Equations in chemical education, Part 1: the historical evolution of conventions
John Oversby, Institute of Education, The University of Reading, Reading, RG6 1HY, UK email: J.P.Oversby@reading.ac.uk
Introduction
A major challenge for learners in chemistry is to deal with explanations at the macroscopic, sub-microscopic and symbolic levels (Gabel, Briner and Haines, 1992; Johnstone, 1991). The links between these representations are simply described in the diagram below but appear to be complex and demanding for novice chemists and tacit for experts.
Representations in chemistry macroscopic sub-microscopic symbolic
In this article, the focus is on symbolic representation and its relationship to the other two forms of representation. Chemical equations contain a peculiar syntax that links both the nature of the entities that are reacting and features about those reactions. Word equations are more closely associated with macroscopic phenomena while symbolic equations represent both macroscopic and sub-microscopic features.
A distinguishing feature of chemistry as a scientific discipline is its use of symbols and signs as a means of communication about chemical reactions. Although , at first sight, there seems to be much in common with algebraic use of symbols and signs, there are important differences when used in chemical contexts. An understanding of how the present use came about may shed light on some of the problems that learners in schools may have with chemical equations.
Equations 1 1

This article aims to explore the relationship between symbolic explanation and the phenomena that require explanation. As a major source of evidence, it refers to textbooks use of chemical symbols and equations. The research questions were:
1.
What chemical equations appear in textbooks of chemistry especially at school level?
2.
How can chemical equations be classified to make sense of the way they represent chemical phenomena?
3.
What are the links between word and symbolic chemical equations?
4.
What changes in chemical equations have taken place over the last 150 years and what has contributed to these changes?
5.
What can a study of chemical symbolism contribute to thinking about learning chemistry?
Methodology
The main source of data about chemical equations is a set of textbooks of chemistry covering the period of investigation. For early textbooks it is not always clear about the targeted reader and assumptions have been made from the content. The set of textbooks is opportunistic rather than a random sample, although it is fairly wide ranging. Those textbooks in the readily accessible archives of The Royal Society of chemistry, UK, were consulted as part of the search. This was supplemented by books in possession of the author. However, there is no reason to suppose that the sample is biased in any particular way.
Chemical syntax and symbol chemical equations
Chemical symbol equations are representations of chemical phenomena. They are bounded by rules of construction in a syntax that is rarely explicitly specified and perhaps even less well understood. They are frequently described as ‘shorthand’ without due consideration for the power of their mode of representation. Chemical formulae and chemical symbol equations do not give direct information about specific quantities but only about ratios. They do not give specific information about the extent of reaction or the position of equilibrium. They do not give information about alternative reactions. Consider the symbol equation for burning methane in oxygen:
CH
4
+ 2O
2

CO
2
+ 2H
2
O
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This symbol equation does not indicate that carbon monoxide, CO, is also a possible product if there is insufficient oxygen. This information may be useful to those people who have natural gas burners in the home. The symbol equation also leaves out the possibility of soot, carbon, production.
An exploration of the value of all chemical equations in relation to chemical phenomena and the limitations of the extent of the representation process is a worthwhile research exercise. There are rules that govern construction and interpretation of symbol equations. Some of these are explicit in textbooks but many are not. Clarification may prove helpful in the learning process.
Let us suppose the reaction between zinc metal and aqueous copper sulphate solution. The following description may be made of the reaction in a particular case:
Silvery grey solid zinc is mixed with blue solution of copper sulphate. If sufficient zinc is used the solution becomes colourless and a redbrown solid can be seen. If the masses of the cleaned and dried solids are measured, then they will always be in the ratio of 65:63.5. The solutions before and afterwards conduct electricity with ease.
How may this reaction to form at least one new substance be represented as an equation? There are many possibilities, all of which have their special syntax. The different representations have some aspects in common. Descriptions of these representations and their features follows.
Word equation representation
This can only be constructed when much detail is known about the materials. For the purpose of this discussion, I suppose that the identity of each chemical involved is well established. zinc + copper sulphate

zinc sulphate + copper zinc crystals + copper sulphate aqueous solution

zinc sulphate aqueous solution + copper crystals zinc(c) + copper sulphate(aq)

zinc sulphate(aq) + copper(c)
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What do they all have in common? They all use an arrow,

