The number density (symbol: n or
Definition
editVolume number density is the number of specified objects per unit volume:[1]
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 because of large-scale features.
Area number density is the number of specified objects per unit area, A:
Column number density is a kind of areal density, the number or count of a substance per unit area, obtained integrating volumetric number density along a vertical path:
Units
editIn SI 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: n0 = 1 amg = 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]
Usage
editUsing the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as
Similar expressions are valid for electric charge or any other extensive quantity associated with countable objects. For example, replacing m with q (total charge) and m0 with q0 (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
editMolar concentration
editFor any substance, the number density can be expressed in terms of its amount concentration c (in mol/m3) as
Mass density
editFor atoms or molecules of a well-defined molar mass M (in kg/mol), the number density can sometimes be expressed in terms of their mass density
Examples
editThe following table lists common examples of number densities at 1 atm and 20 °C, unless otherwise noted.
Material | Number density, n | Amount concentration, c | Mass density, |
Molar mass, M | |
---|---|---|---|---|---|
(1027 m−3 = 1021 cm−3) | (amg) | (103 mol/m3 = mol/L) | (103 kg/m3 = g/cm3) | (10−3 kg/mol = 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 | 1,241.93 | 55.4086 | 0.99820 | 18.01524 |
Diamond | 176.2 | 6,556 | 292.5 | 3.513 | 12.01 |
See also
editReferences and notes
edit- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "number concentration". doi:10.1351/goldbook.N04260
- ^ Clayton T. Crowe; John D. Schwarzkopf; Martin Sommerfeld; Yutaka Tsuji (2011), Multiphase flows with droplets and particles: allelochemical interactions, CRC Press, p. 18, doi:10.1201/b11103, ISBN 9780429106392
- ^ Joseph Kestin (1979), A Course in Thermodynamics, vol. 2, Taylor & Francis, p. 230, ISBN 0-89116-641-6
- ^ For elemental substances, atomic densities/concentrations are used