Values of N_{A} 
Units 
6.022 141 79(30) 
mol^{−1} 
2.731 597 57(14) 
lbmol.^{−1} 
1.707 248 479(85) 
ozmol.^{−1} 
For details, see Terminology and
units below. 
The
Avogadro constant (symbols:
L,
N_{A}) is the number of "elementary entities"
(usually
atoms or
molecules) in one
mole,
that is (from the definition of the mole), the number of atoms in
exactly 12
grams of
carbon12. It was originally called
Avogadro's number. The 2006
CODATA recommended value is:
 N_{\rm A}=6.022\ 141\ 79(30)\times 10^{23}\
\mbox{mol}^{1}
The
Avogadro constant is named after the early nineteenth century
Italian scientist Amedeo
Avogadro, who, in 1811, first proposed that the volume of a gas
(at a given pressure and temperature) is proportional to the number
of atoms or molecules
regardless of the nature of the gas. The French physicist
Jean Perrin in 1909 proposed
naming the constant in honour of Avogadro. Perrin would win the
1926
Nobel Prize in Physics,
in a large part for his work in determining the Avogadro constant
by several different methods.
The value of the Avogadro constant was first indicated by
Johann Josef Loschmidt who, in 1865,
estimated the average diameter of the molecules in air by a method
that is equivalent to calculating the number of particles in a
given volume of gas. This latter value, the
number density of particles in an
ideal gas, is now called the
Loschmidt constant in his honour, and is
approximately
proportional to the Avogadro
constant. The connection with Loschmidt is the root of the symbol
L sometimes used for the Avogadro constant, and
German language literature may refer to both
constants by the same name, distinguished only by the
units of measurement.
Terminology and units
Perrin originally proposed the
name "Avogadro's number" (
N) to refer to the number of
molecules in one
grammolecule of
oxygen (exactly 32 grams of oxygen,
according to the definitions of the period), and this term is still
widely used, especially in introductory works. The change in name
to "Avogadro constant" (
N_{A}) came with the
introduction of the
mole as a separate
base unit in the
International System of Units
(SI) in 1971, which recognised
amount of substance as an independent
dimension of measurement. With
this recognition, the Avogadro constant was no longer a pure number
but a
physical quantity associated
with a
unit of measurement, the
reciprocal mole (mol
^{−1}) in SI units. The change in name
from the possessive form "Avogadro's" to the nominative form
"Avogadro" is a general change in practice since Perrin's time for
the names of all
physical
constants. In effect, the constant is named in honour of
Avogadro: he does not
own it, and it would have been
impossible to measure it during Avogadro's lifetime.
While it is rare to use units of amount of substance other than the
mole, the Avogadro constant can also be defined in units such as
the
pound mole (lbmol.) and the
ounce mole (ozmol.).
 N = 2.731 597 57(14)
lbmol.^{−1} = 1.707 248 479(85)
ozmol.^{−1}
Additional physical relations
Because of its role as a scaling factor, the Avogadro constant
provides the link between a number of useful physical constants
when moving between the
atomic scale and
the macroscopic scale. For example, it provides the relationship
between:
 R = k_{\rm B} N_{\rm A} = 8.314\,472(15)\ {\rm
J\,mol^{1}\,K^{1}}\,
 in J mol^{−1} K^{−1}
 F = N_{\rm A} e = 96\,485.3383(83)\ {\rm C\,mol^{1}} \,
 in C mol^{−1}
The Avogadro constant also enters into the definition of the
unified atomic mass unit,
u:
 1\ {\rm u} = \frac{M_{\rm u}}{N_{\rm A}} = 1.660 \, 538\,
782(83)\times 10^{24}\ {\rm g}
where
M_{u} is the
molar mass constant.
Measurement
Coulometry
The earliest accurate method to measure the value of the Avogadro
constant was based on
coulometry. The
principle is to measure the
Faraday
constant,
F, which is the
electric charge carried by one mole of
electrons, and to divide by the
elementary charge,
e, to obtain
the Avogadro constant.