, that denotes a process where one or more chemicals change to other chemicals. At the macroscopic level, the chemicals possess definite composition and this feature can be represented by the symbols and subscripts in a symbol equation. The symbols constituting the formulae have fixed mass ratios of components. In the word equation, giving a definite label as in copper sulphate is indicating that we have a new and known chemical. There are rules governing the construction of word equations. In a chemical word equation, it would be abnormal to include terms like wood, or food, since these are variable materials. Chemical word equations normally contain only those chemicals whose compositions are or can be reasonably well known. Each word refers to a single, pure, chemical. Of course, this is an ideal situation and only approximates to reality. That is the way that chemistry works. The two + signs have different meanings. The first word equation may be written in a form of English as:” zinc reacts with copper sulphate to give zinc sulphate and copper”. The first + sign means ‘reacts with’ and not ‘plus’, which would be an algebraic meaning. The second + sign means ‘and also’, implying that the chemicals are not combined. Again, use of ‘plus’ would be inappropriate. The 
arrow is another indication that these are chemical equations, not algebraic equations, where an = sign would be expected. The equations have an implied direction, from left to right. In algebra, 2+3 = 4+1 can be read either way. It implies complete equality in both directions. The = sign is an operator in algebra, meaning to sum the two values. This is clearly not the same as the chemical meaning.
A problem of giving meaning to word equations is highlighted by the following two examples: hydrogen + oxygen

water hydrogen + oxygen

dihydrogen monoxide
In the first case the chemical constitution of water is not obvious. Unless it is known that it contains only hydrogen and oxygen, then it would be impossible to surmise how to construct a symbol equation from the word equation. The second equation is more explicit but could be regarded as too complex for the novice. Yet this one gives more of the required information to build a symbol equation, if that is what is needed.
A second problem of giving meaning to word equations is exemplified by this example: carbon + oxygen

carbon oxide
Which oxide of carbon is intended, carbon monoxide or carbon dioxide? Of course, the equation could be modified to make it clear by writing carbon dioxide but what about the next example?
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iron + copper sulphate

iron sulphate + copper.
Is it iron(II) sulphate or iron(III) sulphate that is formed? Again, the word equation can only make sense when a lot more chemistry is understood.
General word equation zinc + copper salt

zinc salt + copper
This generalises the reaction to all copper and zinc salts, focussing attention on the two metallic components. It can also be seen as predictive, that when zinc is added to any copper salt, a displacement reaction will occur. The rest of the syntax is as discussed earlier.
Concept equation reactive metal + less reactive metal salt

reactive metal salt + less reactive metal
This form is constructed from the concept of reactivity and produces a new concept of displacement reaction. Concept equations are highly generalised and therefore potentially powerful in predictive capacity.
Symbol equation
Zn + CuSO
4

ZnSO
4
+ Cu
In this form, very specific knowledge is provided that includes sub-microscopic component ratios, and macroscopic ratios. In copper sulphate, the component ratio of Cu:S:O is 1:1:4. At the macroscopic level, the mole ratios are 1:1:4 also and this implies mass ratios of 63.5:32:64. Thus the symbol equation has both a sub-microscopic and a macroscopic characteristic. In this particular case, the symbol equation as written is also balanced, that is, the coefficients are 1:1 on both sides.
Symbol equation with states
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Zn(s) + CuSO
4
(aq)

ZnSO
4
(aq) + Cu(s)
I have chosen to use the s state symbol, rather than c for crystalline, to be more general. The state symbols represent macroscopic observations and characteristics of the chemicals in the laboratory. There is a correspondence only between some aspects of the characteristics of the chemicals and the state symbols. For example, the colours of the metals and solutions are not represented in this equation.
Ionic equation
Zn(s) + Cu 2+ (aq)

Zn 2+ (aq) + Cu(s)
In the ionic equation for this reaction, the sulphate ions are left out. This implies that the sulphate ion is irrelevant to the reaction taking place, that it should take place if copper chloride, copper nitrate or copper ethanoate were used. In this way, construction of an ionic equation can provide ideas for further experiments to be carried out. The equation is serving a predictive purpose as well as a representative function. This purpose is not readily identified in typical learning contexts, nor in the textbooks surveyed. The ionic equation may also make it easier to see that a redox reaction, in terms of electrons
Half equations
Zn(s)

Zn
2+
(aq)
Cu
2+
(aq)

