- Email: [email protected]
Geometric enclosures: a new notation for chemical symbols
PII:
Computers Chem. Vol. 22, Nos. 2-3, pp. 245±250, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0097-8485/98 $19.00 + 0.00 S0097-8485(97)00039-9
Geometric Enclosures: a New Notation for Chemical Symbols Reuben Rudman* Department of Chemistry, Adelphi University, Garden City, NY 11530, U.S.A. (Received 3 February 1997; Accepted 2 June 1997) AbstractÐThe study of introductory chemistry is, to a large extent, a process of learning a new language along with its alphabet. A detailed examination of a standard introductory chemistry textbook revealed that a ®rst-year chemistry student has to memorize the names and symbols of approximately 200 entities which comprise the alphabet of chemistry (14 SI pre®xes, 35 SI units, 50 chemical elements, 10 operational symbols, 12 physical constants and 80 computational variables). All this is in addition to studying the systematic nomenclature of the chemical compounds and memorizing many mathematical formulas. This formidable task must be accomplished while the student is mastering the fundamental concepts represented by these symbols and learning how to manipulate them in a quantitative fashion. A simple notation system, with basically unlimited potential of expansion and great ease of systematization and recognition, is proposed as follows: Geometric Enclosures, such as w, q, or r, would be used to enclose one- or two-letter symbols and groups of related symbols would utilize the same enclosure geometry. One of the primary advantages of this notational system is the immensely helpful pedagogical feature that allows the immediate identi®cation of the class to which a variable belongs by the noting the shape of its enclosure. The possibility of adapting this notation for introductory courses in other subjects should be explored. # 1998 Elsevier Science Ltd. All rights reserved Key words: chemical notation, computer-aided learning, graphic symbols, introductory chemistry
1. INTRODUCTION
chemists, they are often left with a confused understanding of the fundamental principles of chemistry. Our task as computer-literate chemistry instructors is make use of all the tools at our disposal so as to simplify the learning process for our students. The use of computerized typesetting has increased the number of fonts, symbols and graphics available for use and has simpli®ed their introduction to the printed page. This paper presents a system of computer-generated geometric symbols intended for use in conjunction with the standard letter symbols introduced in introductory chemistry. The purpose of these geometric enclosures is to clarify the meaning of the often confusing nomenclature presented to the students in the introductory courses. These ideas are presented here in the hope that similar systems can be developed in other areas which involve the introduction of many symbols to a student population that is predominantly not going to use it professionally. The study of introductory chemistry is, to a large extent, a process of learning a new language along with its alphabet. Learning the names and sounds of these letters is complicated, in the study of
It is well-known that, as a result of their great exposure to television and computer graphics, today's students are more closely attuned to the visual image than to the written word. Several recent articles have stressed the need for visualization and, even, animation of speci®c concepts taught in various chemistry courses. For example, the use of computer-aided learning in teaching three-dimensional chemistry (Hyde et al., 1996) to pharmacology students and the development of interactive programs for beginning chemistry students (Paelk, 1994) have been described. An even more fundamental need is the use of visualization in teaching the symbols used in the introductory chemistry course. While an ocial IUPAC guide to symbols used in physical chemistry (Mills et al., 1993) does exist, most authors of introductory chemistry textbooks do not follow these guidelines. Furthermore, because relatively few of the students studying introductory chemistry go on to become professional * E-mail address: [email protected]. 245
246
R. Rudman
