# Amount of Substance

In chemistry , the amount of matter in a given sample of matter is defined as the number of discrete atomic scale particles in it divided by the Avogadro constant nA . In a truly atomistic view, the amount of matter is simply the number of particles that make up matter.    Particles or bodies may be molecules , atoms , ions , electrons , or others, depending on the context. The value of Avogadro’s constant N A is defined as 6.022 140 76 × 10 23  mol -1 . In fact, in atomic terms, 1 mol =6.022 140 76 × 10 23 particles ( Avogadro number )  and therefore the conversion constant is only N A = 1.  The amount of a substance is sometimes referred to as a chemical amount .

The mole (symbol: mol) is a unit of the amount of substance in the International System of Units , defined (since 2019) by Avogadro’s constant fixing on the given value. Historically, the mole was defined as the amount of substance in 12 grams of a carbon-12 isotope. As a result, the mass of one mole of a chemical compound , in grams , is numerically (for all practical purposes) equal to the mass of one molecule of the compound, in daltons , and the molar mass of an isotope, in grams, is . Mass is equal to number. For example, one molecule of water has an average mass of about 18.015 Daltons, while one mole of water (which contains6.022 140 76 × 1023 water molecules) has a total mass of about 18.015 g.

In chemistry, due to the law of multiple proportions , it is often more convenient to work with quantities (i.e. moles or number of molecules) of substances than with mass (grams) or volume (litres). For example, the chemical fact ” 1 molecule of oxygen ( O.)2) will react with 2 molecules of hydrogen ( H react)2) to form 2 molecules of water ( H.)2O )” to ” O . 1 mole of” can also be called2will react with 2 moles of H mo2To make 2 moles of water”. The same chemical fact, expressed in terms of mass, “will have 32 g (1 mol) of oxygen which will react with approximately 4.0304 g ( 2 moles of H ).2) hydrogen to make approximately 36.0304 g (2 mol) of water” (and the number will depend on the isotopic composition of the reagents). In terms of volume, the number will depend on the pressure and the 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 in grams per liter.

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

This technical meaning of the term “amount of matter” should not be confused with the general meaning 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 matter” with more easily different terms, such as abundance  and stoichiometric quantity . 

IUPAC recommends that “volume of substance” should be used instead of “number of moles”, just as volume mass should not be called “number of kilograms”.

## nature of particles

To avoid ambiguity, the nature of the particles must be specified in any measurement of the amount of matter: thus, 1 mol of molecules of oxygen ( O2) is about 32 g, while 1 mole of oxygen atoms ( O ) is about 16 g.

## derived quantity

### Molar Volume (per mole)

The quotient of some broad physical quantity of a homogeneous sample by the amount of the substance is an intensive property of the substance , usually designated by the prefix molar . 

For example, molar mass is the ratio of the mass of a sample to the amount of its substance , whose SI unit is kilograms (or, more commonly, grams) per mole; Which is about 18.015 g/mol for water and 55.845 g/mol for iron . From the volume, the molar volume is obtained , which is approximately 17.962 ml /mol for liquid water and 7.092 ml/mol for iron at room temperature. From the heat capacity , one becomes the molar heat capacity , which is about 75.385 J / K /mol for water and about 25.10 J/K/mol for iron.

### Volume Concentration (moles per liter)

Another important derived quantity is the amount of substance concentration  (also called volume concentration , or substance concentration in clinical chemistry ;  which is referred to as a specific substance in a sample of a solution (or some other mixture). is defined as the volume of. ), divided by the volume of the sample.

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

Each solution has a volume, not a solvent. Thus, for example, one liter of standard vodka contains approximately 0.40 liters of ethanol (315 g, 6.85 mol) and 0.60 liters of water. So the volume concentration of ethanol is (6.85 mol ethanol)/(1 L vodka) = 6.85 mol/L, not (6.85 mol ethanol)/(0.60 L water), which would be 11.4 mol/L.

In chemistry, it is customary to read the unit “mole/L” as molar , and is denoted by the symbol “m” (both after the numeric value). Thus, for example, each liter of a “0.5 molar” or “0.5 M” solution of urea ( CH
4No
2o ) There are 0.5 moles of that molecule in water. By extension, the amount of concentration is usually also called the molarity of the substance of interest in the solution. However, as of May 2007, these terms and symbols are not waived 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 sea water).

### Volume fraction (mole per mole)

Confusingly, volume concentration, or “molarity”, should also be distinguished from “molar concentration”, which is the number of moles (molecules) of the substance of interest divided by the total number of moles (molecules) in a sample of solution. needed. , This quantity is more appropriately called the amount fraction.

## history

Alchemists, and especially early metallurgists, probably had some notion of the amount of matter, but there are no surviving records of any generalization of the idea beyond a set of consonants. In 1758, Mikhail Lomonosov questioned the idea that mass was the only measure of the amount of matter,  but he did so only in relation to his theories on gravity. The development of the concept of quantity of matter coincided and was important with the birth of modern chemistry.

