Amount of substance

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Amount of substance
Mole carbon-12 diagram.svg
Approximately 1 mol amount of substance based on 12 grams of carbon-12
Common symbols
n
SI unit mol
Dimension

In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/NA) between the number of elementary entities (N) and the Avogadro constant (NA). The entities are usually molecules, atoms, ions, or ion pairs 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.

Contents

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 or formula unit of the compound, in daltons, and the molar mass of an isotope in grams per mole is approximately equal to the mass number (historically exact for carbon-12 with a molar mass of 12 g/mol). 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". [3]

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. [4] [5]

Derived quantities

Molar quantities (per mole)

A diagram comparing moles and molar masses of iron and gold samples that have equal masses Mass versus moles of iron vs gold.svg
A diagram comparing moles and molar masses of iron and gold samples that have equal masses

The quotient of some extensive physical quantity of a homogeneous sample by its amount of substance is an intensive property of the substance, usually named by the prefix "molar" or the suffix "per mole". [6]

For example, the quotient of the mass of a sample by its amount of substance is its molar mass, for which the SI unit kilogram per mole or gram per mole may be used. This is about 18.015 g/mol for water, and 55.845 g/mol for iron. Similarly for volume, one gets the molar volume, which is about 18.069 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 in grams per mole is the same as that of the mean mass of one molecule or formula unit of the substance in daltons, as the mole was historically defined such that the molar mass constant was exactly 1 g/mol. Thus, given the molecular mass or formula 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. This allows for accurate determination of the amount in moles of a substance by measuring its mass and dividing by the molar mass of the compound: . [7] For example, 100 g of water is about 5.551 mol of water. Other methods of determining the amount of substance include the use of the molar volume or the measurement of electric charge. [7]

The molar mass of a substance depends not only on its molecular formula, but also on the distribution of isotopes of each chemical element present in it. For example, the molar mass of calcium-40 is 39.96259098(22) g/mol, whereas the molar mass of calcium-42 is 41.95861801(27) g/mol, and of calcium with the normal isotopic mix is 40.078(4) g/mol.

Amount (molar) concentration (moles per liter)

Another important derived quantity is the molar concentration () (also called amount of substance concentration, [8] amount concentration, or substance concentration, [9] especially in clinical chemistry), defined as the amount in moles () of a specific substance (solute in a solution or component of a mixture), divided by the volume () of the solution or mixture: .

The standard SI unit of this quantity is mol/m3, although more practical units are commonly used, such as mole per liter (mol/L, equivalent to mol/dm3). 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
4N
2O) 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. [10]

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 (molar) fraction (moles per mole)

Confusingly, the amount (molar) concentration should also be distinguished from the molar fraction (also called mole fraction or amount fraction) of a substance in a mixture (such as a solution), which 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 fraction.

History

The alchemists, and especially the early metallurgists, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758, Mikhail Lomonosov questioned the idea that mass was the only measure of the quantity of matter, [11] but he did so only in relation to his theories on gravitation. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.

See also

Related Research Articles

The molecular mass is the mass of a given molecule. Units of daltons (Da) are often used. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The derived quantity relative molecular mass is the unitless ratio of the mass of a molecule to the atomic mass constant.

<span class="mw-page-title-main">Specific heat capacity</span> Heat required to increase temperature of a given unit of mass of a substance

In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

<span class="mw-page-title-main">Stoichiometry</span> Calculation of relative weights of reactants and products in chemical reactions

Stoichiometry is the relationships among the weights of reactants and products before, during, and following chemical reactions.

<span class="mw-page-title-main">Mole (unit)</span> SI unit of amount of substance

The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for amount of substance, an SI base quantity proportional to the number of elementary entities of a substance. One mole is an aggregate of exactly 6.02214076×1023 elementary entities (approximately 602 sextillion or 602 billion times a trillion), which can be atoms, molecules, ions, ion pairs, or other particles. The number of particles in a mole is the Avogadro number (symbol N0) and the numerical value of the Avogadro constant (symbol NA) expressed in mol-1. The value was chosen on the basis of the historical definition of the mole as the amount of substance that corresponds to the number of atoms in 12 grams of 12C, which made the mass of a mole of a compound expressed in grams, numerically equal to the average molecular mass or formula mass of the compound expressed in daltons. With the 2019 revision of the SI, the numerical equivalence is now only approximate but may be assumed for all practical purposes.

<span class="mw-page-title-main">Avogadro constant</span> Fundamental metric system constant defined as the number of particles per mole

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol−1 (reciprocal moles). It is this defined number of constituent particles (usually molecules, atoms, ions, or ion pairs—in general, entities) per mole (SI unit) and used as a normalization factor in relating the amount of substance, n(X), in a sample of a substance X to the corresponding number of entities, N(X): n(X) = N(X)(1/NA), an aggregate of N(X) reciprocal Avogadro constants. By setting N(X) = 1, a reciprocal Avogadro constant is seen to be equal to one entity, which means that n(X) is more easily interpreted as an aggregate of N(X) entities. In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, denoted N−1. The Avogadro number, sometimes denoted N0, is the numeric value of the Avogadro constant (i.e., without a unit), namely the dimensionless number 6.02214076×1023; the value chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the Italian physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a unit of mass defined as ⁠1/12⁠ of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted mu, is defined identically, giving mu = ⁠1/12⁠m(12C) = 1 Da.

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K−1⋅m−3.

<span class="mw-page-title-main">Solubility</span> Capacity of a substance to dissolve in a homogeneous way

In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.

<span class="mw-page-title-main">Molar mass</span> Mass per amount of substance

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

Relative atomic mass, also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant is defined as being ⁠1/12⁠ of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 revision of the SI.

Avogadro's law or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific case of the ideal gas law. A modern statement is:

Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules."

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm3 in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H+].

<span class="mw-page-title-main">Specific activity</span> Activity per unit mass of a radionuclide

Specific activity is the activity per unit mass of a radionuclide and is a physical property of that radionuclide. It is usually given in units of becquerel per kilogram (Bq/kg), but another commonly used unit of specific activity is the curie per gram (Ci/g).

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.

In chemistry, equivalent weight is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram of hydrogen or 8.0 grams of oxygen or 35.5 grams of chlorine.

The number density is an intensive quantity used to describe the degree of concentration of countable objects in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. Population density is an example of areal number density. The term number concentration is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.

<span class="mw-page-title-main">Chemical substance</span> Form of matter

A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be combined without reacting, they may form a chemical mixture. If a mixture is separated to isolate one chemical substance to a desired degree, the resulting substance is said to be chemically pure.

The molar mass constant, usually denoted by Mu, is a physical constant defined as one twelfth of the molar mass of carbon-12: Mu = M(12C)/12. The molar mass of an element or compound is its relative atomic mass or relative molecular mass multiplied by the molar mass constant.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.

<span class="mw-page-title-main">Atomic mass</span> Rest mass of an atom in its ground state

Atomic mass (ma or m) is the mass of a single atom. The atomic mass mostly comes from the combined mass of the protons and neutrons in the nucleus, with minor contributions from the electrons and nuclear binding energy. The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to (per E = mc2).

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