Search

The most challenging problems in the field of chemico- and bioanalytical measurements are described. These problems are being solved, in particular, by participating in new international comparisons organized by the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology of the International Committee of Weights and Measures (CCQM CIPM). Solutions of these challenging problems are presented. The objectives and tasks of developing key comparisons in the following areas are described: isotopic measurements; determination of the purity of substances; organic analysis; bioanalytical measurements; measurements of aerosol particle parameters; measurements in the field of gas analysis and electrochemistry. It is shown that participation in international key comparisons allows obtaining valid and reliable results of measurements of the composition and properties of gas and liquid media, as well as solid substances and materials.

The kilogram is the unit of mass and was defined in 1889 by the international prototype of the kilogram. The mole is the unit of amount of substance and was defined in 1960 by the number of atoms in 0.012 kg of 12C. These definitions were revised in May 2019. The new definitions of the kilogram and the mole are based on the Planck constant h and the Avogadro constant NA, respectively. The values of h and NA used in the new definitions were determined by summarizing measurement results of the two physical constants by several national metrology institutes around the world. In this review, the history of the two units and measurement technologies used to derive the new definitions are described. The effect of the revision on the development of new measurement technologies is also introduced.

In this paper I take a close look at the SI base quantity “amount of substance”, and its unit, the mole. The mole was introduced as a base unit in the SI in 1971, and there is currently a proposal to change its definition. The current definition of the mole shows a certain ambiguity regarding the nature of the quantity “amount of substance”. The proposed new definition removes the ambiguity, but at a cost: it becomes difficult to justify treating amount of substance as having its own dimension, and hence its own unit, the mole. I argue that the difficulties with amount of substance result from its role as a mediator between macroscopic and microscopic scales. To understand why amount of substance might have its own dimension, we need to connect amount of substance to mass, contra current proposals to separate them.

Redefinition of the basic units of the International System of Units (SI) — the kilogram, mole, ampere, and kelvin, — which are now expressed in terms of fundamental physical constants means a substantial revision of the system. In particular, the new definition of the mole fixing the value of the Avogadro constant sets a unit of the amount of substance, which is independent of the unit of mass. We consider some consequences of redefining (the mole and kilogram) and focus on the uncertainty of measuring the amount of substance and related quantities which are important for description of the mixture composition. The issue regarding the molar mass of the substance and associated uncertainty is considered in detail It is noted that calculation of the molar mass using relative atomic masses, involves the molar mass constant which is not equal exactly to 1 g/'mol in the new SI. This introduces an additional, though very small, uncertainty of less than 1 x 10-9in relative terms. The budget of uncertainty for the amount of substance determined through the mass measurements when the mass is measured with the highest accuracy is scrutinized. It is demonstrated that for substances of less than 99.98% purity, the uncertainty associated to the purity is comparable to that of relative atomic masses of the elements. For high-purity substances, the uncertainty in the relative atomic masses have the largest contribution to the budget. Anyhow, the uncertainty associated to the molar mass constant is three orders of magnitude less than the nearest contribution to the uncertainty attributed to weighing. In the case of derived quantities which are the ratio of two quantities of the same kind, the additional uncertainty does not arise at all. This is illustrated by the calculation of the mole fraction of a component in the gravimetrically prepared gas mixture.

The amount of substance expressed in the units of moles is an essential concept in physics and chemistry. Physics students usually acquired a chemistry background in applying the mole concept. However, research shows that the complexity of interpretations of quantities expressed as molar mass or atomic mass makes formulating a dimensional analysis with these ratios unclear to physics students. This study proposes proportional reasoning, instead of ratios, as the main building block to formulate conversion algorithms from microworlds to macroworlds and vice versa. A deductively designed lecture was conducted with a group of (N = 25) freshman college physics students. While on the pretest, only (N = 4, 16%) correctly converted a mass of a substance expressed in kilograms to a number of moles, on the posttest, the percentage of correct answers increased (N = 20, 80%), suggesting that proportional reasoning has the potential to help students understand the conversion processes and improve understanding of the mole as a unit of substance. This study, in its principal form, was published earlier (see Sokolowski, A., International Journal of Physics & Chemistry Education, 11, 85–92, 2019).

