Chemical Equations


1 Representing a reaction

A reaction such as the combustion of methane can be represented by a chemical equation as follows.

CH4 + 2 O2 CO2 + 2 H2O [Equation 1]

A chemical equation is perhaps the most important statement that can be made in the language of chemistry, and it has a vocabulary and grammar which should be thoroughly understood.

Equation 1 is a statement that a molecule of methane will react with two molecules of oxygen to give a molecule of carbon dioxide and two molecules of water.

In reality, when methane is burnt in air there will be other gases present (especially nitrogen), and a very great excess of oxygen which is not consumed or affected. Since all these are present both before and after the reaction, they are not included in the equation. Species which are present but not changed are often referred to as spectators.

Also, many more than one molecule of methane will react. When a sample of methane burns, an astronomical number of molecules react with twice their number of molecules of oxygen to produce the products. The convention for writing equations is to refer only to the smallest number of species necessary, i.e. to divide through by any common factor.

2 Symbols showing state

Often we add symbols that give information about the physical state of the participants in a reaction (e.g. gaseous, liquid or solid). Table 1 shows the main symbols used.

Table 1

Symbols showing state of a reactant or product

Symbol Meaning
(g) Gaseous or vapour state
(l) Liquid or molten state
(s) Solid state (sometimes written as (c) – crystalline)
(aq) Aquated or hydrated state: this refers to a species loosely bound to water molecules in a water (aqueous) medium.

When methane burns, the temperature will be high enough to ensure that the water produced will be in the form of steam, therefore equation [1] could be rewritten as follows.

CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) [Equation 1a]

It is not usual to add symbols such as (g) unless there are reasons to draw attention to the state, for example when a solid is formed in a solution or a gas is evolved.

3 Reactions involving ions

A solution of common salt contains sodium ions, of formula Na+, and chloride ions, of formula Cl. A solution of silver nitrate contains silver ions, Ag+, and nitrate ions, NO3.

If we mix these two solutions we have a solution containing the four ions Na+, Cl, Ag+ and NO3.

It is known that when silver ions and chloride ions come into contact in solutions of moderate concentration they immediately react to give the crystalline solid silver chloride, of formula AgCl. The white solid silver chloride appearing in the solution is called a precipitate.

No change takes place involving Na+ or NO3.

In this reaction, then, the reactants are Ag+ and Cl and the sole product is AgCl. The appropriate equation is

Ag+ + Cl AgCl(s) [Equation 2]

The symbol (s) is included here in order to emphasise that the reaction has given a solid precipitate.

It is inappropriate to include in the equation the spectators Na+ and NO3. They play no more part in the reaction than the vessel in which the experiment was carried out.

It is also inappropriate to refer in the equation to species such as NaCl or AgNO3, which are the formulae for solid sodium chloride and solid silver nitrate. Neither solid is present in the solutions being mixed. It is even worse to refer to such aquated species as “NaCl(aq)” or “AgNO3(aq)”, as the main species other than water in these solutions are the aquated ions.

The last two paragraphs have been emphasised because you may well have already met equations written in terms of solids when the real reactions are of ions in solution. Such equations are cumbersome and miss the point that equations are about the species which change and the species which are created.

Balancing more difficult equations

One benefit of writing equations in terms of the ionic species involved (sometimes, unnecessarily, referred to as “ionic equations” or “net ionic equations”) is the ease of balancing more difficult equations such as the one we must write for the reaction which occurs when calcium chloride and sodium phosphate solutions are mixed, giving a precipitate of calcium phosphate, Ca3(PO4)2.

Calcium ions have the formula Ca2+ and phosphate ions have the formula PO43. We must set up an equation to represent the fact that

Calcium ions + phosphate ions react to give solid calcium phosphate

How many calcium ions and how many phosphate ions will be involved? From the formula of calcium phosphate the answer is simple. We need three calcium ions and two phosphate ions:

3 Ca2+ + 2 PO43 Ca3(PO4)2(s) [Equation 3]

Finding a formula

What if we knew the formula of calcium ions and phosphate ions but did not know the formula of calcium phosphate? We can still work out the probable formula by making use of the fact that both atoms and charges must balance in a chemical equation. That is, electrons may be rearranged between the atoms but they are not created or destroyed. In Equation 3, for example, the total charge on each side is zero.