Cu(s)
An advantage of half equations is that it focuses on each metal separately, In this sense it is related to the macroscopic electrode reduction potential for each metal. This gives an opportunity for a quantitative approach to the change, in terms of thermodynamics.
Summary of symbols in equations
The ideas indicated in these examples have set the scene for an examination of the syntax of symbols and equations as ways of representing macroscopic chemical phenomena.
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A typology of chemical equations
The table gives the types of equations as they appear in the textbooks analysed.
Equation type
1.
Word equation
Examples a) hydrogen + oxygen

water b) copper oxide + hydrogen

copper + water c) carbon (s) + oxygen (g)

carbon dioxide(g)
2.
General word equation
3.
Concept word equation
4.
Word equation with input conditions d) metal oxide + hydrogen

metal + water e) sodium + halogen

sodium halide f) acid + base

salt + water g) hydrocarbon fuel + oxygen

carbon dioxide + water h) heat carbon + lead oxide

lead + carbon dioxide i) yeast sugar

ethanol + carbon dioxide j) light and chlorophyll carbon dioxide + water

glucose + oxygen
5.
Word equations with k) sugar + oxygen

carbon dioxide + water + energy
Range of uses
Summarises expert knowledge about a chemical reaction.
Focuses on the macroscopic nature of the substances rather than the representation at any other level.
These equations remain specific but are part of the process of generalising a set of reactions.
This is a step further in generalising compared with 2.It links concepts and representations.
These equations focus on the conditions necessary for
‘encouraging’ reactions.
It is said to be a suitable starting point for building symbol equations but this is in some doubt. There seems to be no evidence for this particular assertion
The learner needs to be aware of similarities between class members.
Comments
This builds on understanding of the included concepts. It is therefore dependant on an appreciation of these concepts
These equations include nonchemicals in the equation.
There is a danger that the conditions may be seen as chemicals involved in the reaction. Biological examples can cause this particular problem, particularly if the teacher is not aware of this danger. It is recommended that the inputs be included as a separate statement on a new line to make the point that they are not reacting substances.
These equations focus on the the These equations include non-
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6.
7.
non-chemical outputs
Symbol equation
Balanced symbol equation
8.
Balanced symbol equation with state symbols l) magnesium + oxygen

magnesium oxide + light m) Mg + O
2

MgO n) Na + H
2
O

NaOH +H o) CH q)
4
+ 2 O
2

Fe(s) + CuSO
4
CO
(aq) r) C(diamond) + O
2
2
2
+ 2 H p) 2 Al + 6HCl

2AlCl

3
2
O
+ 3H
2
Cu + FeSO
(g)

CO
2
(g)
4
(aq) significance of the outputs. This is almost always the production of energy at school level.
The emphasis here is on those aspects that can be modelled by symbols i.e. the identities of reacting components, which materials are reactants and which are products. They do not refer to qualities such as smells, colour, states or actual masses.
Compared with 6, the inclusion of ratios (of components and reacting masses) is the major addition here. chemicals in the same place as chemicals. There is a danger that the conditions may be seen as chemicals involved in the reaction. Biological examples can cause this particular problem, particularly if the teacher is not aware of this danger. It is recommended that the outputs be included as a separate statement on a new line to make the point that they are not produced substances.
These are rarely used since there is a sort of Pavlovian instinct to balance the equation.
The inclusion of state symbols simply provides more information.
There is a very strong tendency to alter formulae to balance the reaction. This may indicate that the learner s not conscious of the Law of
Constant Composition for compounds.
Most learners seem to understand the symbols, s, l, g and aq. Specific symbols such as diamond, or c for crystalline are not so well known.
Equations 1 8

9.
Symbol reversible equation
10.
Symbol equilibrium equation
11.
12.
13.
General symbol equation
Ionic equation
Half equation s) NH
3
(g) + HCl(g) t) CaCO
3


NH
CaO + CO
2
4
Cl(s) u) N
2
+ 3H
2

2NH
3 v) Cl
2
(aq) + H
2
O(l)

HCl(a) + HOCl(aq) w) 2 M + O x) RCl + H
2
2

2MO
O

ROH + HCl y) Ca 2+( aq) + CO
3
2(aq)

CaCO
3
(s) z) Mg(s) + 2H
3
O + (aq)

Mg 2+ (aq) + H
2
(g) + 2H
2
O(l) aa) Zn 2+ bb) 2Cl -
(aq) + 2e -
(aq)

Cl

Zn(s)
2
(g) + 2e -
The use of the

arrow is long established, back to the end of the nineteenth century. It introduces the concept of a reaction being bi-directional.
The arrow indicates full reaction in either direction b changing conditions, not an intermediate position of equilibrium.
This arrow indicates not simple reversibility but that the reaction system settles down into an intermediate and measurable position. The distinction between

and

may not be entirely clear.
These equations remain specific but are part of the process of generalising a set of reactions at the symbolic level.
These equations contain the concept of spectator ions, and thus the notion of ion independence in aqueous solutions.
As far as learners in schools are concerned, these are hypothetical constructs to explain reactions occurring at
Up to this point the chemical arrow has indicated that reactions only go in one direction. The possibility of relatively easy reversibility should come as a surprise but does not seem to. Perhaps it indicates rote memory being used rather than deep understanding at school level.
This type of reaction may be explained, at the submicroscopic level by the interaction of reversible reactions, i.e.

