METROLOGY IN CHEMISTRY CHIMIA 2009, 63, No. 10 613 doi:10.2533/chimia.2009.613 Chimia 63 (2009) 613–615 © Schweizerische Chemische Gesellschaft Amount of Substance and the Mole Martin J. T. Milton*a and Ian M. Millsb Abstract: The unit mole is very familiar amongst both chemists and physicists, but the name of the corresponding quantity ‘amount of substance’ is not so familiar and the concept is still a source of difficulty for many students. This paper reviews and clarifies these concepts and also discusses the definition of the unit mole, and its pos- sible revision. Keywords: Amount of substance . Molar mass constant . Mole . Redefinition . SI 1. Amount of Substance concept for chemical reactions. Thus the from a specific number of entities and from ratio of volumes of solutions of X and Y the definition of the unit for amount of sub- Amount of substance is a quantity that that react together in a titration are given by stance. measures the size of an ensemble of enti- The quantity amount of substance (n) ties. It appears in thermodynamic relations is thus an alternative to using the quantity (4) such as the ideal gas law, and in stoichio- number of entities (N). They are related by metric relations between reacting mol- the equation ecules such as the Law of Multiple Pro- portions.[1,2] Familiar equations involving where the quantity (n /n ) is a simple ra- n = N/N (5) X Y A amount of substance (n) are tional fraction. Hence the concentration of an unknown solution may be determined where N is the Avogadro constant. A pV = nRT,(1) from the concentration of a standard solu- One might reasonably ask why we need tion by measuring the volumes in a titration. the quantity amount of substance at all, for an ideal gas, and the equation This is the Law of Multiple Proportions. when the number of entities could be used It is interesting to note that whilst the in its place? We propose three reasons for c = n/V (2) use of amount of substance in the sense preferring to use n rather than N. of referring to a thermodynamic ensemble The first is that equations like Eqn. (3) for the amount of substance concentration can be traced back to Boyle’s research in can be used to determine molar mass M, or (usually called simply the concentration) the 17th century, the development of an amounts in terms of moles, without know- of a solution. Here V is the volume of a understanding of stoichiometry dates to ing the value of theAvogadro constant. The solution containing the amount of solute n. Lavoisier’s work one hundred years later. atomic weights of atoms in the periodic ta- Another important relation is that between Underlying both of the senses in which it ble were known long before the value of amount of substance n and mass m for a is used, is the fact that the quantity amount the Avogadro constant was known with pure sample of substance measures a number of enti- similar accuracy. Even today, the value of ties. This insight can be traced directly to the Avogadro constant is only known to n = m/M (3) two developments made in the early 19th about one part in 107, whereas many atom- century: Dalton’s explanation of his Law ic weights are known to about one part in where M is the mass per amount of sub- of Multiple Proportions and Avogadro’s 109 or better. stance, usually called the molar mass. hypothesis that “samples of different gas- The second reason is practical; the An important application of the quan- es at the same temperature, pressure and number of entities is generally of the or- tity amount of substance in chemistry is volume always contain the same number der 1023, whereas n is generally a number to the way in which molecules react in a of molecules”.[3,4] As discussed below, it is of order 1 when expressed in moles. Thus, titration or more generally in any chemi- now being proposed that the link between for example, in a chemistry laboratory cal reaction. This is the most fundamental the quantity amount of substance and the the concentration of solutions is typically underlying concept of a number of entities quoted in moles per litre, with numbers in should be strengthened by the introduc- the general order of magnitude 1. It would tion of a definition for the unit of amount be inconvenient to quote concentrations in of substance framed directly in terms of a molecules per litre, with numbers of the fixed number of entities. order 1023. Thus we find bottles labelled “Amount of substance is a quantity ‘0.1 M NaOH’, where M is read as ‘molar’ that measures the size of an ensemble of and is an accepted shorthand for the unit . –1 . –3 *Correspondence: Dr. M. J. T. Miltona entities. It is proportional to the number of mol L = mol dm . The quantity amount Tel.: +44 031 943 6826 specified entities and the constant of pro- of substance may be seen as a device to E-mail: [email protected] portionality is the same for all substances. handle the same quantitative information aNational Physical Laboratory NPL Analytical Science Division The entities may be atoms, molecules, with much smaller numbers. Hampton Road, Teddington, ions, electrons, other particles, or speci- The third reason for introducing the Middlesex, TW11 0LW, UK fied groups of particles.” quantity amount of substance, with the bUniversity of Reading School of Chemistry This definition emphasises the nature mole as a base unit, is that it extends the Reading, Berkshire, RG6 6AD, UK of amount of substance, which is distinct power of dimensional analysis to chemis- 614 CHIMIA 2009, 63, No. 10 METROLOGY IN CHEMISTRY try, and to equations involving chemical Molekel” to “Mol” was first recorded in The mole is that amount of substance of quantities. This follows from the fact that 1898 by Nernst.[8] The term ‘mole’appears a system that contains exactly 6.022 141 79 n is a base quantity with its own dimension, in English for the first time in the transla- × 1023 specified elementary entities, which whereas N is dimensionless. tion of Ostwald’s ‘Principles of Inorganic may be atoms, molecules, ions, electrons, Chemistry’ published in 1902, in which other particles or specified groups of such he associated it with a standard number of particles. 2. The Mole molecules. Thus one gram molecule of X The effect of this new definition would became one mole of X. be to fix the value of the Avogadro constant The mole is the SI unit for the quantity It must be admitted that the name to be 6.022 141 79 × 1023 mol−1 exactly. amount of substance.[5] It is currently de- ‘amount of substance’ is not well chosen, The number would be chosen to be the fined by the statements:[6] because the word ‘amount’ has a common best estimate of the numerical value of the The mole is that amount of substance dictionary meaning, and the additional Avogadro constant at the time the new defi- that contains the same number of elemen- words ‘of substance’ seem inadequate to nition is adopted, thus ensuring continuity tary entities as there are atoms in 12 g of imply the chemist’s specialised use for the in the value of the mole.[9] carbon-12. When the mole is used the enti- name. It was the original intention that the This new definition would be concep- ties must be specified and may be atoms, words ‘of substance’ should be replaced tually simpler than the current definition, molecules, ions, electrons, other particles, by the specification of the entity whenever which is chosen to fix the molar mass of or specified groups of such particles. possible, so that one would say (for exam- carbon 12 rather than the number of entities It follows that the numerical value of ple) ‘amount of benzene, C H ’ or ‘amount in a mole. Also the new definition would 6 6 the Avogadro constant,[7] denoted {N }, of hydrogen ions, H+’. no longer be dependent on the kilogram, so A expressed in the unit mol−1, is simply the Another name for n, which is the name that uncertainties in realising the definition number of atoms in 12 g of carbon 12, so that most chemists use, is simply ‘number of the kilogram would no longer be trans- that the value of the Avogadro constant of moles’. However this is not a good mitted to the mole – as they are at present. is directly related to the definition of the name, because it confuses the name of the mole. quantity with the name of the unit. A clear The effect of this definition is that the understanding requires that we always 5. The Molar Mass Constant M u molar mass of carbon 12, M(12C), is exactly distinguish clearly between quantities and 12 g.mol–1, and the molar mass of any atom units. Thus mass is a quantity, for which Many of the relations between the or molecule X is determined from its atom- kilogram (or gram, or milligram) are units, quantities discussed here can be simplified ic or molecular weight by simply multiply- and similarly we wish to say that amount of by introducing the molar mass constant ing by the unit g.mol–1, without the need to substance is a quantity, for which mole (or M , defined as one twelfth of the molar u know the value of the Avogadro constant.