# Mole

Physical unit
Unit name Mole
Unit symbol ${\ displaystyle \ mathrm {mol}}$ Physical quantity (s) Amount of substance
Formula symbol ${\ displaystyle n}$ dimension ${\ displaystyle {\ mathsf {N}}}$ system International system of units
In SI units Base unit
Named after molecule

The mole (unit symbol: mol ) is the SI unit of the amount of substance . Among other things, it is used to indicate the amount of chemical reactions .

By definition, one mole of a substance contains exactly 6.022 140 76e23 particles (Avogadro's constant). That's about 602 trillionparticles. These can beatoms,molecules,electronsor other particles.

The number of particles and the amount of substance are directly proportional to one another; each of these two quantities can therefore serve as a measure for the other.

## definition

Since the redefinition of the International System of Units by the 26th General Conference on Weights and Measures, the mole has been defined using the Avogadro constant . The Avogadro constant was determined to mean that one mole of a substance contains exactly particles. The type of particle must be specified, it can be atoms , molecules , ions , electrons , photons or other particles. ${\ textstyle N _ {\ text {A}} = 6 {,} 022 \, 140 \, 76 \ cdot 10 ^ {23} \ \ mathrm {mol} ^ {- 1}}$ ${\ textstyle 6 {,} 022 \, 140 \, 76 \ cdot 10 ^ {23}}$ ### Old definition until May 19, 2019

The mole was previously defined as the amount of substance in a system that consists of as many individual particles as there are atoms in 12 grams of the isotope carbon -12 ( 12 C). According to definition, 1 mol of 12 carbon atoms thus had a mass of 12 g. (One mole of atoms of natural carbon, on the other hand, has a mass of approx.12.0107 g due to the addition of other isotopes.)

The atomic mass unit (u) was and is defined to this day as 112 of the mass of the 12 carbon atom. Therefore, 1 mol of atoms or molecules of particle mass X  u had by definition the mass X  g. Today this only applies approximately.

According to the old definition, the number of particles in a mole (Avogadro's constant N A ) was a measurable variable and was burdened with an uncertainty. According to the new definition of Avogadro's constant, the number of particles in one mole is precisely defined, but the mass of 1 mol 12 C is now a measurable variable. The now exact value of N A was chosen so that it coincided as closely as possible with the value according to the old definition .

## history

The term “mol” was coined by Wilhelm Ostwald in 1893 and is probably derived from “molecule”. In 1971 the mole was introduced as the basic unit in the SI . This extended the scope of the SI to include chemistry . Before the establishment of the SI, the mole was mainly viewed as a unit of mass . Older labels are gram atom (for elements) and gram molecule (only for connections). So it says in DIN 1310 "Content of solutions" from April 1927: "The mass units are [...] the mole, ie. H. as many grams of the substance as its molecular weight indicates [...] ”. However, by using the molecular “weight”, a mass of substance - not an amount of substance from today's point of view - was described and referred to as the “amount of substance”. In the current mole definition of the SI, on the other hand, the amount of substance is formally clearly distinguished from particle number and mass.

## Decimal multiples

Common decimal parts and multiples of the mole are:

designation unit factor Multiples annotation
Megamol Mmol 10 6 1,000,000 mol corresponds to 1,000,000 moles
Kilomoles kmol 10 3 1000 mol corresponds to 1000 moles
Millimoles mmol 10 −3 0.001 mol corresponds to a thousandth of a mole
Micromoles μmol 10 −6 0.001 mmol corresponds to a millionth of a mole (one thousandth of a millimole)
Nanomoles nmol 10 −9 0.001 µmol corresponds to one billionth of a mole (one millionth of a millimole)
Picomoles pmol 10 −12 0.001 nmol corresponds to one trillionth of a mole (one billionth of a millimole)

## Molar volume

The molar volume of a substance is a substance-specific property that indicates the volume of one mole of a substance. For an ideal gas , one mole takes up a volume of 22.414  liters under normal conditions (273.15 K, 101325 Pa) . For real gases , solids and liquids , on the other hand, the molar volume is dependent on the substance.