chemistry, by the student's need to learn the notations for and names of various classes of chemical entities: elements, units, variables, and operational symbols. Whereas the nomenclature and notation conventions for elements, units, and operational symbols have been, by and large, standardized (one noteworthy exception being the recently named synthetic elements), there is less consistency and great confusion when it comes to the notation used for the many variables that appear in the mathematical equations taught in introductory chemistry. The limitations of symbols based on the Roman and Greek alphabets and the concomitant confusion thereby engendered are well known to all students and instructors of chemistry. The lack of a universally accepted symbol for the molecular weight of a compound; the ease with which k, K, and k can be confused; and the use of the same symbol (p) for momentum, partial pressure, proton, negative logarithm and atomic orbital are just a few representative examples of the confusion which confronts our students as they attempt to learn the language of chemistry. A recent suggestion (Savitz, 1995), to expand the available number of symbols by utilizing a third, or even fourth, alphabet, would not alleviate the situation. It would add a limited number of symbols and would require us to make extraordinary eorts to standardize and familiarize ourselves with new symbols and a revamped system of variables. 2. TEXTBOOK SURVEY A detailed examination of the 4th edition of one well-known textbook* revealed that a ®rst-year chemistry student has to memorize the names and symbols of approximately 200 entities which comprise the alphabet of chemistry. This includes at least 14 SI pre®xes, 35 SI units, 50 chemical elements, 10 operational symbols (Table 1), 12 physical constants and 80 computational variables (Table 2). All this is in addition to studying the systematic nomenclature of the chemical compounds and memorizing many mathematical formulas. This formidable task must be accomplished while the student is mastering the fundamental concepts represented by these symbols and learning how to manipulate them in a quantitative fashion. The survey of this textbook also revealed the following: (a) Authors of chemistry textbooks do not always use accepted nomenclature and symbols. For example, see item (c) below. (b) One symbol can represent more than one entity (a result of the limited number of letters available in the Roman and Greek alphabets). Thus, the one- and two-letter symbols used in chemical notation represent many dierent entities: chemical species (e.g. C = carbon), units (e.g. C = coulombs), physical constants * The speci®c text has not been identi®ed inasmuch as it is representative of this genre of textbook and it is not the intent of this paper to criticize a particular author.
Table 1. List of operational symbols used in introductory chemistry Symbol
Meaning
= 4 _ t []
Equals Reacts to form Reversible reaction Resonance Moles per liter Phase boundaries Degrees or Standard state of X (No. protons ± No. electrons) in chemical species X Identi®er of X Dierence between two values of X
k
X8 X2n Xn DX
Table 2. Symbols (excluding elements and units) used in representative introductory college chemistry textbook Symbol
Name
A A a a b C C c Cm d d d d E E e e eÿ E.A. Ek Ep eq F F F f f f FW G g H h h i I.E. K k k k k Kb Kc Kf l l M m m m Mm MW N N n n n n NA
Arrhenius frequency factor mass number acceleration van der Waals constant van der Waals constant Celsius heat capacity speed of light molality atomic orbital density distance interplanar spacing emf energy electronic charge natural logarithm base electron electron anity kinetic energy potential energy equivalents Fahrenheit Faraday constant force atomic orbital fraction of collisions frequency formula weight free energy gravitational acceleration enthalpy height Planck's constant number of ions formed ionization energy Kelvin Boltzmann's constant constant, radioactive decay general constant rate constant constant, ebullioscopic equilibrium constant constant, cryoscopic length wavelength molarity mass molality slope of line molecular weight molecular weight normality number of radioactive nuclei integer mole neutron number of transferred electrons Avogadro number
Geometric enclosures Table 2ÐContinued Symbol
Name
n P p p p p Pi p P p q Qc RH S S s s s s T t t t1/2 U U u V V v W w w x Xi y Z Z z
