# Particle density

The particle density is the number of in a volume located particles divided by the volume. Your Symbol is usually n or C . Other terms by combining the word parts particles or particles , possibly - number or - number , and with - density or - concentration , are also used. The particle density is an intensive physical quantity .

## Definition, properties and applications

The particle density or is defined as the quotient of the number of particles of the type of particles under consideration and the volume of the system under consideration: ${\ displaystyle n_ {i}}$${\ displaystyle C_ {i}}$ ${\ displaystyle N_ {i}}$ ${\ displaystyle i}$ ${\ displaystyle V}$

${\ displaystyle n_ {i} \ {\ text {or}} \ C_ {i} = {\ frac {N_ {i}} {V}}}$

If the system is not homogeneous , this definition only provides an average particle density; deviating values ​​can then occur in partial volumes of the system.

Particles ” can be microscopic objects such as neutrons , atoms , molecules , ions or formula units , but also mesoscopic objects such as dust particles.

Since the number of particles represents a quantity of the dimension number and the volume occurs as a reciprocal value , the derived SI unit of the particle density is m −3 , in practice dm −3 , cm −3 , l −1 and ml −1 are also often used .

If a system contains a mixture of different types of particles, the total particle density of the system is obtained by adding up the particle densities of all individual types of particles.

The formula symbol for the particle density holds the risk of confusion with the thematically closely related quantity of substance , which also has the formula symbol . In contrast, the alternative formula symbol only overlaps with the less affine quantities electrical capacity or heat capacity . is specified in DIN 1310 in particular as a formula symbol together with the designation " particle number concentration " when it comes to use as a content parameter for the quantitative description of the composition of substance mixtures / mixed phases . ${\ displaystyle n}$${\ displaystyle n}$${\ displaystyle C}$${\ displaystyle C}$

The particle density has a wide range of applications in physics , as many other quantities can be deduced from it. So z. B. the mass or the charge carried by individual particles, so the mass density or charge density can be derived directly from the particle density ( the charge carriers ). In gases hang e.g. B. the pressure and the density almost linearly from the particle density.

As a mere indication of the concentration , the particle number concentration provides handy figures when the concentrations are very small, and is therefore used in the reaction kinetics of trace substances and in astrophysics for the particle density in space . For higher concentrations it is more common to give information as molar concentration in mol / m 3 (possibly also mol / ), for conversion see below. ${\ displaystyle C}$ ${\ displaystyle c}$

The particle number concentrations for a mixture of substances of a given composition are - like all volume-related quantities ( concentrations , volume fraction , volume ratio ) - generally dependent on the temperature (in the case of gas mixtures also on the pressure ), so that the associated temperature (if necessary . also of pressure) heard. As a rule, an increase in temperature causes an increase in the total volume of the mixed phase ( thermal expansion ), which, with the number of particles remaining the same, leads to a reduction in the particle number concentrations of the mixture components. ${\ displaystyle V}$

For mixtures of ideal gases it can be derived from the general gas equation that the particle number concentration of a mixture component is proportional to its partial pressure and inversely proportional to the absolute temperature ( Boltzmann constant ): ${\ displaystyle C_ {i}}$${\ displaystyle i}$ ${\ displaystyle p_ {i}}$ ${\ displaystyle T}$${\ displaystyle k _ {\ mathrm {B}}}$

${\ displaystyle C_ {i} = {\ frac {p_ {i}} {k _ {\ mathrm {B}} \ cdot T}}}$

## Relationships with other salary levels

The following table summarizes the relationships between the particle number concentration and the other content quantities defined in DIN 1310 in the form of size equations . The formula symbols or 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 without an index represents the density of the mixed phase. The index serves as a general index for the total formation (consideration of a general mixture of substances from a total of components) and includes . is Avogadro's constant . ${\ displaystyle C_ {i}}$${\ displaystyle M}$${\ displaystyle \ rho}$${\ displaystyle \ rho}$${\ displaystyle z}$${\ displaystyle Z}$${\ displaystyle i}$${\ displaystyle N _ {\ mathrm {A}}}$ ${\ displaystyle (N _ {\ mathrm {A}} \ approx 6 {,} 022 \ cdot 10 ^ {23} \, \ mathrm {mol} ^ {- 1})}$

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

In the table above in the equations in the mole fraction x and Teilchenzahlanteil X occurring denominator - Terme are equal to the average molar mass of the material mixture and can be replaced in accordance with: ${\ displaystyle {\ overline {M}}}$

${\ displaystyle \ sum _ {z = 1} ^ {Z} (x_ {z} \ cdot M_ {z}) = \ sum _ {z = 1} ^ {Z} (X_ {z} \ cdot M_ {z }) = {\ overline {M}}}$

## Examples

medium Particle density
(in particles / cm 3 = particles / ml)
Particle type
Ethanol - water mixture (a) 2.1 ·  10 22 Total molecules
6.0 · 10 21 Ethanol molecules
1.5 · 10 22 Water molecules
Air (at sea level) (b) 2.55 · 10 19 Total molecules / atoms
2.0 · 10 19 N 2 molecules
5.3 · 10 18 O 2 molecules
2.4 · 10 17 Ar atoms
Air (at a height of 30 km)
(see ozone layer )
3 · 10 17 Total molecules / atoms
of which about 5 · 10 12 O 3 molecules
blood 5 · 10 9 Red blood cells
Drinking water <100 aerobic germs
(a) Mass fractions w ethanol and w water 50% each, temperature 20 ° C.
(b)For standard atmosphere , temperature 15 ° C, pressure 1013.25 hPa.

## Individual evidence

1. a b c Standard DIN 1310 : Composition of mixed phases (gas mixtures, solutions, mixed crystals); Terms, symbols. February 1984, p. 2, sections 3 and 7.
2. a b Standard DIN EN ISO 80000-9 : Quantities and units - Part 9: Physical chemistry and molecular physics. August 2013. Section 3: Terms, symbols and definitions , table entry no. 9-10.
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. 69, 224, 225, 287 , doi : 10.1007 / 978-3-322-83211-5 ( lexical part as PDF file, 71.3 MB ; limited preview in Google Book search).
4. a b Entry on number density . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.N04262 Version: 2.3.3.
5. a b Entry on number concentration . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.N04260 Version: 2.3.3.