proceeding at different rates. The ability to distinguish between equilibrium and reversibility is necessary for this to be understood.
The learner needs to be aware of similarities between class members.
The equations gloss over the function of the hydration of individual ions in formation of solids or gases. Manipulating chemicals in different states may be a difficult task.
The equations contain free electrons whose condition is unclear. This issue is usually ignored in the use of half
Equations 1 9

Equations 1 electrodes. equations in explanations.
10

11
The meanings of chemical signs in textbooks, including chemical arrows
1856
Date Author
Wilson
Equations p120
Before decomposition, KO,NO
5
and HO,SO
3
;
After decomposition, HO,NO
5
and KO,SO3.
Or more fully thus:-
Signs
Combination lines, full and dotted, and the = sign are used in the text. The comma , is used to indicate parts of a compound in combination.
1866 Frankland
KO NO
5
= HO,NO
5
HO SO
3
= KO,SO
3
Here the dotted horizontal lines indicate the bodies in combination at the beginning of the process, the oblique unbroken lines the exchange of acid and base that occurs during the decomposition, and the double horizontal lines = (the algebraic sign of equal to) the bodies in combination at the end of the process.
PO
5
+ 5C = P and 5CO
This equation (p162) shows the symbol + on the left hand side and uses 'and' on the right hand side. p16 The sign +, …is placed between the formulae of the molecules of the different substances which are brought into contact
Comments
Word equations are not used although the names of some materials are placed under the appropriate formulae.
Frankland is unusual in being specific about the meaning of the
+ sign.
Chemical symbols, signs and syntax © John Oversby, October 2002

1894 Jago
12 p117
Na
2
O + H
2
O = 2NaHO
Sodium oxide Sodium hydrate before the reaction, and of those which result from the change. This sign must never be used to connect together the constituents of one and the same chemical compound.
Chemical changes are most conveniently expressed by what are termed 'chemical equations'; these consist of the symbols and formulae of the bodies participating placed just before the sign =, while those of the resultant bodies follow.
As no chemical change affects the weight of matter, the weight of the quantity of a compound represented by its formula must be the sum of those constituent elements; so, too, the weight of the bodies resulting from a chemical change must be the same as that of the bodies before the change, whatever it may be, had occurred.
Also the same number of atoms of each element must appear on each side of the equation. Although from a chemical equation and table
No use of arrows in this book
Jago expresses the macroscopic interpretation of an equation I terms of conservation of mass.
Chemical symbols, signs and syntax © John Oversby, October 2002

1899
1913
1930
1954
13
Newth
Schmidt
Hooton
Holderness &
Lambert
P54 Atomic equation , Hg + 2Cl = HgCl
Molecular equation , Hg + Cl
2
= HgCl
2
2 of combining weights it is possible to state what relative weight of each element is concerned in each reaction, it must never be forgotten that the combining weights were first determined by experiment, and then the table combined therefrom.
P22 The sign + has a different significance as used on the left side of the equation to that which it bears upon the right. On the left side it implies that chemical action takes place between the substances, while on the opposite side it has the simple algebraic meaning … "and also"
Used the arrow

sign for formulae and
= for line equations mainly using = signs.
P65 C
6
H
5
AsCl
4
+ 3H
2
O =
C
6
H
5
AsO(OH)
2
+ 4HCl
But (on the same page) (C
6
H
5
)
3
As + Cl
2

(C
6
H
5
)
3
AsCl
2
Elements and Symbols
Mercuric oxide = mercury + oxygen
The sign of equality indicates that the total weight remains unchanged; mercuric oxide breaks up into the two elements, mercury and oxygen, and their weights are together equal to the oxide which yields them.
HgO = Hg + O
P47-48
P24 Zn + H
2
SO
4

ZnSO
4
+ H
2
This equation is interpreted in terms of
for reversible reactions
P83 Up arrows and down arrows are mentioned on this page and occasionally
A word equation is given here.
Holderness and Lambert are explicit about the way that the
Chemical symbols, signs and syntax © John Oversby, October 2002

1956
1989
1995
1995
14
Clynes &
Williams
Hill, Holman,
Lazonby,
Raffan &
Waddington
Larousse
Lister &
Renshaw molecules, not macroscopic.
Later on the same page:
Mg + H
2
SO
4