frequency pressure atomic orbital fraction of collisions negative logarithm proton partial pressure constant (3.14...) osmotic pressure pi bond heat reaction quotient Rydberg constant entropy solubility atomic orbital second speci®c heat sigma temperature temperature time half-life internal energy lattice energy average speed voltage volume velocity number of possible arrangements width work coordinate mole fraction coordinate atomic number collision frequency coordinate
247
Bond order 1=2 nb ÿ na , where n now represents the number of electrons in the bonding and anti-bonding orbitals, respectively. Is this the format for an equation or for a de®nition? (f ) In an attempt to distinguish between a twoletter symbol and the product of two one-letter symbols, the distracting use of periods is introduced. I.e., I.E. (ionization energy) and E.A. (electron anity) are used; note that E has a dierent meaning in each term even though they are introduced at the same time. It is obvious that in our introductory texts, of which the one analyzed is but a representative example, there is the potential for immense confusion as the students attempt to master the elementary language of this discipline. It is true that once the students have grasped the idea that many of these symbols represent dierent classes of chemical entities, they acquire the ability to distinguish between chemical species and physical units from the context in which they appear. However, since there are so many other symbols, there inevitably is confusion when physical constants and equation variables are encountered. Assuming that inconsistencies within the text are eliminated, there is still a large number of terms (Table 2) which employ the same symbol*. It is also clear from this analysis that the author(s) limit their use of Greek letters, probably due to the fact that they are of the opinion that modern students are not receptive to the presentation of too many letters from non-Roman alphabets. Thus, the suggestion referred to above, that the problem of the shortage of symbols could be alleviated by the introduction of letters from other alphabets (Cyrillic, Hebrew, Gothic, Japanese, Korean and Arabic were mentioned), does not seem practical. Even if it were possible to introduce this idea for use by professionals in the ®eld, it appears quite hopeless to expect introductory students to be able to master so many dierent symbols. Alternatively, we might suggest increasing the number of usable symbols by restricting ourselves to the Roman alphabet and using a consistent set of upper case and lower case letters each as a plain, boldface or italic character. Unfortunately, the distinctions between these dierent forms would be dicult for the student to remember and would become blurred in the instructor's presentation and probably obliterated in the students' notes.
(e.g. c = speed of light); and variables used in quantitative calculations (e.g. C = heat capacity or Celsius degrees). (c) One entity can be represented by more than one symbol. For example, in this text, both MW and Mm are used to represent molecular weight, u and v describe velocity and/or speed, and kf and k1 (as well as kr and kÿ1) stand for the rate constants of the forward (and reverse) reactions. (d) For a given variable, one symbol represents its numerical value while another symbol represents its unit. For example, Q, the number of coulombs, uses C as the coulomb unit; n represents the number of moles for which mol is the unit name; and P, pressure, has units of Pa or atm. (e) n many instances in this text, the authors utilize a 0non-equation equation0. That is, in order not to have to introduce a new symbol (either because it is too early in the book, or because the standard symbol con¯icts with one already used in another context, or because there is no convenient symbol to use), they use a format of the type 0word = symbols0. For example, we ®nd the following:
A much simpler system, with basically unlimited potential of expansion and great ease of systematization and recognition, is proposed as follows:
* Symbols for elements and units have not been included in this discussion.
Geometric Enclosures: Geometric ®gures, such as w, q, or r, would be used to enclose one- or two-letter symbols.
