Degree of concentration of countable objects
The number density (symbol: n or ρN) is an
N) is sometimes used in chemistry for the same quantity, particularly when comparing with other
concentrations.
Definition
Volume number density is the number of specified objects per unit volume:[1]
where
N is the total number of objects in a volume
V.
Here it is assumederror, 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:
Similarly, linear number density is the number of specified objects per unit
length,
L:
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:
It's related to
column mass density
, with the volumetric number density replaced by the volume mass density.
Units
In
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
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
where d
V = d
x d
y d
z 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
Similar expressions are valid for
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
).
Relation to other quantities
Molar concentration
For any substance, the number density can be expressed in terms of its
amount concentration
c (in
mol/m
3) as
where
NA is 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 cm
−3 and
c is in mol/cm
3, or if
n is in
L −1 and
c is in mol/L, etc.
Mass density
For
mass density
ρm (in kg/m
3) as
Note that the ratio
M/
NA is the mass of a single atom or molecule in kg.
Examples
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[citation needed]
Material
|
Number density, n
|
Amount concentration , c
|
Mass density , ρm
|
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
References and notes
-
-
-
- ^ For elemental substances, atomic densities/concentrations are used