MgSO
4
+ H
2
Fe + H
2
SO
4

FeSO
4
+ H
2
The equations correspond to, and represent, the observed fact that when these two metals are brought into contact with dilute sulphuric acid, hydrogen is liberated and the metals are converted into their sulphates.
P 135, 136 By use of equations the materials taking part in a reaction and the products of reaction can be shown, and it is possible, moreover, to calculate the weights of the different substances concerned.
Magnesium and Oxygen give Magnesium oxide
Or, Magnesium + Oxygen

Magnesium oxide
2Mg + O
2
= 2MgO
P9: calcium + water

calcium hydroxide + hydrogen
P12 questions: magnesium + copper(II) oxide

copper + magnesium oxide p25: methane + oxygen

carbon dioxide + water
CH
4
(g) + O
2
(g)

CO
2
(g) + 2H
2
O(l).
A quantitative symbolic representation of the changes occurring in a chemical reaction, based on the requirement that matter is neither added nor removed during the reaction.
Chapter 6 Equations
Word equations (p27) Equations are used as a simple way to represent what is happening in used elsewhere. Arrows are used throughout.
The + sign on the left of the equation means “reacts with”, but on the right it means simply “and”, while the arrow means “producing”.
Both arrows and = signs are used p176 Zn + 2HCl = ZnCl
2
+ H
2
↑
Equations are not mentioned in the index.
No discussion of signs is apparent
Signs are not discussed equation represents the macroscopic change.
These authors draw together a prose version, the word equation and a symbol equation in the same discussion.
This is aimed at the 16-18 age range
Chemical symbols, signs and syntax © John Oversby, October 2002

1996 McLean a chemical reaction, and the simplest is the word equation. … equations should always be based on experimental evidence.
Equations do not say how fast a reaction happens. Conditions (heat, pressure, etc.) may be shown on arrows, for example –heat

{heat over arrow}
Only reference to equations in the index is to balancing equations. This is treated as writing the word equation, then the formulae and then checking the atom numbers. Finally, adding state symbols. On this page the explanation is algorithmic.
15
McLean is explicit in describing the order of equation construction from word equation to symbol equation.
Chemical symbols, signs and syntax © John Oversby, October 2002

16
Explanation of the syntax of chemical equations is rarely given in textbooks, old or modern. This is rather surprising since chemical equations link the macroscopic description with the sub-microscopic symbolic level. This section is aimed at clearing up this lack of clarity. It also points up the points of correspondence between symbolic equations and descriptions of the phenomena.
The + sign
This section is deliberately not headed ‘the plus sign’. The + sign in chemical equations has a meaning that is distinct and significantly different from the algebraic meaning. In historical terms, Berzelius, in 1813, had a great influence on chemical notation. Compounds were denoted at first (the early part of the eighteenth century) by a + sign between the constituents element symbols e.g. copper oxide was Cu+O.
The exact meaning of the + sign is not made explicit, for example in Wilson (1856), but it would seem reasonable to suggest that it meant ‘combined together’. The + sign was dispensed with later but it may have been kept as a symbol for 'reacts with' or joins with’. The + sign on the right of the equation has a different meaning. It simply means ‘and also’. Wilson (1856) often writes symbolic equations with the term ‘and’ on the right hand side where we would put + today. The + sign then refers, at the macroscopic level, to the existence of a chemical reaction in which one or more new substances are formed. The use of the + sign here is peculiar to chemistry and contrary to the meaning in algebra..
The equation arrow 
This section deals with the meaning of the main equation arrow although other equation arrows will be treated later. It seems to mean the process of a chemical change, or ‘yields’, ‘to give’. When chemistry teachers from a variety of countries were questioned, they all responded with this meaning e.g. ça donne, by a French colleague. The arrow corresponds to chemical change and is thus fundamental to the nature of chemistry.
The position about the development of equation signs is not entirely clear. There is a tendency for chemistry textbooks in the mid- and late nineteenth century to use the more descriptive form and restrict the use of equations. This is understandable in terms of printing technology for such equations would have to be specially set up by the printer.
The equation arrow,

, has not always been used to denote the process of chemical change. From the beginning of writing chemical equations (1830s) until about the
1960s, textbooks used the = sign for the process of chemical change. This is in contradistinction to other opportunities chemists chose to use symbols and signs in a different way to that used in algebra. Brock (1992) suggests that this may be the influence of the printers who did not have the

in their printers’ box of type. I have identified that books that used the letterpress method of printing, where the type leaves an indentation in the page, always used the = sign for the equation arrow. This method of printing was in common use until the early part of this century. A survey of
PGCE student science teachers demonstrated their unanimous preference for

over
=, most justifying this in terms of the chemical equation being distinct from algebraic equations.
Chemical symbols, signs and syntax © John Oversby, October 2002