Solid calcium phosphate, like any other compound, is electrically neutral, hence the charges on the left–hand side must cancel to zero to match the right–hand side. The only way that this can happen is for there to be three Ca2+ ions to every two PO43 ions, and Ca to PO4 in calcium phosphate must be in the ratio 3:2. Ca3(PO4)2 is the smallest unit possible in this ratio.

The same principle can be applied to working out the formulae of solids such as calcium chloride and sodium phosphate. Ca2+ must be balanced by two Cl ions, hence the formula of calcium chloride is CaCl2. PO43– requires three Na+ ions: Na3PO4.

There's no salt in the sea!

The sea contains the ions Na+, K+, Mg2+, Fe3+, Cl, Br, I, SO42–, HCO3–, and many more in smaller quantities. The total charges on the positive ions balance the total charges on the negative ions. There is no sodium chloride or any other salt as such. Natural waters always contain mixtures of ions.

Even an artificial solution made by dissolving sodium chloride in water contains no NaCl species, only Na+ and Cl and water.

To see why equations such as NaCl + AgNO3 AgCl(s) + NaNO3 have no real meaning, consider the following simple experiment:

Solution A is prepared by adding NaCl and KNO3 in equal quantities to water.

Solution B is prepared by adding NaNO3 and KCl in equal quantities to water.

Is there a difference between the two solutions? No. Each is simply a solution containing Na+, K+, Cl, and NO3–.

Should there be a different equation for the reaction which takes place when you add AgNO3 solution to each, forming precipitates of AgCl? No. The reaction is exactly the same for each::

Ag+ + Cl AgCl(s)

4 Showing equilibrium in an equation

If we stir salt with water until no more will dissolve, and then add a little more, we have a dynamic equilibrium in which salt is dissolving in water and also precipitating out on the surface of the solid so that the total amount of solid remains constant.

The two reactions occurring simultaneously can be depicted in Equations 4 and 5:

DISSOLUTION: NaCl(s) Na+(aq) + Cl(aq) [Equation 4]
PRECIPITATION: Na+(aq) + Cl(aq) NaCl(s) [Equation 5]

To express a situation in which these processes are taking place simultaneously in a system at equilibrium, we use a reversible arrow symbol, “

NaCl(s) Na+(aq) + Cl(aq) [Equation 6]

For clarity of thought and expression it should be remembered that the equilibrium arrow should be used only to tell the reader about a system at equilibrium, and never to describe a reaction.

That is,

  • ” describes a situation.
  • ” describes a process or event.

An equilibrium equation such as Equation 6 can be written backwards without changing the meaning:

Na+(aq) + Cl(aq) NaCl(s) [Equation 7]

This is not true of a reaction equation. Equations 6 and 7 mean the same thing, Equations 4 and 5 do not.

5. Writing equations for reactions

5.1 Basic rules

Equation writing: the basics

  1. On the left, write the formulae of all major species which change as a result of the reaction. Omit those which do not. It is optional whether or not to show the state - (aq), (g), (s), (l) - but preferred when there is a change such as a gas being formed or consumed.
  2. On the right, write the formulae of all major new species finally present as a result of the reaction. (See remarks above about state).
  3. Join the reactants to the products with the arrow symbol “”.
  4. Apply coefficients to the species in the equation so that the atoms of each element and the charges balance (strictly it isn't an equation until then).
  5. Divide through where necessary to remove common factors.

If the equation is to describe an equilibrium, the rules are the same as above except that the symbol is “” and it does not matter if reactants and products are interchanged as a whole.

5.2 Knowing what the reactants and products are

The hardest part of equation-writing is to know what actually happens: what species react and what products are formed. Without this knowledge, it is impossible to write an equation. This information cannot be obtained algebraically by manipulating the symbols.

To a request for an equation for the reaction which takes place when copper(II) oxide, CuO, is treated with dilute sulphuric acid, H2SO4, only desperation can produce equations like Equation 8

CuO + H2SO4 CuO2 + H2S + 3O [Equation 8]

All that can be said for Equation 8 is that it is an equation - it is balanced. H2SO4 is not a reacting species (the solution contains H+(aq), SO42(aq), and HSO4(aq)); the reacting species are CuO(s) and H+(aq), and the products are Cu2+(aq) and H2O). Equation 9 is not only balanced but is the actual equation for the reaction.