3. NEW NOTATION
248
R. Rudman
Classi®cation: groups of related symbols would utilize the same enclosure geometry. The advantages of this notational system are obvious: (1) It would be possible to immediately identify the class to which a variable belongs by the shape of its enclosure. This is an immensely helpful pedagogical feature. (2) Most of the symbols that are currently in use could be retained. (3) Con¯icting de®nitions of symbols would be eliminated. Assuming that there are now about 75 easily recognized symbols available (upper case and lower case Roman and Greek letters), the use of only six additional symbols (for example, circular, square, rectangular, triangular, pentagonal, and hexagonal enclosure geometries) would allow for the exact speci®cation of more than 500 unique symbols. (4) Additional enclosure geometries could be added as needed. 4. CLASSES OF SYMBOLS The following is a proposed classi®cation of variables and suggested geometric enclosures. They are listed in detail in Table 3. The selection of enclosure shape is arbitrary. However, an attempt has been to use the more easily drawn symbols for those classes of variables that are most Table 3. Symbols with geometric enclosures representing classes of variables (a) General variables A area a acceleration C Celsius d distance F Fahrenheit f frequency h height K Kelvin k general constant l length l wavelength m slope of line n integer n frequency t time u average speed V volt v velocity w width x coordinate y coordinate z coordinate (b) Constants c eÿ e F g h k N p p R RH
speed of light electronic charge natural logarithm base Faraday constant gravitational acceleration Planck's constant Boltzmann's constant Avogadro number negative logarithm constant (3.14...) universal gas law constant Rydberg constant
Table 3ÐContinued (c) Physical Properties mass number van der Waals constant van der Waals constant density interplanar spacing electron anity force formula weight ionization energy constant, radioactive decay molecular weight mass number of radioactive nuclei mole pressure partial pressure osmotic pressure temperature temperature half-life volume atomic number
Geometric enclosures Table 3ÐContinued energy kinetic energy potential energy free energy
249
term, temperature (T), is listed under physical properties. (b) Constants: Physical and mathematical constants are printed in bold characters. (c) Physical properties: Variables describing properties that are speci®c to a given substance or to a particular sample of that substance are enclosed in squares (q). Thus, the symbol for molecular weight is the unique symbol
enthalpy number of ions formed constant, ebullioscopic
(d) Solutions and concentrations: The geometric enclosure is a circle
equilibrium constant constant, cryoscopic number of transferred electrons
(e) Thermodynamic parameters: Both thermodynamic terms and equilibrium variables are enclosed in pentagons,
heat reaction quotient entropy speci®c heat
(f ) Kinetics and electrochemistry: These variables use triangles,
internal energy lattice energy
as their geometric enclosure.
number of possible arrangements work (f) Kinetics and electrochemistry Arrhenius frequency factor emf fraction of collisions rate constant fraction of collisions collision frequency
commonly encountered in a ®rst-year chemistry course. (a) General variables: Symbols for terms in general use, not speci®cally for chemistry, are written in plain text. Included in this category are the symbols for the temperature scales (C,K, and F). Although they are really units, these terms are used in scale-conversion equations and are often treated as variables. The more general
5. EXAMPLES As a result of using geometric enclosures, symand are immediately identi®able bols such as as representing dierent entities: a physical property and a solution or concentration variable. Similarly, reference to Table 3 will identify the following k, k, and and N, unique terms: C and and Some well-known equations would then appear as: (see page 250) 6. CONCLUDING REMARKS As previously mentioned, learning introductory chemistry has many similarities with learning how to read. A ®rst-grader who can barely make out the simplest words requires much practice before attaining the ability to appreciate good literature. In chemistry also, one must be able to 0read chemistry0 before being able to appreciate 0good chemistry0. It is not surprising that the complicated ABCs of chemistry act as a barrier to beginning students who would like to progress beyond the 0McGuey Reader0 level and attain the 0Shakespeare0 level of chemistry, wherein they could appreciate the beauty and power of modern chemistry. The use of geometric enclosures would reduce confusion, minimize the introduction of new sym-
250
R. Rudman
bols, lend itself to computerized printing, and greatly improve symbol recognition. It would also allow for ease of standardizing the notation used in dierent textbooks. As a ®nal remark, it is strongly suggested that authors of introductory chemistry textbooks present a table of all the symbols and notations used in that text with a clear description as to what each represents. The time it would take to prepare this table is negligible compared to the time it takes to write the text. It would help the students immensely to have such a table for reference (for example, on the inside of the back cover) and it would enable the
authors to identify and eliminate any redundancies or con¯icts in their use of symbols and notations. REFERENCES Hyde, R. T., Shaw, P. N. and Jackson, D. E. (1996) Computers Educ. 26, 233±239. Mills, I., Cvitas, T., Homann, K., Kallay, N. and Kuchitsu, K. (1993) Quantities, Units and Symbols in Physical Chemistry, 2nd edn. Blackwell Scienti®c Publications. Paelk, R. A. (1994) J. Chem. Educ. 71, 225. Savitz, S. (1995) Chem. Eng. News 74(Nov. 15), 4.
