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The Avogadro constant (symbols: L, N_{A}), also called Avogadro's number, 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 carbon-12. The 2006 CODATA recommended value is entities per mole.## In other units

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 (lb-mol.) and the ounce mole (oz-mol.).
## Application

The Avogadro constant can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 g/mol, so N_{A} iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains N_{A} iron atoms. The Avogadro constant also enters into the definition of the unified atomic mass unit, u:
## 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:## Measurement

### Historical methods

### 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.
^{–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:

### X-ray crystal density method

^{3}mol^{–1}, with a relative standard uncertainty of 9.1.## See also

## References and notes

## External links

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.

- N = 2.731 597 57(14) lb-mol.
^{–1}= 1.707 248 479(85) oz-mol.^{–1}

- $1\; mathrm\{u\}\; =\; frac\{1\}\{N\_A\}\; mathrm\{g\}\; =\; (1.660\; ,\; 538,\; 86\; pm\; 0.000,\; 000,\; 28)\; 10^\{-24\}\; mathrm\{g\}$

- the gas constant R and the Boltzmann constant k
_{B}:

- $R\; =\; k\_BN\_A\; =\; 8.314\; ,\; 472\; ,\; pm\; ,\; 0.000\; ,\; 015\; ,\; mbox\{J\}cdotmbox\{mol\}^\{-1\}mbox\{K\}^\{-1\},$

- the Faraday constant F and the elementary charge e:

- $F\; =\; N\_Ae\; =\; 96\; ,\; 485.3383\; ,\; pm\; ,0.0083\; ,,\; mbox\{C\}cdotmbox\{mol\}^\{-1\}\; ,$

- $N\_\{rm\; A\}\; =\; frac\{F\}\{e\}$

- $F\; =\; frac\{A\_\{rm\; r\}M\_\{rm\; u\}It\}\{m\}$

- $N\_\{rm\; A\}\; =\; frac\{A\_\{rm\; r\}(\{rm\; e\})M\_\{rm\; u\}\}\{m\_\{rm\; e\}\}$

- $m\_\{rm\; e\}\; =\; frac\{2R\_\{infty\}h\}\{calpha^2\}$

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 | — |

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 unit cell volume can be obtained by X-ray 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 3.128 775 48(27) m^{3}.

The molar volume requires a series of measurements to be determined. Silicon occurs with three stable isotopes – ^{28}Si, ^{29}Si, ^{30}Si – and the natural variation in the proportions of these isotopes is greater than the other uncertainties in the other measurements, so the proportions must be determined for each crystal which is used. With these values, the atomic weight A for that crystal can be calculated, as the relative atomic masses of the three nuclides are known with great accuracy. The crystal must also be weighed and measured to determine its density ρ. Once all these quantities are known, the molar volume V is given by:

- $V\_\{rm\; m\}\; =\; frac\{A\_\{rm\; r\}M\_\{rm\; u\}\}\{rho\}$

As of the 2006 CODATA recommended values, the relative uncertainty in determinations of the Avogadro constant by the X-ray crystal density method is 1.2, about two and a half times higher than that of the electron mass method.

- 1996 definition of the Avogadro constant from the IUPAC Compendium of Chemical Terminology ("Gold Book")
- Some Notes on Avogadro's Number, 6.022 (historical notes)
- An Exact Value for Avogadro's Number -- American Scientist

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