CuO + 2 H+ Cu2+ + H2O [Equation 9]

But how do we know what reacts with what to give what? There is no substitute for knowing the specific reaction, but a great deal of information can be gained by reference to generalisations.

The properties of elements for example are fairly well-defined, especially when the information is related to the Periodic Table. You need to prepare tables showing generalisations about what to expect when metals are added to water and to dilute acids, or when metal oxides, hydroxides or carbonates are treated with dilute acid, or when metal hydroxides, carbonates and nitrates are heated. Generalisations about non-metals are more difficult to define.

The following pages provide some generalisations, and familiarity with them gives you a feel for what chemistry is about, and confidence in studying it and applying it.. You need also to master further general principles governing oxidation-reduction reactions. Organic chemistry covers a further, very large number of reactions which can fortunately be grouped into generalisations (e.g. alcohols react with sodium to give hydrogen)

Don't try to learn by rote

Even though the facts of chemistry usually fall into groups there is still far too much information to try to commit it all to memory. Yet if we had to look everything up we would be as helpless as a taxi driver who didn't know the streets. Only repeated use of information can build the familiarity that makes further use a pleasure and not a chore. The information should be used in the beginning as a data base to refer to. With practice - on written exercises, and in the laboratory, and (over time) in application to other areas of knowledge - the necessary familiarity will come.

5.2.1 Combustion of compounds of C, H and O

When a compound containing carbon and hydrogen (a hydrocarbon) or one containing carbon, hydrogen and oxygen burns in air, the products depend on the conditions - especially the air supply. However, if there is plenty of oxygen and combustion is complete,

  • all carbon is converted into CO2
  • all hydrogen is converted into H2O

Table 2 shows the procedure for writing a balanced equation for complete combustion and relates it to an example.

Table 2

Rules for writing a balanced combustion equation for CxHyOz

Step Application to combustion of acetaldehyde, C2H4O
Place on the left-hand (reactant) side the formula of the compound being burned. (C2H4O) Leave room for the other reactant (O2) and draw the reaction arrow.
On the products side enter enough CO2 molecules to account for all the carbon and enough H2O molecules to account for all the hydrogen.
C2H4O   2 CO2 + 2H2O
Balance the oxygen with O2
C2H4O + 2½O2 2 CO2 + 2H2O
If necessary, multiply both sides by a factor to clear fractions
2 C2H4O + 5 O2 4 CO2 + 4H2O
CHECK 4 C, 4C; 8 H, 8 H, 12 O, 12 O

5.2.2 Reactions involving ionic crystals and/or ionic solutions Dissolution of ionic solids in water

If an ionic compound is added to water, dissolution occurs until the solution is saturated. The amount that dissolves before this depends on the solubility of the solid. For convenience it is usual to divide salts into insoluble (under about 1 gram per litre ), slightly soluble (up to about 10 g/L) and soluble. Equation 4 is a typical equation for dissolution.

NaCl(s) Na+(aq) + Cl(aq) [Equation 4]

When the solid first starts to dissolve, the solution is unsaturated, which means all solid dissolves and if a small amount more solid is added it will dissolve too. After a while, as more and more solid is added, the solution becomes saturated, and no more solid will dissolve. Precipitation of ionic solids from water solution

Earlier we saw what happens when solutions of sodium chloride and silver nitrate are mixed. The result is a precipitate of the insoluble silver chloride. In general, precipitates are formed by bringing together the component ions of an insoluble salt in the one solution.

(a) Deciding what precipitate (if any) forms

To decide when a precipitate will be formed, first list all ions present in the mixed solution, then check Table 3 to see if any pair of oppositely charged ions relates to an insoluble salt. If so, there will be a precipitate. If the salt is slightly soluble and the concentrations of contributing ions are high enough it will precipitate.

(b) Predicting observations

If a precipitate forms we can predict an observation. What colour is it? Are any coloured ions formed or lost at the same time?