Computers Chem. Vol. 22, Nos. 2-3, pp. 245±250, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0097-8485/98 $19.00 + 0.00 S0097-8485(97)00039-9
Geometric Enclosures: a New Notation for Chemical Symbols Reuben Rudman* Department of Chemistry, Adelphi University, Garden City, NY 11530, U.S.A. (Received 3 February 1997; Accepted 2 June 1997) AbstractÐThe study of introductory chemistry is, to a large extent, a process of learning a new language along with its alphabet. A detailed examination of a standard introductory chemistry textbook revealed that a ®rst-year chemistry student has to memorize the names and symbols of approximately 200 entities which comprise the alphabet of chemistry (14 SI pre®xes, 35 SI units, 50 chemical elements, 10 operational symbols, 12 physical constants and 80 computational variables). All this is in addition to studying the systematic nomenclature of the chemical compounds and memorizing many mathematical formulas. This formidable task must be accomplished while the student is mastering the fundamental concepts represented by these symbols and learning how to manipulate them in a quantitative fashion. A simple notation system, with basically unlimited potential of expansion and great ease of systematization and recognition, is proposed as follows: Geometric Enclosures, such as w, q, or r, would be used to enclose one- or two-letter symbols and groups of related symbols would utilize the same enclosure geometry. One of the primary advantages of this notational system is the immensely helpful pedagogical feature that allows the immediate identi®cation of the class to which a variable belongs by the noting the shape of its enclosure. The possibility of adapting this notation for introductory courses in other subjects should be explored. # 1998 Elsevier Science Ltd. All rights reserved Key words: chemical notation, computer-aided learning, graphic symbols, introductory chemistry
1. INTRODUCTION
chemists, they are often left with a confused understanding of the fundamental principles of chemistry. Our task as computer-literate chemistry instructors is make use of all the tools at our disposal so as to simplify the learning process for our students. The use of computerized typesetting has increased the number of fonts, symbols and graphics available for use and has simpli®ed their introduction to the printed page. This paper presents a system of computer-generated geometric symbols intended for use in conjunction with the standard letter symbols introduced in introductory chemistry. The purpose of these geometric enclosures is to clarify the meaning of the often confusing nomenclature presented to the students in the introductory courses. These ideas are presented here in the hope that similar systems can be developed in other areas which involve the introduction of many symbols to a student population that is predominantly not going to use it professionally. The study of introductory chemistry is, to a large extent, a process of learning a new language along with its alphabet. Learning the names and sounds of these letters is complicated, in the study of
It is well-known that, as a result of their great exposure to television and computer graphics, today's students are more closely attuned to the visual image than to the written word. Several recent articles have stressed the need for visualization and, even, animation of speci®c concepts taught in various chemistry courses. For example, the use of computer-aided learning in teaching three-dimensional chemistry (Hyde et al., 1996) to pharmacology students and the development of interactive programs for beginning chemistry students (Paelk, 1994) have been described. An even more fundamental need is the use of visualization in teaching the symbols used in the introductory chemistry course. While an ocial IUPAC guide to symbols used in physical chemistry (Mills et al., 1993) does exist, most authors of introductory chemistry textbooks do not follow these guidelines. Furthermore, because relatively few of the students studying introductory chemistry go on to become professional * E-mail address: [email protected]. 245
246
R. Rudman
