Thus, equal masses have different numbers of atoms, molecules, or moles. On the other hand, equal numbers of moles of different substances have different masses. The stoichiometric relationships among reactants and products may be complicated in units of g, but much simpler relationships are seen if we deal with units of moles or natural units of atoms and molecules. Moles mol represent amounts of substances in the unit of Avogadro's number 6.

The mole unit is very important for chemical reactions, as is the skill to convert masses in g to mol. The number of moles of a substance in a sample is the mass in g divided by the molar mass , which gives the amount in moles.

Another common measure of substances is volume. Since density is the mass divided by its volume, conversion between volume and mass is accomplished by the formula:. Skill: convert amounts between moles and kg of compounds represented by chemical formulas. Learning Objectives Express amounts of substances in g, kg, or mL, or L. Gilbert et al. The amount that contains a number of objects equal to the number of atoms in exactly 12 g of carbon which is 6.

A mole is the amount 10 of material containing 6. Notice that the definition of the mole is an amount of substance.

We will often refer to the number of moles of substance as the amount of the substance. The second, and more fundamental, thing to understand about the mole is how it gets its specific value.

The draft retains a stumbling block to understanding, the term amount of substance. The mole is a convenient package, like a dozen or a gross; but numerically it is much larger. Thus a mole can be further defined as The mole is defined as the amount of substance that contains as many elementary entities as there are atoms in exactly 12 g of carbon Amount of substance is defined to be proportional to the number of specified elementary entities in a sample, the proportionality constant being a universal constant which is the same for all samples.

The kilogram is equal to the mass of the international prototype of the kilogram. Thus in many cases the name of the base quantity is shortened to amount and to avoid possible confusion with the general meaning of the word the attribute chemical is added.

Strictly, neither alternative is appropriate. The mole is the amount of substance containing the same number of molecules or atoms or radicals or ions or electrons as there are atoms in exactly 12 g of 12 C. Such wrong interpretations are also present among prestigious authors and publications [emphases added] and in educators, But the educator should be aware that this choice has been made on idiosyncratic grounds differing from the prevailing scientific view, expressed by the scientific community through SI [emphasis added].

It seems that the definition [that is, its official definition and adoption into SI] has led to difficulties which either did not previously exist or of which we were unaware. The insightful comments of the anonymous referees were most useful in focusing and clarifying the arguments and assertions set out in this essay.

Neither the referees nor NTS is responsible for whatever deficiencies remain. Its numerical value technically depends on the units in which it is expressed, but those units are invariably mol —1. None of the chemistry textbooks consulted herein uses the term Avogadro constant. Emphasis in quoted text, such as bold or italic text, is present in the original, except where stated otherwise. The history of such changes is briefly but informatively addressed in.

I believe that the authors would say that the meanings in question apply to the term as it is currently understood. View Author Information. Cite this: J. Article Views Altmetric -. Citations 7. For example, the ACS Committee on Nomenclature, Terminology, and Symbols has been monitoring proposals on these units for several years, sponsoring symposia on the subject at national meetings and publishing comments in Chemical and Engineering News.

This article focuses on the current definition of the mole, 5 as well as the definition contained in the draft brochure of the new SI, 2 with an eye toward teaching the mole in introductory chemistry classes. Some current textbooks are examined for how they teach about the mole in order to compare the official definition to current educational practice. In order to put the likely effects of the proposed change into historical perspective, a comparison is made to effects from an earlier major change in SI for chemists, namely, the inclusion of the mole as an SI base unit in The Mole in Current Textbooks.

The mole is key content in every introductory chemistry textbook, and teaching the mole is a perennial subject in chemistry education. The current official definition of the mole reads 5 The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0. Here is the definition given in the draft of the new SI: 2 The mole, symbol mol, is the SI unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be exactly 6.

The treatment within the body of a textbook includes examples, and relates the mole to mass as well as number of entities. The next paragraph says 8 The second, and more fundamental, thing to understand about the mole is how it gets its specific value. Comparing the draft definition of the mole to current textbook treatments suggests two implications: 1. The expectation that textbooks of the future will not change their definitions of the mole very much in response to the change in the SI definition is based partly on the fact that the draft SI is in some respects closer than the current definition to what many textbooks have already.

But it is also based on the fact that textbooks did not greatly change how they introduced the mole over the years. Consider textbook definitions from before the inclusion of the mole into the SI. The term and unit mole had been in use in chemistry since roughly the start of the 20th century; 11 however, it was incorporated into the SI as a base unit, along with the base quantity amount of substance only in Mortimer happens to be the last example selected from this time period, but I do not want to imply that eventually textbook authors followed his example and adopted the official SI definition; examining recent textbooks as done above shows that this is not the case.

Indeed, this glimpse at how the mole has been described in textbooks over the past 50 years or so suggests that textbook authors have emphasized throughout that a mole contains a definite number of entities. Of Official Definitions and Textbooks.

It may be that textbooks will not adapt to or reflect changes in official definitions of the SI. That would not necessarily be an unfortunate development. Let us look more closely at these assertions in the light of current practices and a few examples from the pedagogical literature. Having concentrated above on the mole, what follows will focus on the quantity of which the mole is the unit, amount of substance.

This is the law of multiple proportions. It is difficult to give formal definitions for quantities, particularly base quantities, such as length, mass, time, temperature, and amount of substance. The most useful definitions of quantities are in terms of the equations that relate them to other quantities, and, in this way, derived quantities are defined in terms of base quantities.

But defining the base quantities is more difficult. Amount of substance is a quantity proportional to the number of entities N in a sample. The proportionality constant is the same for all substances and is the reciprocal of the Avogadro constant N A. The entities may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

The quantity amount of substance, n, is thus an alternative to using the quantity number of entities, N. They are related by the equation. Because the number of entities N is a dimensionless number, the dimension of N A is the reciprocal of the dimension of n and is thus amount of substance One might reasonably ask why we need the quantity amount of substance n at all. Why not simply use number of entities N in its place? There are three reasons for preferring the use of n rather than N:.

First, equations, such as Equation 3, can be used to determine molar mass M, or amounts in terms of moles, without knowing the value of the Avogadro constant. The atomic weights of atoms in the periodic table were known long before the value of the Avogadro constant was known with similar accuracy. Even today, the value of the Avogadro constant is known only to about a part in 10 7 , whereas many atomic weights are known to about a part in 10 9 or better.

A second reason is practical: The number of entities is generally of the order 10 23 , whereas n is generally a number of order 1 when expressed in moles.

Thus, for example, in a chemistry laboratory, the concentration of solutions is typically quoted in moles per litre, with numbers in the general order of magnitude 1.

It would be inconvenient to quote concentrations in molecules per litre, with numbers of the order 10 The quantity amount of substance may be seen as a device used to handle the same quantitative information with much smaller numbers. A third motivation for introducing the quantity amount of substance with the mole as a base unit is that it extends the power of dimensional analysis in chemistry, and to equations involving chemical quantities. This follows from the fact that n is a base quantity with its own dimension, whereas N is dimensionless.

The mole, with symbol mol, is the SI unit for the quantity amount of substance. It is currently defined as follows:. The mole is that amount of substance that contains the same number of elementary entities as there are atoms in 12 g of carbon When the mole is used, the entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The present best estimate of the Avogadro constant is. This is summarized in the relations.

Here, A r X is the recommended symbol for the molecular weight of the entity X. The atomic or molecular weight of an entity is actually the relative atomic or molecular mass, relative to the value for the carbon 12 atom taken as exactly Its origin has been discussed in several publications. As the term implies, one gram molecular weight of a substance X is that amount in a mass equal to the molecular weight expressed in grams.