New definitions of the units for amount of substance – the mole – and for mass – the kilogram – will presumably come into force on the World Metrology Day 2019. In the revised SI, the mole will be defined by a fixed value of the Avogadro constant and the kilogram by a fixed value of the Planck constant. The X-ray-crystal-density (XRCD) method has been used for the determination of these fundamental constants by counting the number of atoms in 28Si-enriched spheres. Thus, silicon spheres will – after the redefinition – be used to realize the definitions of the mole and the kilogram. This is possible by SI-traceable measurements of lattice parameter, isotopic composition, volume, and surface properties, yielding a relative standard uncertainty below 2⋅10−8. Whereas this high accuracy is only reached with isotopically enriched silicon, it is also planned to use natural silicon spheres on a slightly lower level of accuracy. The future definitions will allow also new realization methods using silicon, in particular for small mass values.

This discussion article begins by highlighting the benefits of the mole's incorporation within the international system of units (SI), in particular by bringing chemical measurement within formal metrology structures. The origins of the confusion that has consistently existed between amount of substance (the base quantity of which the mole is the SI base unit) and counting quantities are examined in detail and their differentiating characteristics fully elaborated on. The importance and benefits of distinguishing between these different quantities and the role that the Avogadro constant plays in doing this are highlighted. It is proposed that these issues are becoming increasingly important for two reasons. First, as chemistry and biology consider increasingly small size domains, measurements are being made of significantly reduced collections of entities. Second, the proposed re-definition of the mole makes the link between amount of substance and the number of elementary entities more transparent. Finally, proposals for new ways of expressing very low amounts of substance in terms of new prefixes based on the numerical value of the Avogadro constant are presented as a way to encourage the use of the mole, when appropriate, even for ultra-low level chemical measurement.

Оригинал опубликован в журнале Metrologia (2013. V. 50. № 5. P. 158-163) под названием "The mole, amount of substance and primary methods". Материал получен 25 февраля 2013 г., в окончательной форме - 8 марта 2013 г., опубликован 2 апреля 2013 г. Оригинальный текст доступен на сайте IOP Science. URL:stacks.Iop.org/Met/50/158. В данном докладе представлены принципы, разработанные для применения метрологии в сфере химии и, в частности, аналитической химии. Доклад начинается с обсуждения моля, основной единицы Международной системы единиц (СИ), которая более всего относится к аналитической химии. Моль стал предметом отдельной дискуссии совсем недавно, с момента публикации предложений дать ему новое определение вместе с тремя другими основными единицами СИ. Эта дискуссия также породила интерес к происхождению термина «количество вещества», которое используется как количество, а моль - как единица. В данном докладе рассматривается происхождение термина и объясняется, почему недостаточно было бы заменить его альтернативными вариантами, такими как «число единиц». В заключение идет дискуссия о том, как используется моль в первичных методах измерений.

Wilhelm Ostwald was a notable holdout against the acceptance of the reality of atoms. He steadfastly maintained a positivist perspective, that the empirical facts of chemistry implied no underlying meaning about the nature of matter. The amount of substance definition of the mole aligned with this view. He was moved to accept the reality of atoms based on the results of experimental work on Brownian motion by Jean Perrin, that gave a name to, and a value for, Avogadro’s constant. Ostwald could have modified the definition of the mole, making use of the constant to incorporate the atomic nature of matter into the concept. If he had, difficulties with the definition that persist today might have been avoided.

Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized.

The base quantity ‘amount of substance’ is poorly understood and the name and symbol usually avoided. This is because of its formal interpretation as the number of entities multiplied by the reciprocal of the mysterious Avogadro constant, N A. If X signifies the kind of entities involved, the number of entities in a sample, N(X), is easily comprehended, and if m av(X) is the sample-average entity mass, the total mass, m(X) = N(X)m av(X)—an aggregate of N(X) average entity masses—is also conceptually straightforward. However, the corresponding amount of substance, n(X) = N(X)(1/N A)—an aggregate of N(X) ‘reciprocal Avogadro constants’—is incomprehensible unless some physical meaning can be attached to 1/N A. By contrast, the base unit, mole, is thought of by chemists as an aggregate of a particular number of entities: mol = $$ {\mathcal N}_{\rm{Avo}} $$ ent, where $$ {\mathcal N}_{\rm{Avo}} $$ is the Avogadro number (equal to g/Da) and ent represents one entity. It makes sense, therefore, to interpret amount of substance as an aggregate of a general number of entities: n(X) = N(X) ent—an easily grasped concept. A ‘reciprocal Avogadro constant’ is thus seen to actually be exactly one entity. One mole then corresponds to setting N(X) = $$ {\mathcal N}_{\rm{Avo}} $$ , for which the total mass is the relative entity mass in grams—conforming to the original mole concept.