chemistry, by the student's need to learn the notations for and names of various classes of chemical entities: elements, units, variables, and operational symbols. Whereas the nomenclature and notation conventions for elements, units, and operational symbols have been, by and large, standardized (one noteworthy exception being the recently named synthetic elements), there is less consistency and great confusion when it comes to the notation used for the many variables that appear in the mathematical equations taught in introductory chemistry. The limitations of symbols based on the Roman and Greek alphabets and the concomitant confusion thereby engendered are well known to all students and instructors of chemistry. The lack of a universally accepted symbol for the molecular weight of a compound; the ease with which k, K, and k can be confused; and the use of the same symbol (p) for momentum, partial pressure, proton, negative logarithm and atomic orbital are just a few representative examples of the confusion which confronts our students as they attempt to learn the language of chemistry. A recent suggestion (Savitz, 1995), to expand the available number of symbols by utilizing a third, or even fourth, alphabet, would not alleviate the situation. It would add a limited number of symbols and would require us to make extraordinary eorts to standardize and familiarize ourselves with new symbols and a revamped system of variables. 2. TEXTBOOK SURVEY A detailed examination of the 4th edition of one well-known textbook* revealed that a ®rst-year chemistry student has to memorize the names and symbols of approximately 200 entities which comprise the alphabet of chemistry. This includes at least 14 SI pre®xes, 35 SI units, 50 chemical elements, 10 operational symbols (Table 1), 12 physical constants and 80 computational variables (Table 2). All this is in addition to studying the systematic nomenclature of the chemical compounds and memorizing many mathematical formulas. This formidable task must be accomplished while the student is mastering the fundamental concepts represented by these symbols and learning how to manipulate them in a quantitative fashion. The survey of this textbook also revealed the following: (a) Authors of chemistry textbooks do not always use accepted nomenclature and symbols. For example, see item (c) below. (b) One symbol can represent more than one entity (a result of the limited number of letters available in the Roman and Greek alphabets). Thus, the one- and two-letter symbols used in chemical notation represent many dierent entities: chemical species (e.g. C = carbon), units (e.g. C = coulombs), physical constants * The speci®c text has not been identi®ed inasmuch as it is representative of this genre of textbook and it is not the intent of this paper to criticize a particular author.
Table 1. List of operational symbols used in introductory chemistry Symbol
Meaning
= 4 _ t []
Equals Reacts to form Reversible reaction Resonance Moles per liter Phase boundaries Degrees or Standard state of X (No. protons ± No. electrons) in chemical species X Identi®er of X Dierence between two values of X
k
X8 X2n Xn DX
Table 2. Symbols (excluding elements and units) used in representative introductory college chemistry textbook Symbol
Name
A A a a b C C c Cm d d d d E E e e eÿ E.A. Ek Ep eq F F F f f f FW G g H h h i I.E. K k k k k Kb Kc Kf l l M m m m Mm MW N N n n n n NA
Arrhenius frequency factor mass number acceleration van der Waals constant van der Waals constant Celsius heat capacity speed of light molality atomic orbital density distance interplanar spacing emf energy electronic charge natural logarithm base electron electron anity kinetic energy potential energy equivalents Fahrenheit Faraday constant force atomic orbital fraction of collisions frequency formula weight free energy gravitational acceleration enthalpy height Planck's constant number of ions formed ionization energy Kelvin Boltzmann's constant constant, radioactive decay general constant rate constant constant, ebullioscopic equilibrium constant constant, cryoscopic length wavelength molarity mass molality slope of line molecular weight molecular weight normality number of radioactive nuclei integer mole neutron number of transferred electrons Avogadro number
Geometric enclosures Table 2ÐContinued Symbol
Name
n P p p p p Pi p P p q Qc RH S S s s s s T t t t1/2 U U u V V v W w w x Xi y Z Z z
frequency pressure atomic orbital fraction of collisions negative logarithm proton partial pressure constant (3.14...) osmotic pressure pi bond heat reaction quotient Rydberg constant entropy solubility atomic orbital second speci®c heat sigma temperature temperature time half-life internal energy lattice energy average speed voltage volume velocity number of possible arrangements width work coordinate mole fraction coordinate atomic number collision frequency coordinate
247