17
The symbol = is used in equations from the mid part of the nineteenth century. It was available as a standard printer symbol and was so easy to use. The arrow symbol
 was occasionally used from the middle of the nineteenth century, especially in organic chemical reactions using displayed formulae. In the early books, it was clearly a special symbol devised by the printers (often parts of the arrow were not perfectly aligned showing its construction from component lines) and so may have been something of a nuisance. Its use seems to be largely restricted to the line drawings used for displayed formula equations used in organic chemistry. Even until the 1950s, the = sign was commonly used. This may be the influence of the printing technology i.e. using what is commonly available and, therefore, cheap.
Chemical equations
Brock (p156 - 157) tabulates the development of the chemical equation:
Bergman (mid nineteenth century) placed alchemical symbols in a four cornered diagrammatic scheme.
Bergman's system was modified by the acceptance of the Berzelian symbols e.g.
This system is also found in Wilson (1856). Faraday and others in the mid-nineteenth century used diagrams and additive linear equations that included reacting masses. In the 1840s, Thomas Graham introduced the balanced linear form we see today, although using the = sign exclusively rather than arrows.
The = sign, used in an equation to represent the process of chemical change, provides a conflict with its use in algebra. Chemists such as Berzelius devising the notation we use today were aware of this potential confusion. Widespread use of the arrow symbol may have been delayed by difficulties in printer technology but that problem is now behind us. It is one of the tools we use to differentiate between chemical and algebraic equations. Its use, in this respect, might be better exploited in early teaching of word equations, to point up the distinction between the two types of equations.
The use of the equilibrium sign,

, and the two arrows pointing in different directions needs also to be explored. They may be taken to represent different aspects of chemical notation, although it is recognised that the two arrows mode was accepted in response to the demands of printing technology.
The two arrows may be used in a macroscopic mode in the first instance. An arrow represents a chemical change, with an indication of direction of process. The arrow of time has imposed its direction on the chemical arrow. As first introduced in chemical learning, it represents a complete change. The reaction goes the whole way,
Chemical symbols, signs and syntax © John Oversby, October 2002

18 apparently. Thus, two arrows would represent a reversible reaction, that is one that can go in both directions, completely, on changing the conditions. The two arrows are used in a sub-microscopic mode in the second instance. At the sub-microscopic level of representation, where an equation represents individual chemical changes, there is no possibility of an equilibrium process. In this case, the two arrows can represent, at the same time, two opposite and complete reactions.
The equilibrium symbol,

, is a macroscopic representation. It extends the notion of chemical reaction by focussing on the extent of reaction. Extent of reaction is a macroscopic concept. It is explained as arising from two opposite sub-microscopic processes each taking place at a different rate. The macroscopic 'extent of the equilibrium' is derived from two sub-microscopic processes. Thus the

sign might be reserved for macroscopic representations.
The + sign is the last symbol to be considered. Again, it is potentially a source of confusion with algebraic notation. In algebra, the + sign is an operator, signifying the requirement to carry out to carry out an addition of two numbers, or two functions. In chemistry it has two uses. The first, on the left-hand side of the equation, indicates a chemical reaction. It implies a change in the chemical nature of the species taking part. On the right-hand side, it has a different meaning: 'and'. This is apparent in the quotation below from Wilson (1856) who uses the two forms explicitly. The use of
'and' has now been dropped in favour of the second use of +, although with the different meaning. It may be necessary to be explicit about this different meaning which depends on position in the equation. Again, an expert chemist may intuitively be aware of this while the young learner needs it to be clarified at the start.
Chemical word equations
Wilson (1856) gives a chemical equation of this type.
Hydrochloric
Acid
Peroxide of
Manganese
Hydrochloric
Acid
{
{
Chorine
Hydrogen
Manganese
Oxygen
Chlorine
Hydrogen
Chlorine
Water
Chloride of
Manganese
Water
This is an early type of word equation. It is an example of the Bergman-Berzelius 
{ continues at least until the end of the nineteenth century
.

