World Library  
Flag as Inappropriate
Email this Article

Number density

Article Id: WHEBN0002127679
Reproduction Date:

Title: Number density  
Author: World Heritage Encyclopedia
Language: English
Subject: Beer–Lambert law, Density, Bethe formula, Particle density, Deposition (aerosol physics)
Publisher: World Heritage Encyclopedia

Number density

In physics, astronomy, chemistry, biology and geography number density (symbol: n) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volume number density, two-dimensional area number density, or one-dimensional line number density. Population density is an example of areal number density. The term number concentration (symbol: C) is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.


Volume number density is the number of specified objects per unit volume:[1]

n = \frac{N}{V} ,


N is the total number of objects in a volume V.

Here it is assumed[2] that N is large enough that rounding of the count to the nearest integer does not introduce much of an error, however V is chosen to be small enough that the resulting n does not depend much on the size or shape of the volume V.


In SI system of units, number density is measured in m−3, although cm−3 is often used. However, these units are not quite practical when dealing with atoms or molecules of gases, liquids or solids at room temperature and atmospheric pressure, because the resulting numbers are extremely large (on the order of 1020). Using the number density of an ideal gas at 0 °C and 1 atm as a yardstick: 1 amagat = 2.6867774×1025 m−3 is often introduced as a unit of number density, for any substances at any conditions (not necessarily limited to an ideal gas at 0 °C and 1 atm).[3]


Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as

N=\iiint_V n(x,y,z)\;dV ,


dV=dx\,dy\,dz is a volume element. If each object possesses the same mass m0, the total mass m of all the objects in the volume V can be expressed as
m=\iiint_V m_0\, n(x,y,z)\;dV .

Similar expressions are valid for electric charge or any other extensive quantity associated with countable objects. For example, replacing m\rightarrow q (total charge) and m_0\rightarrow q_0 (charge of each object) in the above equation will lead to a correct expression for charge.

The number density of solute molecules in a solvent is sometimes called concentration, although usually concentration is expressed as a number of moles per unit volume (and thus called molar concentration).

Relation to other quantities

Molar concentration

For any substance, the number density n (in units of m−3) can be expressed in terms of its molar concentration c (in units of mole/m3) as:

n=N_{\rm A}\,c ,

where NA is the Avogadro constant ≈ 6.022×1023 mol−1. This is still true if the spatial dimension unit, metre, in both n and c is consistently replaced by any other spatial dimension unit, e.g. if n is in units of cm−3 and c is in units of mole/cm3, or if n is in units of L−1 and c is in units of mole/L, etc.

Mass density

For atoms or molecules of a well-defined molar mass M (in units of kg/mole), the number density can be expressed in terms of the mass density of a substance ρ (in units of kg/m3) as

n=\frac{N_{\rm A}}{M}\rho .

Note that the ratio M/NA is the mass of a single atom or molecule in units of kg.


The following table lists common examples of number densities at 1 atm and 20 °C, unless otherwise noted.

Molecular[4] number density and related parameters of some materials
Material Number density (n) Molar concentration (c) Density (\rho) Molar mass (M)
Units (1027 m−3) or
(1021 cm−3)
(amagat) (103 mol/m3) or (mol/L) (103 kg/m3) or (g/cm3) (10−3 kg/mol) or (g/mol)
ideal gas 0.02504 0.932 0.04158 41.58×10−6×M M
dry air 0.02504 0.932 0.04158 1.2041×10−3 28.9644
water 33.3679 1241.93 55.4086 0.99820 18.01524
diamond 176.2 6556 292.5 3.513 12.01

See also

References and notes

  1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "number concentration".
  2. ^ Clayton T. Crowe; Martin Sommerfeld; Yutaka Tsuji (1998), Multiphase flows with droplets and particles: allelochemical interactions,  
  3. ^ Joseph Kestin (1979), A Course in Thermodynamics 2, Taylor & Francis, p. 230,  
  4. ^ For elemental substances, atomic densities/concentrations are used
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.