Bond order 1=2 nb ÿ na , where n now represents the number of electrons in the bonding and anti-bonding orbitals, respectively. Is this the format for an equation or for a de®nition? (f ) In an attempt to distinguish between a twoletter symbol and the product of two one-letter symbols, the distracting use of periods is introduced. I.e., I.E. (ionization energy) and E.A. (electron anity) are used; note that E has a dierent meaning in each term even though they are introduced at the same time. It is obvious that in our introductory texts, of which the one analyzed is but a representative example, there is the potential for immense confusion as the students attempt to master the elementary language of this discipline. It is true that once the students have grasped the idea that many of these symbols represent dierent classes of chemical entities, they acquire the ability to distinguish between chemical species and physical units from the context in which they appear. However, since there are so many other symbols, there inevitably is confusion when physical constants and equation variables are encountered. Assuming that inconsistencies within the text are eliminated, there is still a large number of terms (Table 2) which employ the same symbol*. It is also clear from this analysis that the author(s) limit their use of Greek letters, probably due to the fact that they are of the opinion that modern students are not receptive to the presentation of too many letters from non-Roman alphabets. Thus, the suggestion referred to above, that the problem of the shortage of symbols could be alleviated by the introduction of letters from other alphabets (Cyrillic, Hebrew, Gothic, Japanese, Korean and Arabic were mentioned), does not seem practical. Even if it were possible to introduce this idea for use by professionals in the ®eld, it appears quite hopeless to expect introductory students to be able to master so many dierent symbols. Alternatively, we might suggest increasing the number of usable symbols by restricting ourselves to the Roman alphabet and using a consistent set of upper case and lower case letters each as a plain, boldface or italic character. Unfortunately, the distinctions between these dierent forms would be dicult for the student to remember and would become blurred in the instructor's presentation and probably obliterated in the students' notes.
(e.g. c = speed of light); and variables used in quantitative calculations (e.g. C = heat capacity or Celsius degrees). (c) One entity can be represented by more than one symbol. For example, in this text, both MW and Mm are used to represent molecular weight, u and v describe velocity and/or speed, and kf and k1 (as well as kr and kÿ1) stand for the rate constants of the forward (and reverse) reactions. (d) For a given variable, one symbol represents its numerical value while another symbol represents its unit. For example, Q, the number of coulombs, uses C as the coulomb unit; n represents the number of moles for which mol is the unit name; and P, pressure, has units of Pa or atm. (e) n many instances in this text, the authors utilize a 0non-equation equation0. That is, in order not to have to introduce a new symbol (either because it is too early in the book, or because the standard symbol con¯icts with one already used in another context, or because there is no convenient symbol to use), they use a format of the type 0word = symbols0. For example, we ®nd the following:
A much simpler system, with basically unlimited potential of expansion and great ease of systematization and recognition, is proposed as follows:
* Symbols for elements and units have not been included in this discussion.
Geometric Enclosures: Geometric ®gures, such as w, q, or r, would be used to enclose one- or two-letter symbols.
3. NEW NOTATION
248
R. Rudman
Classi®cation: groups of related symbols would utilize the same enclosure geometry. The advantages of this notational system are obvious: (1) It would be possible to immediately identify the class to which a variable belongs by the shape of its enclosure. This is an immensely helpful pedagogical feature. (2) Most of the symbols that are currently in use could be retained. (3) Con¯icting de®nitions of symbols would be eliminated. Assuming that there are now about 75 easily recognized symbols available (upper case and lower case Roman and Greek letters), the use of only six additional symbols (for example, circular, square, rectangular, triangular, pentagonal, and hexagonal enclosure geometries) would allow for the exact speci®cation of more than 500 unique symbols. (4) Additional enclosure geometries could be added as needed. 4. CLASSES OF SYMBOLS The following is a proposed classi®cation of variables and suggested geometric enclosures. They are listed in detail in Table 3. The selection of enclosure shape is arbitrary. However, an attempt has been to use the more easily drawn symbols for those classes of variables that are most Table 3. Symbols with geometric enclosures representing classes of variables (a) General variables A area a acceleration C Celsius d distance F Fahrenheit f frequency h height K Kelvin k general constant l length l wavelength m slope of line n integer n frequency t time u average speed V volt v velocity w width x coordinate y coordinate z coordinate (b) Constants c eÿ e F g h k N p p R RH