Wilson (1999) mentions word equations as a representation of a chemical process.
The general form is given as:
Reactant(s) special encouragement conditions
 Product(s)
Chemical symbols, signs and syntax © John Oversby, October 2002

19
Discussion of word equations
The exact origin of word equations is more mysterious than the details of how it was used. The early word equations seem to have been created in the absence of any other form of notation. The examples given in Wilson (1856) and Jago (1894) contain information about a possible mechanism. They do not just record start and end materials. The lack of arrows has already been alluded to but it is just possible that the lines used in the diagrams may be precursors of arrows.
Word equations are not mentioned in the fairly comprehensive Larousse Dictionary of
Science and Technology (Larousse,1995) but seem to be used by some chemists to explain their work. They are more frequently introduced to young learners but rarely in a coherent or explicit form in the texts studied. Only Wilson (1999) generalises the form of a word equation. She is very clear about the place of the special conditions in word equation, over the arrow. This is also seen in some of the other texts. There does not seem to be a definitive authoritative set of instructions for the construction of word equations.
Wilson (1856) and Jago (1894) restrict their use of word equations to correct nomenclature (for their time) for the chemicals provided. This is the case for most of the recent authors, too.
Word equations and their meanings are the most problematic areas of teaching about equations in chemistry ( refer to QCA here ). They are essentially macroscopic in nature and they require a sense of what is a chemical change. In some cases, word equations are used for what might not be seen as a chemical change eg: water liquid → water gas
Some authors do not put the states in word equation but others put them in as they feel it is appropriate e.g. Muir (1907, p442): sulphur rhombohedric → sulphur monoclinic
The nature and status of word equations in chemistry needs to be clarified, especially as they are a required part of the school chemistry curriculum.
Conclusion
The research questions can now be answered based on the data provided.
1.
What chemical equations appear in textbooks of chemistry especially at school level?
In historical order these are full symbolic equations (firstly with equal signs, then single arrows, then the

arrow, then the

arrow); ionic equations and half equations (with arrows); and, more recently, word equations. Explicit meanings of signs and equation syntax are more frequently provided in older textbooks than in recent textbooks.
2.
How can chemical equations be classified to make sense of the way they represent chemical phenomena?
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20
A typology has been provided. Word equations represent macroscopic features only. Symbol equations represent both macroscopic and sub-microscopic features.
Balancing represents the law of Conservation of Matter although many recent textbooks ignore this and treat balancing as an algorithmic process of equating symbol numbers.
3.
What are the links between word and symbolic chemical equations?
In older textbooks, words were added after the symbol equations were provided.
There is no evidence that early textbooks saw the construction of word equations as the first step, rather that the words simply provided further information about materials at the macroscopic level.
4.
What changes in chemical equations have taken place over the last 150 years and what has contributed to these changes?
Arrows are used in the place of the = sign. In the twentieth century an variety of arrows has appeared as the focus on reversible and equilibrium equations has developed. Balancing of symbol equations has been routine throughout this period. Word equations appeared in the early and mid nineteenth century and declined as symbol equations developed. Recently, in the past 50 years, word equations have been introduced as an introduction to chemical equations.
5.
What can a study of chemical symbolism contribute to thinking about learning chemistry?
The use of the symbolic level representation for more advanced learners of chemistry, as well as by chemists themselves is by far the most common representation of chemical change. As chemistry has been introduced to a wider ability range of students in comprehensive schools, word equations have been used in textbooks in lower secondary schools. There is an assumption that this bridges the link between the macroscopic and the sub-microscopic levels of representation but this is far from being justified.
Conclusions
The work reported here indicates that chemical notation is a neglected part of learning about chemistry in secondary schools now compared with the past. Reference to empirical origins is rare. Chemical word equations mean different things to different authors and the lack of consistency is obvious. Balancing chemical equations has little chemical purpose and is rule oriented rather than based on understanding of fundamental chemical laws.
Chemical notation should be an essential part of the initial programme for the chemistry curriculum. It may be of some help to introduce into undergraduate chemistry degree courses a compulsory module on the structure of chemical knowledge. A sound base in experimental knowledge should be re-established. This could include personal practical work and an examination of the accounts of practical work of past chemists. The history of chemical notation should be an essential component of initial teacher education and professional development. Further work needs to be done on understandings of chemical equations by both teachers and their learners.
Lost beginnings
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21
Larousse makes it clear that there has been very little change in the meanings of symbols and equations since they were first established at the beginning of the nineteenth century. However, recent textbooks are at odds with these very principled meanings. How may this have come about? With regard to the symbols, the loss is the quantitative macroscopic meaning. Chemistry has moved on from equivalents to moles and the discussion here recognises this change. Similarly, chemistry now recognises a range of entities and representations, such as the bull's eye diagrams for electronic structures. The language used in the textbooks appears to be one of finality.
The authors leave no room for a development of the explanation they give. The message they leave us with is not one that accredits a progressive understanding of the meaning of symbols as the reader's knowledge improves. Rather, it is a cut and dried view, this is the meaning of symbol that will stand the test of your improving knowledge. There is no later reflection on these meanings at the end of the book to suggest there is any need for a rethink. Perhaps the authors believe that their explanation of the meaning of symbol is the end of the story. If chemistry is to come alive a developing subject then this should be reflected in the structure of the textbook. A section at the end relating an improved meaning of the term and relating to the history of how this term was established would be a helpful contribution to understanding the structure of chemistry.
Chemical equations are poorly discussed in every single one of the recent textbooks.
There is no indication of a quantitative macroscopic meaning and this original meaning has been lost. At the start of the nineteenth century the sub-microscopic view was a modern contribution. The use of symbols was an accreditation of the need to include this sub-microscopic approach. Now the macroscopic position has been left out and the result is a detachment from empirical evidence. This may go some way to explain why some students fail to maintain chemical formulae when balancing equations. They are simply not aware of the strength of the law of constant composition so well established by Richter and others at the turn of the nineteenth century. It is little wonder that they have such little regard for the constancy of the formulae. In a similar light, the focus on rules for balancing equations has led to a detachment of stoichiometry from the law of conservation of matter. This ought to be trumpeted in the texts as the basis for balancing equations. The place of the different notations of coefficients and numbers of atoms, crafted from the numerous discussions two hundred years ago, needs to be emphasised. The lack of explicit teaching of this part of the chemistry curriculum suggests that it may not be appreciated by the authors.
Word equations are a more modern phenomenon, while retaining their roots in the
Bergman-Berzelius forms. These are more used as a teaching tool. The teaching community, rather than the community of academic chemists may better clarify their meanings.
Chemical equations in The Journal of Chemical Education
The Journal of Chemical Education is a journal that appears to be most closely related to teaching and learning of chemistry than most. It was, therefore, chosen to investigate the appearance of chemical equations in the articles it provides for US high school and college level chemistry. Nine issues from 2002 (January –
September) were examined for the presentation of chemical equations. Many articles
Chemical symbols, signs and syntax © John Oversby, October 2002