Recent results of measurements of the Avogadro constant by the method of crystal silicon spheres in connection with the planned transition to a new definition of the basic SI unit, the mole, are discussed.

Quantitative analysis is an important field in the quality control of medicinal plants, aiming to determine the amount of pharmacologically active constituents in complex matrices. Often biological effects of herbal drugs are not restricted to single compounds, but are rather caused by a number of often biogenetically related plant metabolites. Depending on the complexity of the analyzed plant extract, conflicts between accuracy, such as total content assays using photometric or colorimetric methods, and comprehensiveness, e.g. quantification of one or a few lead compounds can occur. In this study, we present a qHNMR approach determining the total amount of cycloartanoids in black cohosh (Actaea racemosa) rhizomes. Perdeuterated methanol containing 1,2,4,5-tetrachloro-3-nitrobenzene as an internal standard was used for extraction. Amounts of cycloartanoids were then measured by integrating 1H NMR signals of all cycloartenoids' H-19 exo protons. Due to their unusually low chemical shifts, these signals are well separated from all remaining signals in crude extracts. Thus, accurate (recovery rates of 99.5-102.5%) and precise (relative standard deviations below 2.5%) quantification of cycloartanoids was accomplished. To the best of our knowledge, this is the first example of a quantification of the total amount of a pharmacologically relevant compound class by integration of one 1H NMR signal characteristic for all members of this particular compound class. Additionally, we propose a new term and unit for the evaluation of medicinal plants and herbal medicinal products: the "specific partial amount of substance" of pharmacologically active constituents, indicated in mmol/g.

Understanding Concepts for Calculations: Amount of Substance and Mole

Just as the gram is an Avogadro number of daltons, g = (g/Da) Da, the current definition of the mole can be interpreted as an Avogadro number of entities, as it is often thought of by chemists—and it should be explicitly redefined this way. By introducing a hitherto missing atomic-scale unit for the amount of any substance, the entity (symbol ent), analogous to the dalton for mass, we can then define the mole as: mol = (g/Da) ent—i.e., an Avogadro number of entities. It is argued that the name for the base quantity should be “chemical amount,” by analogy with “electric current.” Recent proposals and counterproposals for redefining the mole (and renaming “amount of substance”) are critically discussed in light of the above intuitively obvious definition.

The mole is a difficult concept. Surveys have shown that even many teachers do not have a proper understanding of it. To help to meet this problem, the SI/IUPAC formulation of the mole is carefully presented and explained. New SI proposals are also briefly discussed.

The concept of mole is an abstract concept of sub-micro level. The main problem in chemistry that should be encounter by educators is students’ inability to transfer understanding between macro level and sub-micro level. Particle-oriented approach is created due to improper expression in the term of mole on books and classroom learning. A mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0,012 kg of carbon-12. When the mole is used, the elementary entities must be specified; they may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The study presented here focuses on students’ activity and response taught by mole triangle implemented in German and Indonesian classroom. Two classes of grade-10 were involved in each country. The way of students perform in the test was analyzed. Hands-on activities were used as an entrance and followed by particle-oriented expression. In worksheets of each hands-on experience, students should write the correct expression of mole concept. The results of the study indicated that there is different level of understanding in representing knowledge in learning the mole. The use of correct expression will ensure that students see meaningful relationships and can easily go back and forth between macro, sub-micro and symbolic level.

