Amount of substance

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Amount of substance
SI unit
mol
Dimension

In

molecules, atoms, or ions of a specified kind. The particular substance sampled may be specified using a subscript, e.g., the amount of sodium chloride (NaCl) would be denoted as nNaCl. The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit.[1]
Since 2019, the value of the Avogadro constant NA is defined to be exactly 6.02214076×1023 mol−1. Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter.

Usage

Historically, the mole was defined as the amount of substance in 12 grams of the carbon-12 isotope. As a consequence, the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the mass of one molecule of the compound, in daltons, and the molar mass of an isotope in grams per mole is equal to the mass number. For example, a molecule of water has a mass of about 18.015 daltons on average, whereas a mole of water (which contains 6.02214076×1023 water molecules) has a total mass of about 18.015 grams.

In chemistry, because of the law of multiple proportions, it is often much more convenient to work with amounts of substances (that is, number of moles or of molecules) than with masses (grams) or volumes (liters). For example, the chemical fact "1 molecule of oxygen (O
2
) will react with 2 molecules of hydrogen (H
2
) to make 2 molecules of water (H2O)" can also be stated as "1 mole of O2 will react with 2 moles of H2 to form 2 moles of water". The same chemical fact, expressed in terms of masses, would be "32 g (1 mole) of oxygen will react with approximately 4.0304 g (2 moles of H
2
) hydrogen to make approximately 36.0304 g (2 moles) of water" (and the numbers would depend on the isotopic composition of the reagents). In terms of volume, the numbers would depend on the pressure and temperature of the reagents and products. For the same reasons, the concentrations of reagents and products in solution are often specified in moles per liter, rather than grams per liter.

The amount of substance is also a convenient concept in thermodynamics. For example, the pressure of a certain quantity of a noble gas in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through the ideal gas law), not to its mass.

This technical sense of the term "amount of substance" should not be confused with the general sense of "amount" in the English language. The latter may refer to other measurements such as mass or volume,[2] rather than the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms, such as enplethy[3] and stoichiometric amount.[2]

The

IUPAC recommends that "amount of substance" should be used instead of "number of moles", just as the quantity mass should not be called "number of kilograms".[4]

Nature of the particles

To avoid ambiguity, the nature of the particles should be specified in any measurement of the amount of substance: thus, a sample of 1 mol of molecules of oxygen (O
2
) has a mass of about 32 grams, whereas a sample of 1 mol of atoms of oxygen (O) has a mass of about 16 grams.[5][6]

Derived quantities

Molar quantities (per mole)

A diagram comparing moles and molar masses of iron and gold samples that have equal masses

The quotient of some

intensive property of the substance, usually named by the prefix "molar" or the suffix "per mole".[7]

For example, the quotient of the mass of a sample by its amount of substance is its

millilitres per mole for liquid water and 7.092 mL/mol for iron at room temperature. From the heat capacity, one gets the molar heat capacity, which is about 75.385 J/(K
⋅mol) for water and about 25.10 J/(K⋅mol) for iron.

Molar mass

The molar mass of a substance is the ratio of the mass of a sample of that substance to its amount of substance. The amount of substance is given as the number of moles in the sample. For most practical purposes, the numerical value of the molar mass expressed with the unit gram per mole is the same as that of the mean mass of one molecule of the substance expressed with the unit dalton, as the mole was historically defined such that the molar mass constant was exactly 1 g/mol. This allows for accurate determination of the amount in moles of a substance by measuring mass. Given the molecular mass in daltons, the same number in grams gives an amount very close to one mole of the substance. For example, the average molecular mass of water is about 18.015 Da and the molar mass of water is about 18.015 g/mol.[8] Other methods include the use of the molar volume or the measurement of electric charge.[8]

The number of moles of a substance in a sample is obtained by dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about 5.551 mol of water.[8]

The molar mass of a substance depends not only on its

calcium-42 is 41.95861801(27) g/mol, and of calcium
with the normal isotopic mix is 40.078(4) g/mol.

Molar concentration

The molar concentration, also called molarity, of a solution of some substance is the number of moles per unit of volume of the final solution. In the SI its standard unit is mol/m3, although more practical units, such as mole per litre (mol/L) are used.

Molar fraction

The

molar fraction or mole fraction
of a substance in a mixture (such as a solution) is the number of moles of the compound in one sample of the mixture, divided by the total number of moles of all components. For example, if 20 g of NaCl is dissolved in 100 g of water, the amounts of the two substances in the solution will be (20 g)/(58.443 g/mol) = 0.34221 mol and (100 g)/(18.015 g/mol) = 5.5509 mol, respectively; and the molar fraction of NaCl will be 0.34221/(0.34221 + 5.5509) = 0.05807.

In a mixture of gases, the partial pressure of each component is proportional to its molar ratio.

Amount concentration (moles per liter)

Another important derived quantity is the

amount of substance concentration[9] (also called amount concentration, or substance concentration in clinical chemistry;[10]
which is defined as the amount of a specific substance in a sample of a solution (or some other mixture), divided by the volume of the sample.

The SI unit of this quantity is the mole (of the substance) per liter (of the solution). Thus, for example, the amount concentration of sodium chloride in ocean water is typically about 0.599 mol/L.

The denominator is the volume of the solution, not of the solvent. Thus, for example, one liter of standard vodka contains about 0.40 L of ethanol (315 g, 6.85 mol) and 0.60 L of water. The amount concentration of ethanol is therefore (6.85 mol of ethanol)/(1 L of vodka) = 6.85 mol/L, not (6.85 mol of ethanol)/(0.60 L of water), which would be 11.4 mol/L.

In chemistry, it is customary to read the unit "mol/L" as

molar, and denote it by the symbol "M" (both following the numeric value). Thus, for example, each liter of a "0.5 molar" or "0.5 M" solution of urea (CH
4
N
2
O
) in water contains 0.5 moles of that molecule. By extension, the amount concentration is also commonly called the molarity of the substance of interest in the solution. However, as of May 2007, these terms and symbols are not condoned by IUPAC.[11]

This quantity should not be confused with the mass concentration, which is the mass of the substance of interest divided by the volume of the solution (about 35 g/L for sodium chloride in ocean water).

Amount fraction (moles per mole)

Confusingly, the amount concentration, or "molarity", should also be distinguished from "mole fraction", which should be the number of moles (molecules) of the substance of interest divided by the total number of moles (molecules) in the solution sample. This quantity is more properly called the

amount fraction
.

History

The

gravitation
. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.

See also

References

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