22 and three complete issues did not present chemical equations at all. Nevertheless, 35 papers provided examples of 116 chemical equations. While this does not constitute a rigorous or comprehensive survey, it provides a flavour of recent practice. Within this sample there were (the numbers do not all tally to 116 since there was multiple use in some equations):

4 word equations

50 formulae equations, many concerning molecular reactions that could not be represented as ionic equations

9 half equations in ionic form

57 ionic equations
 only 4 equations that were general ionic or formulae while the rest were specific

12 equations were provided with state symbols

8 equations that were only partial i.e. unbalanced
 a variety of arrows in use (

, 86;

, 1;

, 1;

, 20; =, 8). The use of the = sign was restricted to one paper which also used the ↓ arrow.
 The following pseudo symbols were used: Ac, Et, Ph, R, R’, py (pyridine), p-O
2
N-C
6
H
5
, Hb (haemoglobin), DNA, L (ligand), NAPDH, NADH, m-CPBA, t-Bu, M (for metal), e without the minus, e
-
with the minus.
It would seem that there is a lack of consistency and very little editorial direction over the representation of chemical equations.
A timeline of equation and signs in chemistry
1856 Wilson uses + on reactant side and 'and' on product side of equation
Wilson uses the = sign for 'reacts with'
Wilson explanation of the order of symbols in a compound
1856 Miller uses the comma as a combination sign.
1864 Frankland uses subscripts but symbols in order reverse to the convention of metals first. Formulae are related to reacting weights. The + sign is explained as it is today.
1887 Gautier uses superscripts and = signs. He puts words under symbols.
1894 Jago uses + on both sides of the equation.
Jago clarifies symbols as abbreviations for names, and representing both atoms and macroscopic quantities.
1899 Newth uses + sign but "and also" for different sides of the equation
He characterises atomic and molecular equations.
1900s The use of the = sign begins to be replaced by the

in textbooks. This is not generally complete until the 1960s
1913 Schmidt uses

and = signs
1920s Use of

for reversible and equilibrium reactions.
1940s Use of

sign for equilibrium reactions. The  sign is less commonly used in the
1970s but never disappears entirely.
Chemical symbols, signs and syntax © John Oversby, October 2002

23
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Chemical symbols, signs and syntax © John Oversby, October 2002