# Amount of substance

Physical size
Surname Amount of substance
Formula symbol ${\ displaystyle n}$
Size and
unit system
unit dimension
SI mol N

The amount of substance (outdated molar amount or molar number ) with the formula symbol is a basic quantity in the International System of Units  (SI) and indirectly indicates the number of particles in a substance portion. Particles can be atoms , ions , molecules , formula units or electrons . Formula symbol and particle type X are given together as n X or n (X). ${\ displaystyle n}$

The unit of measurement for the amount of substance is the mole , an SI base unit. An amount of substance of 1 mol ( = 1 mol) contains that determined by the Avogadro constant ( N A6${\ displaystyle n}$ .022e23 mol −1 ) specified number of particles. The Avogadro constant is theproportionality factorbetween the amount of substance and the number of particles N(X):

{\ displaystyle {\ begin {aligned} n (X) \ cdot N _ {\ mathrm {A}} & = N (X) \\\ Leftrightarrow n (X) & = {\ frac {N (X)} {N_ {\ mathrm {A}}}} \ end {aligned}}}

Amount of substance and the quantities derived from it, such as concentration of substance , amount of substance and ratio of substance, are important in stoichiometry . The use of the quantity of substance shifts considerations of chemical reactions from the atomic or molecular range to weighable substance masses with a very high number of particles.

For the amount of substance  n X and the mass  m X of a substance portion of a substance X and its molar mass  M X :

${\ displaystyle n _ {\ mathrm {X}} = {m _ {\ mathrm {X}} \ over M _ {\ mathrm {X}}}}$

## Calculating the amount of substance

The relationship between mass, amount of substance, volume and number of particles.

The amount of substance is calculated

### ... from the crowd

The calculation from the mass is possible using the equation given above.

Example: The molar mass of water is 18 grams per mole. 9 grams of water correspond to an amount of substance of 0.5 mol.

${\ displaystyle n _ {\ mathrm {H_ {2} O}} = {\ frac {m _ {\ mathrm {H_ {2} O}}} {M _ {\ mathrm {H_ {2} O}}}} = \ mathrm {9 \; g \ over {18 \; {g \ over mol}}} = 0 {,} 5 \, \ mathrm {mol}}$

### ... from the volume

One mole of an ideal gas takes up an approximate volume of V m  = 22.4 l / mol under standard conditions . This volume is called the standard molar volume (molar volume). The amount of substance results directly from the volume.

Example: How many moles is equivalent to 5 liters of oxygen ?

${\ displaystyle n _ {\ mathrm {O_ {2}}} = {V _ {\ mathrm {O_ {2}}} \ over {V _ {\ mathrm {m}}}} = {{5 \, \ mathrm {l }} \ over {22 {,} 4 {\ mathrm {l \ over mol}}}} = 0 {,} 22 \, \ mathrm {mol}}$

### ... from the number of particles

Since the number of particles N is proportional to the amount of substance n (the proportionality factor is the Avogadro constant N A = 6.022 · 10 23 / mol), the amount of substance can be calculated from the number of particles.

Example: Given are N = 10 25 particles.

${\ displaystyle n = {\ frac {N} {N _ {\ mathrm {A}}}} = {\ frac {10 ^ {25}} {6 {,} 022 \ cdot 10 ^ {23} \; \ mathrm {mol} ^ {- 1}}} = 16 {,} 606 \; \ mathrm {mol}}$

### ... out of concentration

Since the concentration c X (mol / l) is a measure of the concentration for solutions , which relates the amount of substance X to the volume V of the solution, this can also be calculated back to the amount of substance.

Example: How many moles of sodium chloride are in 0.22 liters of a 0.6 molar NaCl solution?

${\ displaystyle n _ {\ mathrm {NaCl}} = c _ {\ mathrm {NaCl}} \ cdot V = 0 {,} 6 \; {\ frac {\ mathrm {mol}} {\ mathrm {l}}} \ cdot 0 {,} 22 \; \ mathrm {l} = 0 {,} 132 \; \ mathrm {mol}}$