Table 4 gives colours of ions and precipitates referred to in Table 3. If a colour is not given it may be assumed that the precipitate is white or that the ion is colourless. The texture of a precipitate is sometimes distinctive. Precipitates of the hydroxides of the transition metals and of aluminium are gelatinous. The other precipitates from Table 3 are crystalline. It is not necessary to state if a precipitate is crystalline, but should be noted if it is gelatinous (as this is different from the norm).

Clear language:

Never write “clear” when you mean colourless. Copper(II) solutions are blue. They are also clear. The opposite to “clear” is “cloudy”, or “turbid”.

Table 3

Solubilities of salts

This table refers only to the following restricted list of ions.

Na+, K+
Mg2+, Ca2+, Sr2+, Ba2+
Sn2+, Sn4+, Pb2+
Cr3+, Mn2+, Fe2+, Fe3+, Co2+, Ni2+,
Cu2+, Zn2+
Cl, Br, I
NO3, SO42, OH, CO32,
PO43, S2


All salts of NH4+, Na+ or K+
Solutions of NH4+ and OH (The main dissolved species in these solutions is NH3)
All salts of Cl, Br, I except those of Ag+ and Pb2+
All salts of NO3
All salts of SO42, except CaSO4, SrSO4, BaSO4 and PbSO4
MgS, CaS, SrS and BaS


AgCl, AgBr, AgI, PbI2
SrSO4, BaSO4 and PbSO4
All saltsa of OH except NaOH, KOH and solutions of NH4+ and OH(mainly NH3)
All salts of CO32, except Na2CO3, K2CO3 and (NH4)2CO3
All salts of PO43, except Na3PO4, K3PO4 and (NH4)3PO4
All salts of S2, except Na2S, K2S, (NH4)2S, MgS, CaS, SrS and BaS. When S2 is added to Al3+ ,Cr3+ or Fe3+, a reaction takes place which will not be considered further.

Slightly soluble

PbCl2, PbBr2, CaSO4, Ag2SO4, Ca(OH)2, Sr(OH)2

a Hydroxides do not fit an old definition of salts as compounds formed by neutralisation of acids but do fit the more modern definition as solid compounds composed of oppositely charged ions.

Table 4

Colours of some ions and some solids

The ions and solids are those referred to in Table 3. If the colour of an ion is not given it is colourless, and if a precipitate is not included it is white.


Cr3+, greenish blue; Fe2+, pale green; Co2+, pink; Cu2+, blue; Mn2+, very pale pink; Fe3+, yellow; Ni2+, green; the rest, colourless.


Cation Cl Br I OH CO32 PO43 S2
Ag+ white cream yellow deca yellow yellow black
Pb2+ white white yellow white white white black
Sn2+ white white white brown
Sn4+ white deca deca yellow
Cr3+ green-blue deca green deca
Mn2+ very pale
pink pink pink
Fe2+ pale green grey-green off-white black
Fe3+ brown deca yellow deca
Co2+ rose-red red red black
Ni2+ green green green black
Cu2+ deca blue green-blue blue black

a“dec” (decomposes) means the substance cannot be formed as it is unstable. Formation of molecules

(a) Water

Water is formed when neutralisation takes place by treatment of solid oxides, solid hydroxides or dissolved hydroxide ion with acids.

When the acid is a strong acid (fully dissociated into ions), the H+ from the acid combines with the oxide or hydroxide in the solid, or the hydroxide in solution, e.g.

Solid oxide: ZnO(s) + 2 H+ Zn2+ + H2O [Equation 10]
(Observation: The solid goes into solution)
Solid hydroxide: Zn(OH)2(s) + 2 H+ Zn2+ + 2 H2O [Equation 11]
(Observation: The solid goes into solution)
Hydroxide solution: OH + H+ H2O     [Equation 12]
(No change is directly visible, but the solution becomes less alkaline, or becomes neutral or acidic, depending on how much acid has been added)

The reaction is similar if the acid is weak, but the molecules of weak acid, rather than the H+ ions, appear as reactant, e.g.

ZnO(s) + 2 HOAc * Zn2+ + H2O + 2 OAc [Equation 13]
Zn(OH)2(s) + 2 HOAc Zn2+ + 2 H2O + 2 OAc [Equation 14]
OH + HOAc H2O + OAc     [Equation 15]

(Observations: The observations are similar to those for strong acids. However, practically all water-soluble weak acids have an odour. Provided enough of the oxide or hydroxide is present to react with all the acid, the odour will disappear. In the case of acetic acid, the odour is that of vinegar).