The mole is the most recent addition to the set of base units that form the International System of Units, although its pre-cursor the ‘gram-molecule’, had been in use by both physicists and chemists for more than 120 years. A proposal has been published recently to establish a new definition for the mole based on a fixed value for the Avogadro constant. This would introduce consistent relative uncertainties for the molar and the atomic masses while making no change to the system of relative atomic masses (‘atomic weights’). Although the proposal would have little impact on the measurement uncertainty of practical work, it has stimulated considerable debate about the mole and the nature of the quantity amount of substance. In this paper, the rationale for the new definition is explained against the background of changes in the way the quantity amount of substance has been used, from its first use during the early development of thermodynamics through to the use of the ‘number of gram-molecules’ at the end of the nineteenth century.

The fundamental concept of the mole stems from the idea of the gram-atom (or gram-molecule): that an amount of one mole of a given substance has an associated mass, in grams, numerically exactly equal to the relative atomic (or molecular) mass of the substance. This means that the particular number of entities comprising one mole, Avogadro’s number, must be exactly equal to the gram-to-dalton mass ratio. Various interpretations of what a mole actually means and how this affects the ideal gas equation depend on how the amount of a given substance, n, is related to the corresponding number of entities, N. We look at three alternatives: (1) the conventional interpretation in which n is directly proportional to N, where the proportionality factor is the reciprocal of the (evidently poorly understood) Avogadro constant; (2) a more easily comprehended alternative in which n is equal to N entities; and (3) an interpretation in which n and N both represent the number of entities, but expressed in different ways. Regardless of these different interpretations, the form of the stoichiometric equations (relating N, n and the total sample mass) and the form of the relationship between the universal gas constant and the Boltzmann constant remain the same.

There is a common misconception among educators, and even some metrologists, that the Avogadro constant NA is (or should be) a pure number, and not a constant of dimension N?1 (where N is the dimension amount of substance). Amount of substance is (and always has been) measured as a ratio of other physical quantities, and not in terms of a specified pure number of elementary entities. Hence the Avogadro constant has always been defined in terms of the unit of amount of substance, and not vice versa. The proposed redefinition of the mole in terms of a fixed value of the Avogadro constant is examined, and it is shown that such a redefinition would not bring any significant metrological benefit. It is contended that such a redefinition would only add to the confusion in this field, and so should be rejected.

‘Amount of substance’ was introduced in the end of the 1950s as the physical quantity whose unit of measurement is the mole. Fundamental problems associated with this physical quantity have caused a never-ending discussion that continues to this day. One of the reasons for this is the fact that the expression ‘amount of substance’ is not a good choice, due to its generality and inclusion of the word ‘substance’. Considering that samples of matter commonly handled by chemists are extremely numerous in entities and that the quality of being numerous or many is referred to as numerosity (a concept related to numerical cognition), this concept is reproposed as a replacement for amount of substance. Then, taking into account ongoing discussions toward a redefinition of the mole, the following definition is proposed for this SI base unit: “the mole is the numerosity of a sample of entities numbering exactly 6.022 141 794 × 1023”. The relationships between four extensive properties of matter (mass, volume, numerosity and number of entities) are detailed and the resulting intensive physical quantities (proportionality constants) are discussed. The concept numerosity is not the product of an invented synonym; furthermore, as a consequence of its generality, it can be used to express the quantity of entities in samples of matter, as well as of light, chemical reactions, etc. The acceptance that mole is the SI unit of numerosity might also solve most of the pedagogic problems associated heretofore with teaching of mole and amount of substance.

Most base units in the SI relate to specific sensoric qualities our body is able to observe: space, heat, brightness, etc. The base unit ‘mole’ incorporates intellectual insight: the atomistic perception of the world. This perception is a quintessence of over 300 years of scientific research. The quintessence, from Dalton’s ‘The sceptical chymist’ to Perrin’s Nobel Prize in 1926 and Pauling’s ‘Nature of the Chemical Bond’ in 1939, results in the conclusion that the base unit of the SI quantity ‘amount of substance’ is not the mole but the dimensionless entity.

There has been considerable discussion about the merits of redefining four of the base units of the SI, including the mole. In this paper, the options for implementing a new definition for the mole based on a fixed value for the Avogadro constant are discussed. They are placed in the context of the macroscopic nature of the quantity amount of substance and the opportunity to introduce a system for molar and atomic masses with unchanged values and consistent relative uncertainties.