## Molar mass

The molar mass is the quotient of the mass and amount of material of a substance. In the unit g / mol it has the same numerical value as the atomic or molecular mass of the substance in the unit ( atomic mass unit ). Their meaning is equivalent to the earlier “atomic weight” in chemistry. ${\ displaystyle M}$ ${\ displaystyle u}$ ## Calculation of substance quantities

The following formula is used for the calculation : ${\ displaystyle n = {\ frac {m} {M}}}$ It denotes the amount of substance , the mass and the molar mass. can be taken from tables for chemical elements and calculated from such values ​​for chemical compounds of known composition. ${\ displaystyle n}$ ${\ displaystyle m}$ ${\ displaystyle M}$ ${\ displaystyle M}$ The atomic mass, which is given in tables for each chemical element, relates to the natural isotope mixture . For example, the atomic mass for carbon is 12.0107 u. This value does not apply to material enriched in 13 C , for example . While the deviations from isotope mixtures as they occur in nature are relatively small with stable elements, the isotope mixture in particular with radioactive elements can depend heavily on the origin and the age of the material.

## Use of the unit mol when specifying concentrations

The unit mole is often used in compound units to indicate concentrations (salt content of solutions, acidity of solutions, etc.). One of the most common uses is the x-molar solution (the x stands for any rational positive number).

example
A 2.5 molar A solution contains 2.5 mol of the solute A in 1 liter of the solution.

## Examples

### Mass of 1 mol of helium

• 1 atom of helium has a mass of about 4 u (u is the atomic mass unit ; one helium atom has 2 protons and 2 neutrons ). Helium gas is monatomic, so in the following example the mole refers to He atoms without needing to be specifically mentioned.
• So 1 mol of helium has a mass of about 4 g and contains about 6.022e23 helium atoms.

### Mass of 1 mol of water

• 1 mol of a substance contains about 6.022e23 particles.
• 1 water molecule H 2 O consists of 1 oxygen atom and 2 hydrogen atoms.
• The oxygen atom usually has 16 nucleons (core particles, i.e. neutrons and protons), a hydrogen atom usually has 1 core particle (a proton).
• A water molecule usually contains 18 nucleons.
• The mass of a core particle is approximately 1.6605e-24 g.
• 1 water molecule therefore usually has the mass 18 · 1.6605e-24 g.
• The mass of 1 mol of water is the 6th.022e23 times the mass of a water molecule.
• The mass of 1 mol of water is therefore 6.022e23  ·18 · 1.6605e-24 g= 18 g (the numerical value is equal to the molecular mass in u).

If one takes the more precise atomic masses instead of the number of nucleons , the result is a slightly higher value of 18.015 g.

### Production of lithium hydroxide from lithium and water

${\ displaystyle \ mathrm {2 \, Li + 2 \, H_ {2} O \ rightarrow 1 \, H_ {2} +2 \, LiOH}}$ When LiOH is formed, two water molecules are split by two lithium atoms into one H and one OH part. Because there are the same number of particles in every mole of every substance (see above), you need, for example, 2 moles of lithium and 2 moles of water (or any other amount of substance in a 2: 2 ratio).

For example, 6.94 g lithium twice and 18 g water twice react to form 2 g hydrogen and 47.88 g lithium hydroxide.

## literature

• Beat Jeckelmann: A milestone in the further development of the international system of units . In: METinfo, Vol 25, No2 / 2018.
• Julian Haller, Karlheinz Banholzer, Reinhard Baumfalk: Redefinition of the units kilogram, ampere, kelvin and mole. How does the kilogram get into my laboratory balance? In: Chemistry in our time , 53, 2019, pp. 84–90, doi: 10.1002 / ciuz.201800878 .
• Karl Rauscher, Reiner Friebe: Chemical tables and calculation tables for analytical practice. 11th edition. Verlag Harri Deutsch, Frankfurt am Main 2004, ISBN 3-8171-1621-7 , p. 31 ( limited preview in the Google book search).