Amount Of Substance

In chemistry, the amount of substance (symbol ) in a given sample of matter is defined as a ratio () between the number of elementary entities () and the Avogadro constant (). The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. p. 134 Since 2019, the mole has been defined such that the value of the Avogadro constant is exactly , defining a macroscopic unit convenient for use in laboratory-scale chemistry. The elementary entities are usually molecules, atoms, ions, or ion pairs of a specified kind. The particular substance sampled may be specified using a subscript or in parentheses, e.g., the amount of sodium chloride (NaCl) could be denoted as or . 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. The amount of substance in a sample can be calculated from measured quantities, such as mass or volume, given the molar mass of the substance or the molar volume of an ideal gas at a given temperature and pressure.

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 (i.e., its molar mass in g/mol or kg/kmol), 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 18.0153 daltons on average, whereas a mole of water (which contains water molecules) has a total mass of about 18.0153 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 () will react with 2 molecules of hydrogen () to make 2 molecules of water ()" can also be stated as "1 mole of will react with 2 moles of to form 2 moles of water". The same chemical fact, expressed in terms of masses, would be "32.0 g of oxygen (1 mole of ) will react with approximately 4.0 g hydrogen (2 moles of ) to make approximately 36.0 g of water (2 moles of )" (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, although the volume of an ideal gas is proportional to the amount in moles or number of molecules at constant temperature and pressure. 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, rather than the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms, such as enplethy and stoichiometric amount.

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 (kilo)grams".

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 () has a mass of about 32.00 g, whereas a sample of 1 mol ''of atoms'' of oxygen () has a mass of about 16.00 g.

Derived quantities

Molar quantities (per mole)

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".

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 and molar volume

The molar mass ($M$) of a substance is the ratio of the mass ($m$) of a sample of that substance to its amount of substance ($n$): $M=m/n$. 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: $n=m/M$.International Bureau of Weights and Measures
Realising the mole
. Retrieved 25 September 2008. For example, 100 g of water is about 5.5509 mol of water.

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 , whereas the molar mass of calcium-42 is , and of calcium with the normal isotopic mix is .

Other methods of determining the amount of substance include the use of the molar volume ($V_m$) for ideal gases at a given temperature $T$ and pressure $P$ (through the relationship $V_m = V/n = RT/P$) or the measurement of electric charge (using Faraday's laws of electrolysis). For example, the molar volume of an ideal gas under standard conditions of 0  °C (273.15  K) and 1  atm (101.325 kPa) is about 22.414  L/mol, and 1  m³ of an ideal gas under the same conditions is about 44.615 mol of gas.

Amount (molar) concentration (moles per liter)

Another important derived quantity is the molar concentration ($c$) (also called ''amount of substance concentration'', ''amount concentration'', or ''substance concentration'', especially in clinical chemistry), defined as the amount in moles ($n$) of a specific substance (solute in a solution or component of a mixture), divided by the volume ($V$) of the solution or mixture: $c=n/V$.

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 () 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.

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 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 will be .

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, 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.
* 1777: Wenzel publishes ''Lessons on Affinity'', in which he demonstrates that the proportions of the "base component" and the "acid component" (cation and anion in modern terminology) remain the same during reactions between two neutral salts..
* 1789: Lavoisier

HOME


Content is Copyleft
Website design, code, and AI is Copyrighted (c) 2014-2017 by Stephen Payne


Consider donating to Wikimedia



As an Amazon Associate I earn from qualifying purchases