前報では，物質量とモルを学ぶための生徒用「学習シート」を提案した。本論文では，このシートを用いて授業実践をするために，教師用指導案を研究する。第2節では物質量指導の考え方を考察し，第3節ではモルの導入法を検討し，第4節では相対質量とモル質量を扱う。第5節では，関連する教育資料にみられる諸解釈を取り上げる。最後に「学習シート」の最初の部分（物質量の考え方）を板書する仕方の一例を示す。物質量とモルを物理量として指導するには，物理量の単位独立性や測定原理などを学習ずみであることが不可欠である。, A previous paper (Vol. 22, No. 2, 2003) proposed a new set of students' sheets for learning 'amount of substance' and the mole. This paper deals with an instruction plan for teachers who adopt the set in school practice. The second segment describes a method of teaching 'amount of substance'; how to introduce the mole is shown in the third segment; the topics in the fourth segment are relative atomic mass and molar mass; the fifth segment analyzes some interpretations of the mole appearing in teaching materials; and in the last segment an example of how to write part of the sheets on a blackboard is presented. A class of students who have mastered some principles such as unit-independence and measurement of physical quantities is indispensable for instruction plans that lead to 'amount of substance' and the mole. Bulletin of Joetsu University of Education (ISSN 0915-81621, Vol. 23, No. 1, pp.245-260（2003)

本論文ではまず，物質量とモルを教える方法と発展を概括し，次いで，新しい授業用シートを提案する。ここでの指導法は，現在の化学教科書の伝統とは違っていて，基礎に「物理量は数値と単位との積」と「量バランス法」をすえている。前者は英語圏でいう quantity calculus における原理であり，後者は物理量を選び比較し等号で結ぶ方法である。このシートではまず，要素粒子を説明する。次に，物質量の新しい定義「要素粒子1個の量（amount）はどの要素粒子でも同じ」と「系の物質量はその系を構成する要素粒子の物質量の和に等しい」を採用する。生徒は，各種の化学法則を物質量バランスとして学習しながら，量バランス法によって，ある物質量と特別な物質量であるモルを比較し測定する。その結果は「物理量は数値と単位との積」と表記される。最後に，要素粒子の相対質量とモル質量を導入する。, This paper firstly reviews methods and developments for teaching 'amount of substance' and the mole, and secondly suggests a new set of sheets for student learning. The process of learning the mole in the set violates the tradition of chemistry textbooks in Japan. The background is based on both 'a physical quantity is the product of a numerical value and a unit' and 'amount balance'; the former is the basic principle in quantity calculus, and the latter is a way of balancing between amounts of substances in the chemical world. The set deals with the concept of elementary entity in the first step in the learning process. In the second step, 'amount of substance' is defined as follows: The 'amount of substance' of one elementary entity is the same for every elementary entity, even if they are different in kind from one another; and the 'amount of substance' of a system that contains elementary entities is equal to the summation of the amounts of the elementary entities. A variety of laws in chemistry are described as amount balance in the third step, and then the way of amount balance makes it possible for students to measure a given amount of substance in terms of the mole. The set of sheets in the last step introduces students to the concepts of relative atomic mass and molar mass.

This letter calls for reconsidering the new definition of the mole, which has been proposed in the draft chapter 2 for the SI Brochure, posted on the BIPM website. It is argued that the list of particles should be deleted from the new definition of the mole. The necessary elements of the definition are summarized and another wording is suggested. Proposals to rename ?amount of substance? are briefly discussed.

International audience; The ‘‘amount of substance’’ and its unit the ‘mole’ are concepts that have been a frequent subject of discussion among science education researchers. These concepts present difficulties to students and teachers. The attempt to make two incompatible paradigms, the equivalentist and the atomistic paradigm, converge helped the scientific community to reach agreement on what the word “mole” actually means. However, the consequences of the convergence were that multiple meanings and conceptual contradictions resulting from the historical evolution of the mole have become sedimented in the SI definition of the mole. I’m interested about the way the mole concept is presented in classrooms. I used for this pilot study two videos of two teachers presenting the amount of substance and the mole in their classes. They use the same teaching sequence and they give to students a document with a summary of the knowledge to be learned designed and improved by the SESAME group. In one hand, the analysis of the summary document is based on the semantic mistakes. In the other hand, based on the concept map linking idea were searched in the postlab session. The analysis shows that the summary document uses the correct expression. The analysis of videos shows that the mole concept was defined with emphasis on the mole as a number. Neither the SI definition in terms of 12 grams of 12C nor the connection between molar mass and relative atomic mass was explicitly explained. As suggested by Fang (2011) because of the differences in how the mole concept has been conceptualized between the scientific and the educational domains, through their training, teachers learn to use the mole concept as a ‘tool’. This content analysis formed a part of a project that will investigate the process of teaching and learning the mole concept in secondary classrooms.