 N_{\rm A} = \frac{F}{e}
The classic experiment is that of Bowers and Davis at
NIST, and relies on dissolving
silver metal away from the
anode
of an
electrolysis cell, while passing
a constant
electric current
I for a known time
t. If
m is the mass
of silver lost from the anode and
A the atomic weight of
silver, then the Faraday constant is given by:
 F = \frac{A_{\rm r}M_{\rm u}It}{m}
The NIST workers devised an ingenious method to compensate for
silver that was lost from the anode for mechanical reasons, and
conducted an
isotope analysis of
their silver to determine the appropriate atomic weight. Their
value for the conventional Faraday constant is
F =
96 485.39(13) C/mol, which corresponds to a value for the
Avogadro constant of 6.022 1449(78) mol
^{–1}: both
values have a relative standard uncertainty of 1.3 .
Electron mass method (CODATA)
The
CODATA value for the Avogadro constant is
determined from the ratio of the molar mass of the
electron A (
e)
M to the
rest mass of the electron
m :
 N_{\rm A} = \frac{A_{\rm r}({\rm e})M_{\rm u}}{m_{\rm e}}
The "relative atomic mass" of the electron,
A
(
e), is a directlymeasured quantity, and the
molar mass constant,
M , is a
defined constant in the SI system. The electron rest mass, however,
is calculated from other measured constants:
 m_{\rm e} = \frac{2R_{\infty}h}{c\alpha^2}
As can be seen from the table of 2006 CODATA values below, the main
limiting factor in the accuracy to which the value of the Avogadro
constant is known is the uncertainty in the value of the
Planck constant, as all the other constants
which contribute to the calculation are known much more
accurately.
Constant 
Symbol 
2006 CODATA value 
Relative standard uncertainty 
Correlation coefficient
with N 
Electron relative atomic mass 
A (e) 
5.485 799 0943(23) 
4.2 
0.0082 
Molar mass constant 
M 
0.001 kg/mol 
defined 
— 
Rydberg constant 
R 
10 973 731.568 527(73) m^{–1} 
6.6 
0.0000 
Planck constant 
h 
6.626 068 96(33) Js 
5.0 
–0.9996 
Speed of light 
c 
299 792 458 m/s 
defined 
— 
Fine structure
constant 
α 
7.297 352 5376(50) 
6.8 
0.0269 
Avogadro constant 
N 
6.022 141 79(30) mol^{–1} 
5.0 
1 

Xray crystal density method
One modern method to calculate the Avogadro constant is to use
ratio of the
molar volume,
V ,
to the unit cell volume,
V , for a single crystal of
silicon:
 N_{\rm A} = \frac{8V_{\rm m}({\rm Si})}{V_{\rm cell}}
The factor of eight arises because there are eight silicon atoms in
each unit cell.
The unit cell volume can be obtained by
Xray crystallography; as the unit
cell is cubic, the volume is the cube of the length of one side
(known as the unit cell parameter,
a. In practice,
measurements are carried out on a distance known as
d
(Si), which is the distance between the planes denoted by the
Miller indices {220}, and is equal to
a/√8. The 2006 CODATA value for
d (Si) is
192.015 5762(50) pm, a relative uncertainty of 2.8 ,
corresponding to a unit cell volume of 1.601 933 04(13)
m
^{3}.
The
isotope proportional composition of the
sample used must be measured and taken into account. Silicon occurs
with three stable isotopes –
^{28}Si,
^{29}Si,
^{30}Si – and the natural variation in their proportions is
greater than other uncertainties in the measurements. The
atomic weight A for the sample
crystal can be calculated, as the
relative atomic masses of the three
nuclides are known with great accuracy.
This, together with the measured
density
ρ of the sample, allows the molar volume
V to be
found by:
 V_{\rm m} = \frac{A_{\rm r}M_{\rm u}}{\rho}
where
M is the molar mass constant. The 2006 CODATA value
for the molar volume of silicon is
12.058 8349(11) cm
^{3}mol
^{−1}, with a
relative standard uncertainty of 9.1 .
As of the 2006 CODATA recommended values, the relative uncertainty
in determinations of the Avogadro constant by the Xray crystal
density method is 1.2 , about two and a half times higher than that
of the electron mass method.
See also
References and notes
 .
 English translation.
 Extract in English, translation by Frederick
Soddy.
 Oseen, C.W. (December 10, 1926).
Presentation Speech for the 1926 Nobel Prize in
Physics.
 English translation.
 See, e.g.,
 Resolution 3, 14th General Conference of
Weights and Measures (CGPM), 1971.
 This account is based on the review in
External links