Specific amount of partial substances

The specific Partialstoffmenge ( Symbols : q ) according to DIN 1310 and DIN 32625 a so-called content size , which is a physico-chemical quantity for quantitative description of the composition of mixtures / mixed phases (eg. Solution ). Here, the amount of substance of a considered mixture component is related to the total mass of the mixed phase .

Definition and characteristics

The specific partial substance amount q _i is defined as the quotient of the substance amount n _{i of} a considered mixture component i and the total mass m of the mixed phase:

${\displaystyle q_{i}={\frac {n_{i}}{m}}}$

The total mass m of the mixed phase is the sum of the masses of all components of the mixture, formulated below for a general mixture of a total of Z components (index such as a general running index for the summation includes i with a):

${\displaystyle m=\sum _{z=1}^{Z}m_{z}}$

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 reference to the total mass m of the mixed phase distinguishes the specific partial substance amount q _i from the very similar content quantity molality b _i . In the case of the content quantity restricted to solutions , the amount of substance of a considered dissolved substance i is related to the mass of the solvent ( indicated below with j ):

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

Both content quantities have the same dimension and accordingly the same derived SI unit mol / kg .

Advantageously, the specific partial substance amount as well as the molality - in contrast to the volume-related content variables ( concentrations such as the molar concentration ; volume fraction ; volume ratio ) - is independent of temperature and pressure , since masses and substance quantities, 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.

use

The content size specific partial substance amount is very well suited for many applications in the field of solid-state chemistry , analytical chemistry and stoichiometry . This applies in particular to the description of the chemical composition of solid mixtures whose volumes are poor or not at all, but whose masses can be determined easily, for example alloys and solid chemical compounds including macromolecular compounds ( polymers , including functionalized polymers such as Ion exchanger ). Depending on the application, other terms may also be used, e.g. B. Capacity (ion exchanger), occupancy (functionalized polymers), specific amount of substance ( elemental analysis ).

In the case of titrations (weighing titrations ) carried out gravimetrically - instead of volumetrically, as is usual - specific amounts of partial substances are used to indicate the content of the standard solutions .

Relationships with other salary levels

The following table shows the relationships between the specific amount of partial substance q _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 substance mixture) of the respective pure substance identified by the index . The symbol ρ without an index represents the density of the mixed phase. As above, the index z serves as a general index for the sums and includes i . N _A is Avogadro's constant ( N _A ≈ 6.022 · 10 ²³  mol ⁻¹ ).

Relationship of the specific partial substance amount q _i with other content quantities

	Masses - ...	Amount of substance - ...	Particle number - ...	Volume - ...
... - share	Mass fraction w	Amount of substance fraction x	Particle number fraction X	Volume fraction φ
	${\displaystyle q_{i}={\frac {w_{i}}{M_{i}}}}$	${\displaystyle q_{i}={\frac {x_{i}}{\sum _{z=1}^{Z}(x_{z}\cdot M_{z})}}}$	${\displaystyle q_{i}={\frac {X_{i}}{\sum _{z=1}^{Z}(X_{z}\cdot M_{z})}}}$	${\displaystyle q_{i}={\frac {\varphi _{i}\cdot \rho _{i}}{M_{i}\cdot \sum _{z=1}^{Z}(\varphi _{z}\cdot \rho _{z})}}}$
… - concentration	Mass concentration β	Molar concentration c	Particle number concentration C	Volume concentration σ
	${\displaystyle q_{i}={\frac {\beta _{i}}{M_{i}\cdot \rho }}}$	${\displaystyle q_{i}={\frac {c_{i}}{\rho }}}$	${\displaystyle q_{i}={\frac {C_{i}}{N_{\mathrm {A} }\cdot \rho }}}$	${\displaystyle q_{i}={\frac {\sigma _{i}\cdot \rho _{i}}{M_{i}\cdot \rho }}}$
... - ratio	Mass ratio ζ	Molar ratio r	Particle number ratio R	Volume ratio ψ
	${\displaystyle q_{i}={\frac {1}{\sum _{z=1}^{Z}\zeta _{zi}}}\cdot {\frac {1}{M_{i}}}}$	${\displaystyle q_{i}=r_{ij}\cdot q_{j}={\frac {1}{\sum _{z=1}^{Z}(r_{zi}\cdot M_{z})}}}$	${\displaystyle q_{i}=R_{ij}\cdot q_{j}={\frac {1}{\sum _{z=1}^{Z}(R_{zi}\cdot M_{z})}}}$	${\displaystyle q_{i}={\frac {\rho _{i}}{M_{i}\cdot \sum _{z=1}^{Z}(\psi _{zi}\cdot \rho _{z})}}}$
Quotient amount of substance / mass	Molality b
	${\displaystyle q_{i}=b_{i}\cdot q_{j}\cdot M_{j}}$ ( i = solute, j = solvent)
	specific amount of partial substances q
	${\displaystyle q_{i}}$