自然科学の記号表現，例えば物理量や数値とか法則の等式あるいは計算式には，科学の考え方や理解の仕方が端的に現れる。この論文では，これらの表現を取り上げ，科学演習全般の方略を検討した。第2節ではまず，二つの物理量の商が新しい物理量となる場合，量商とよび，これを科学教育的な視点から議論した。科学教育における問題演習は，科学の理解を深めるために課すものだから，問題の表現と解法は，科学の考え方と方法に基づいて組み立てられることになる。第3節では，物理量の記号処理でまず必要となる「物理量の表記法」「物理量間の演算法」「表とグラフの表現法」の試案をまとめた。「物質量とモル」は，生徒・学生にとって化学学習における陸路である。そこで第4節では「物質量とモル」演習問題を新規に作成しあるいは文献から採録し，学習者の理解を促すための検討を試みた。第5節では，高校教育にみられる典型的な，モル化学計算問題を取り上げた。各種の問題を整理し，問題の本質と形式とを見通せるように，相互に変換される問題群として定めた。本論文で採用する「物理量バランス法」は，日本の現行中等教育での「数の比例計算法」とは全く違っている。等式の物理的な意味をはっきりさせ，物理量間でバランスをとることで，方程式を立てるのである。最後の節で初等数学と「物理量バランス法」の立式法を比較し，両者の連携を論じた。, The essence of thinking and understanding about natural science appears directly in symbolic expressions such as physical quantities, numerical values, equations of laws, and formulations in problem solving. This paper describes the handling of such expressions and the planning of mole calculation in science education. In section 2, the quotient between physical quantities is discussed from the educational point of view. Formulating scientific problems and problem solving should be constructed on the basis of scientific principles, because every exercise in science education is given to students for deeper understanding of natural science. Three proposals are summarized in section 3; a method of expression for physical quantities, a method of calculation for physical quantities, and a method of representation for tables and graphs. Section 4 deals with a collection of many exercises with relation to amount of substance and the mole, and with their solutions. Section 5 shows a group of exercises for mole calculation in high school chemistry, between which the transformation throws light upon the essence as well as the outward form. The method of "balancing of physical quantities" in this paper makes an equation for each exercise after balancing of two physical quantities, called PQE (physical quantity for equating), on both sides of the equation.

モル（と物質量）の教材化の要点は，その次元の導入法にある。まず化学量論にみられる「一対一対応」などの比較の方法を採用し，次にその方法を用いて化学物質に附随していて釣り合わせられる（等置できる）量をさがし，最後にそのようにして同一視できる量を集めて類をつくることで，物質量の次元は構成される。本論文では，この流れに沿って，物理量としての物質量の次元を考察し，その教材化を試みた。この方向は，SIにおけるモルをめぐる誤解を取り除く道にも通じている。化学教育で扱われる各種の法則を物質量間の等式（釣り合い）として記述することで，化学物質の世界から原子・分子の世界が垣間見られる。化学における物質量の役割を上述の視点から論じることで，生徒・学生の質問「化学では，モルがなぜ必要なのか」に答えることができる。最後の節で，モルの次元指導の骨子をまとめた。, The essential point in teaching amount of substance and the mole is how to introduce students to the dimension. One can construct the dimension by first adopting methods of comparison such as one-to-one correspondence in stoichiometry, secondly equating between quantities with relation to chemical substance by means of one of the methods, and lastly collecting such quantities as a class. This paper shows the dimension as a class of amounts of chemical substance as well as a teaching material. Balancing amounts of substances makes it possible for students to appreciate the atomic/molecular world through the substance world. From the above-mentioned point of view the teachers can show students why chemistry needs the mole. The outline of teaching the dimension is summarized in the last section.