho _ {k} -c_ {i} \ cdot M_ {i}}}}$ ${\ displaystyle b_ {i} = {\ frac {C_ {i}} {C_ {j} \ cdot M_ {j}}}}$ ${\ displaystyle b_ {i} = {\ frac {\ sigma _ {i} \ cdot \ rho _ {i}} {\ sigma _ {j} \ cdot \ rho _ {j} \ cdot M_ {i}}} }$
... - ratio Mass ratio ζ Molar ratio r Particle number ratio R Volume ratio ψ
${\ displaystyle b_ {i} = {\ frac {\ zeta _ {ij}} {M_ {i}}}}$ ${\ displaystyle b_ {i} = {\ frac {r_ {ij}} {M_ {j}}}}$ ${\ displaystyle b_ {i} = {\ frac {R_ {ij}} {M_ {j}}}}$ ${\ displaystyle b_ {i} = {\ frac {\ psi _ {ij} \ cdot \ rho _ {i}} {\ rho _ {j} \ cdot M_ {i}}}}$
Quotient
amount of substance / mass
Molality b
${\ displaystyle b_ {i}}$
specific amount of partial substances q
${\ displaystyle b_ {i} = {\ frac {q_ {i}} {q_ {j} \ cdot M_ {j}}}}$

## example

An aqueous solution of common salt ( sodium chloride NaCl) of exactly half a mole of NaCl (using the molar mass of NaCl, this corresponds to a mass of 0.5 mol · 58.44 g / mol = 29.22 grams) and a half Kilograms, i.e. 500 grams of water (H 2 O) produced; the total mass of the solution is thus around 529.2 grams. The molality of NaCl in this solution is then:

${\ displaystyle b _ {\ mathrm {NaCl}} = {\ frac {n _ {\ mathrm {NaCl}}} {m _ {\ mathrm {H_ {2} O}}}} = {\ frac {\ mathrm {0 { ,} 5 \ mol}} {\ mathrm {0 {,} 5 \ kg}}} = \ mathrm {1 {,} 000 \ {\ frac {mol} {kg}}}}$

The specific partial substance amount of NaCl in this solution is somewhat smaller:

${\ displaystyle q _ {\ mathrm {NaCl}} = {\ frac {n _ {\ mathrm {NaCl}}} {m}} = {\ frac {\ mathrm {0 {,} 5 \ mol}} {\ mathrm { 0 {,} 5292 \ kg}}} \ approx \ mathrm {0 {,} 945 \ {\ frac {mol} {kg}}}}$

In practice, the designation "1-molal" aqueous NaCl solution is often to be expected for such an exemplary solution (contrary to the definition in the DIN 32625 standard, the designation "molal" for the unit mol / kg no longer applies) .