Since the molar volume V _m of a pure substance equal to the quotient of the molar mass and its density (at a given temperature and pressure) in the above table, in some equations can in the reciprocal form of occurring terms will be replaced:

${\displaystyle {\frac {M_{i}}{\rho _{i}}}=V_{\mathrm {m} ,i}\ \Leftrightarrow \ {\frac {\rho _{i}}{M_{i}}}={\frac {1}{V_{\mathrm {m} ,i}}}}$

The summation of the specific partial substance quantities of all mixture components results in the reciprocal value of the mean molar mass of the mixed phase (total substance quantity n = sum of the individual substance quantities of all mixture components ): ${\displaystyle {\overline {M}}}$

${\displaystyle \sum _{z=1}^{Z}q_{z}=\sum _{z=1}^{Z}{\frac {n_{z}}{m}}={\frac {n}{m}}={\frac {1}{\overline {M}}}}$

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:

${\displaystyle b_{\mathrm {NaCl} }={\frac {n_{\mathrm {NaCl} }}{m_{\mathrm {H_{2}O} }}}={\frac {\mathrm {0{,}5\ mol} }{\mathrm {0{,}5\ kg} }}=\mathrm {1{,}000\ mol/kg} }$

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

${\displaystyle q_{\mathrm {NaCl} }={\frac {n_{\mathrm {NaCl} }}{m}}={\frac {\mathrm {0{,}5\ mol} }{\mathrm {0{,}5292\ kg} }}\approx \mathrm {0{,}945\ mol/kg} }$

Individual evidence

1. ↑ ^{a b} Standard DIN 1310 : Composition of mixed phases (gas mixtures, solutions, mixed crystals); Terms, symbols. February 1984 (definition and unit given, own designation and own formula symbols left open).
2. ↑ ^{a b c} standard DIN 32625: quantities and units in chemistry; Amount of substance and quantities derived from it; Terms and definitions. December 1989 (withdrawn without replacement by the German Institute for Standardization in April 2006, because no need for this standard was assumed due to a lack of further cooperation and feedback from industry, science, research and other circles).
3. ↑ ^{a b} P. Kurzweil: The Vieweg unit lexicon: terms, formulas and constants from natural sciences, technology and medicine . 2nd Edition. Springer Vieweg, 2013, ISBN 978-3-322-83212-2 , p. 372 , doi : 10.1007 / 978-3-322-83211-5 ( limited preview of the 1st edition in the Google book search; limited preview of the 2nd edition in the Google book search - softcover reprint of the 2nd edition in 2000). Lexical part (PDF; 71.3 MB).
4. ↑ J. Graßmuck, K.-W. Houben, RM Zollinger: DIN standards in process engineering: A guide to technical rules and regulations . 2nd Edition. Springer Vieweg, 2014, ISBN 978-3-322-90353-2 , p. 17 , doi : 10.1007 / 978-3-322-90352-5 ( limited preview in the Google book search - softcover reprint of the 2nd edition 1994).
5. ↑ ^{a b c} G. Jander, KF Jahr, R. Martens-Menzel, G. Schulze, J. Simon: Measure analysis: theory and practice of titrations with chemical and physical indications . 18th edition. De Gruyter, Berlin / Boston 2012, ISBN 978-3-11-024898-2 , pp. 63 , doi : 10.1515 / 9783110248999 ( limited preview in Google Book search).