Avogadro constant

SI defining constant

Name	Symbol	Base units
Avogadro constant	N_A	mol⁻¹
The numerical value of the Avogadro constant, symbol N_A, is defined to be exactly 6.022 140 76 × 10²³ when expressed in the unit reciprocal mole, symbol mol⁻¹. The numerical value of the Avogadro constant is known as the Avogadro number.
${N_A} = 6.022 \mspace{4mu} 140 \mspace {4mu} 76 \times 10^{23} \mspace{6mu} \text{mol}^{-1}$

Amount of substance

The Avogadro constant, N_A, forms the basis for the definition of the unit of amount of substance, the mole.

The fixed numerical value of the Avogadro constant, N_A, is defined exactly:

$N_A \mspace{4mu} = 6.022 \mspace{4mu} 140 \mspace {4mu} 76 \times 10^{23} \ \text{mol}^{-1}$

Inverting this relation gives an exact expression for the mole in terms of the Avogadro constant, N_A :

$1 \mspace{4mu} \text{mol} \mspace{6mu} = \dfrac{1}{6.022 \mspace{4mu} 140 \mspace {4mu} 76 \times 10^{23}} \mspace{6mu} N_A$

The ideal gas constant

The ideal gas constant, R, also known as the molar gas constant, is the molar equivalent of the Boltzmann constant. It is equal to the product of two of the SI defining constants – the Boltzmann constant, k, and the Avogadro constant, N_A.

$R \ = k \mspace{4mu} N_A \\ \\ R \ = 1.380 \mspace{4mu} 649 \times 10^{-23} \mspace{6mu} \text{J K}^{-1} \ \times \ 6.022 \mspace{4mu} 140 \mspace{4mu} 76 \mspace{4mu} \times 10^{23} \mspace{6mu} \text{mol}^{-1} \\ \\ R \ = 8.314 \mspace{4mu} 462 \mspace{4mu} 618 \mspace{4mu} 153 \mspace{4mu} 24 \mspace{6mu} \text{J K}^{-1} \text{mol}^{-1}$

Molar heat capacity

Inverting the definition for the ideal gas constant gives an exact expression for the unit of molar heat capacity, the joule per mole kelvin, in terms of the Boltzmann constant, k, and the Avogadro constant, N_A :

$1 \mspace{4mu} \text{J} / (\text{mol} \mspace{4mu} \text{K}) \mspace{6mu} = \dfrac{1}{8.314 \mspace{4mu} 462 \mspace{4mu} 618 \mspace{4mu} 153 \mspace{4mu} 24} \mspace{6mu} k \mspace{4mu} N_A$

The Faraday constant

The Faraday constant, symbol F, is the molar equivalent of the elementary charge. It is named after the English scientist Michael Faraday.

It is equal to the total electric charge of one mole of particles, each with an electric charge equal to the elementary charge, e.

The Faraday constant is equal to the product of two of the SI defining constants – the elementary charge, e, and the Avogadro constant, N_A.

$F \ = e \mspace{4mu} N_A \\ \\ F \ = 1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \mspace{4mu} \text{C} \mspace{4mu} \times \mspace{4mu} 6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23} \mspace{4mu} \text{mol}^{-1} \\ \\ F \ = 9.648 \mspace{4mu} 533 \mspace{4mu} 212 \mspace{4mu} 331 \mspace{4mu} 001 \mspace{4mu} 84 \times 10^4 \mspace{6mu} \text{C} \mspace{4mu} \text{mol}^{-1}$

Molar electric charge

Inverting the definition for the Faraday constant gives an exact expression for the unit of molar electric charge, the coulomb per mole, in terms of the elementary charge, e, and the Avogadro constant, N_A :

$1 \mspace{4mu} \text{C} \mspace{4mu} \text{mol}^{-1} \mspace{6mu} = \dfrac{1}{96 \mspace{4mu} 485.332 \mspace{4mu} 123 \mspace{4mu} 310 \mspace{4mu} 018 \mspace{4mu} 4} \mspace{6mu} e \mspace{4mu} N_A$

Nature

The Avogadro constant, N_A, is a proportionality constant between the quantity amount of substance (with unit mole) and the quantity for counting entities (with unit one, symbol 1). Thus it has the character of a constant of proportionality similar to the Boltzmann constant, k.