speed of light electronic charge natural logarithm base Faraday constant gravitational acceleration Planck's constant Boltzmann's constant Avogadro number negative logarithm constant (3.14...) universal gas law constant Rydberg constant
Table 3ÐContinued (c) Physical Properties mass number van der Waals constant van der Waals constant density interplanar spacing electron anity force formula weight ionization energy constant, radioactive decay molecular weight mass number of radioactive nuclei mole pressure partial pressure osmotic pressure temperature temperature half-life volume atomic number
Geometric enclosures Table 3ÐContinued energy kinetic energy potential energy free energy
249
term, temperature (T), is listed under physical properties. (b) Constants: Physical and mathematical constants are printed in bold characters. (c) Physical properties: Variables describing properties that are speci®c to a given substance or to a particular sample of that substance are enclosed in squares (q). Thus, the symbol for molecular weight is the unique symbol
enthalpy number of ions formed constant, ebullioscopic
(d) Solutions and concentrations: The geometric enclosure is a circle
equilibrium constant constant, cryoscopic number of transferred electrons
(e) Thermodynamic parameters: Both thermodynamic terms and equilibrium variables are enclosed in pentagons,
heat reaction quotient entropy speci®c heat
(f ) Kinetics and electrochemistry: These variables use triangles,
internal energy lattice energy
as their geometric enclosure.
number of possible arrangements work (f) Kinetics and electrochemistry Arrhenius frequency factor emf fraction of collisions rate constant fraction of collisions collision frequency
commonly encountered in a ®rst-year chemistry course. (a) General variables: Symbols for terms in general use, not speci®cally for chemistry, are written in plain text. Included in this category are the symbols for the temperature scales (C,K, and F). Although they are really units, these terms are used in scale-conversion equations and are often treated as variables. The more general
5. EXAMPLES As a result of using geometric enclosures, symand are immediately identi®able bols such as as representing dierent entities: a physical property and a solution or concentration variable. Similarly, reference to Table 3 will identify the following k, k, and and N, unique terms: C and and Some well-known equations would then appear as: (see page 250) 6. CONCLUDING REMARKS As previously mentioned, learning introductory chemistry has many similarities with learning how to read. A ®rst-grader who can barely make out the simplest words requires much practice before attaining the ability to appreciate good literature. In chemistry also, one must be able to 0read chemistry0 before being able to appreciate 0good chemistry0. It is not surprising that the complicated ABCs of chemistry act as a barrier to beginning students who would like to progress beyond the 0McGuey Reader0 level and attain the 0Shakespeare0 level of chemistry, wherein they could appreciate the beauty and power of modern chemistry. The use of geometric enclosures would reduce confusion, minimize the introduction of new sym-
250
R. Rudman
bols, lend itself to computerized printing, and greatly improve symbol recognition. It would also allow for ease of standardizing the notation used in dierent textbooks. As a ®nal remark, it is strongly suggested that authors of introductory chemistry textbooks present a table of all the symbols and notations used in that text with a clear description as to what each represents. The time it would take to prepare this table is negligible compared to the time it takes to write the text. It would help the students immensely to have such a table for reference (for example, on the inside of the back cover) and it would enable the
authors to identify and eliminate any redundancies or con¯icts in their use of symbols and notations. REFERENCES Hyde, R. T., Shaw, P. N. and Jackson, D. E. (1996) Computers Educ. 26, 233±239. Mills, I., Cvitas, T., Homann, K., Kallay, N. and Kuchitsu, K. (1993) Quantities, Units and Symbols in Physical Chemistry, 2nd edn. Blackwell Scienti®c Publications. Paelk, R. A. (1994) J. Chem. Educ. 71, 225. Savitz, S. (1995) Chem. Eng. News 74(Nov. 15), 4.