• 1777 : Wenzel published the text on affinity , in which he demonstrated that the ratio of the “base component” and “acid component” (cation and anion in modern terminology) remains the same during reactions between two neutral salts. 
• 1789 : Lavoisier publishes the treatise Elementary Chemistry , introducing the concept of a chemical element and explaining the law of conservation of mass for chemical reactions . 
• 1792 : Richter publishes the first volume of stoichiometry, or The Art of Measuring Chemical Elements (later volumes continue to be published until 1802). The term “stoichiometry” is used for the first time. The first table of equivalent weights for acid-base reactions is published. Richter also notes that, for a given acid, the equivalent mass of the acid is proportional to the mass of oxygen in the base. 
• 1794 : Proust’s law of definite proportions generalizes the concept of equal weight to all types of chemical reactions, not just acid-base reactions. 
• 1805 : Dalton publishes his first paper on modern atomic theory, which includes a “Table of the Relative Weights of Final Particles of Gaseous and Other Bodies”. The concept of atoms called into question their weight. While many were skeptical about the reality of atoms, chemists quickly found atomic weights to be an invaluable tool in expressing stoichiometric relationships.
• 1808 : The publication of Dalton’s A New System of Chemical Philosophy , including the first table of atomic weights (based on H = 1). 
• 1809 : Gay-Lussac’s law of combining quantities, stating an integer relationship between the amounts of reactants and products in chemical reactions of gases. 
• 1811 : Avogadro’s hypothesis that equal volumes of different gases (at the same temperature and pressure) contain the same number of particles, now known as Avogadro’s law. 
• 1813/1814 : Berzelius publishes the first of several tables of atomic weights based on scale = 100   
• 1815 : Prout published his hypothesis that all atomic masses are integer multiples of the atomic mass of hydrogen.  The hypothesis was later abandoned in view of the observed atomic mass of chlorine (about 35.5 relative to hydrogen).
• 1819 : Dulong-Petit law relating the atomic mass of a solid element to its specific heat capacity. 
• 1819 : Mitscherlich’s work on crystal isomorphism allows many chemical formulas to be clarified, resolving many ambiguities in the calculation of atomic weights. 
• 1834 : Clapeyron states the ideal gas law. The ideal gas law was the first to be discovered apart from its mass, the many relationships between the number of atoms and molecules in a system, and other physical properties of the system. However, this was not enough to convince all scientists about the existence of atoms and molecules, with many considering it only a useful tool for calculations.
• 1834 : Faraday states his laws of electrolysis, specifically that ” the chemical decomposition of a current is constant for a constant amount of electricity “. 
• 1856 : Kronig derived the ideal gas law from kinetic theory.  Clausius publishes an independent etymology the following year. 
• 1860 : The Congress of Karlsruhe debates the relationship between “physical molecules”, “chemical molecules” and atoms without reaching a consensus. 
• 1865 : Losschmidt makes the first estimate of the size of gas molecules and therefore the number of molecules in a given volume of gas, now known as the Loschmidt constant. 
• 1886 : Vant Hoff showed similarities in the behavior of dilute solutions and ideal gases.
• 1886 : Eugene Goldstein observed discrete particle rays in a gas discharge, laying the foundation for mass spectrometry, an instrument later used to establish the masses of atoms and molecules.
• 1887 : Arrhenius describes the dissociation of an electrolyte in solution, solving a problem in the study of collinear properties. 
• 1893 : The term mole is used for the first time by Ostwald in a university textbook to describe a unit of quantity of matter . 
• 1897 : The word mole was used for the first time in English. 
• By the twentieth century , the concept of atomic and molecular entities was generally accepted, but many questions remained, not least the size of the atoms and their number in a given sample. Concurrent developments in mass spectrometry, starting in 1886, supported the concept of atomic and molecular masses and provided a tool for direct relative measurement.
• 1905 : Einstein’s paper on Brownian motion dispels any final doubts about the physical reality of atoms, and opens the way to the precise determination of their masses. 
• 1909 : Perrin named the Avogadro constant and estimated its value. 
• 1913 : Discovery of isotopes of non-radioactive elements by Sodi  and Thomson. 
• 1914 : Richards received the Nobel Prize in Chemistry for “his determination of the atomic weights of a large number of elements”. 
• 1920 : Aston proposes the whole number rule, an updated version of Prout’s hypothesis. 
• 1921 : Sodi receives the Nobel Prize in Chemistry for “his work on the chemistry of radioactive substances and investigations into isotopes”. 
• 1922 : Aston receives the Nobel Prize in Chemistry “for the discovery of a large number of isotopes of non-radioactive elements, and for his whole-number rule”. 
• 1926 : Perrin receives the Nobel Prize in Physics, partly for his work in measuring the Avogadro constant. 
• 1959/1960 : Unified atomic mass unit scale based on 12 = C 12 adopted by IUPAP and IUPAC. 
• 1968 : The mole is recommended for inclusion in the International System of Units (SI) by the International Committee for Weights and Measures (CIPM). 
• 1972 : The mole is approved as the SI base unit for the amount of a substance. 
• 2019 : Mole is redefined in SI as “the amount of matter of a system that contains”6.022 140 76 × 10 23 Specified Primary Bodies”.