* “Ac” is the acetyl group, or –COCH3. Thus HOAc is HO-COCH3 or CH3COOH, and OAc is CH3CO2

(b) Weak acid molecules

If the anion of a weak acid is treated with a solution of a strong acid, the weak acid molecule will form. Taking H+ as the reactant species, this can be represented by Equation 16.

OAc + H+ HOAc [Equation 16]
Since acetic acid is soluble, there will be no visible change in this instance. However, as soon as strong acid is added the mixture will smell of vinegar which is the odour of molecular acetic acid. Most weak acids are insoluble in water and will be precipitated on addition of strong acid - e.g. benzoic acid, C6H5COOH, from mixing a solution of sodium benzoate with dilute hydrochloric acid:
C6H5CO2 + H+ C6H5COOH(s) [Equation 17]
Instead of being in solution, the anion of a weak acid may be part of a solid. In that case the solid is brought into solution by the addition of strong acid, even if it is insoluble in water. An example is the reaction of water-insoluble calcium oxalate, CaC2O4, with dilute hydrochloric acid (Equation 18).
CaC2O4(s) + 2 H+ H2C2O4(aq) + Ca2+(aq) [Equation 18]

(H2C2O4 is not very soluble but is much more soluble than CaC2O4).

Note that oxalate requires two protons. Oxalic acid is called a diprotic acid. In fact, the protonation to generate diprotic acids takes place in two stages:

C2O42 + H+ HC2O4 [Equation 18a]
HC2O4 + H+ H2C2O4 [Equation 18b]

HC2O4 is named the hydrogenoxalate ion. “Hydrogenoxalate” should be written as one word to indicate that it is one ion.

(c) Gases

Many metals react with water or with dilute acid to form hydrogen gas. Other gases can also be produced from solutions at room temperature. The most important of these reactions are those that lead to hydrogen sulphide, carbon dioxide and ammonia.

Hydrogen, H2, is formed when a very reactive metal is added to water or a moderately active metal is added to dilute acid.

From water: 2HOH + 2 Na 2 OH + 2Na+ + H2(g) [Equation 19]
From acid: 2H+ + Fe Fe2+ + H2(g)     [Equation 20]

Hydrogen sulphide, H2S, is a very weak acid which is formed when the sulphide ion is present in an acidic solution:

S2 + 2 H+ H2S(g) [Equation 21]

Treatment of solutions of the sulphide ion or of many metal sulphides with acid leads to evolution of this colourless, poisonous and (unless extremely pure) malodorous gas. Water-insoluble metal sulphides from those in Table 4 which yield hydrogen sulphide on treatment with dilute acid are MnS, ZnS, FeS, CoS and NiS.

Carbon dioxide is formed when CO32 (carbonate) ions are protonated, giving the unstable carbonic acid, H2CO3 which immediately decomposes to give bubbles of carbon dioxide (Equation 22).

H2CO3 H2O + CO2(g) [Equation 22]

(Carbonic acid is stable under pressure. Soda water is carbonic acid solution. As soon as the pressure is released carbon dioxide is generated).

The equation for the reaction of carbonate ion with an excess of strong acid is

CO32 + 2 H+ H2O + CO2(g) [Equation 23]

The process takes place in two stages (see (b) above):

CO32 + H+ HCO3         [Equation 23a]
HCO3 + H+ H2CO3 H2O + CO2(g) [Equation 23b]

In systematic nomenclature HCO3 is the hydrogencarbonate ion, but it is also commonly called the bicarbonate ion.

If an excess of strong acid is added to a solid carbonate (e.g. zinc carbonate) the solid passes into solution and carbon dioxide is evolved:

ZnCO3 + 2 H+ Zn2+ + H2O + CO2(g) [Equation 24]

Ammonia is formed when the ammonium ion, NH4+, loses a proton. To achieve this we treat a solution of an ammonium salt with a base, typically hydroxide.

NH4+ + OH NH3(g) + H2O [Equation 25]

Ammonia is extremely soluble in cold water, and effervescence will not be observed. However, NH4+ is odourless and NH3 has a characteristic odour. The odour is detected immediately base is added to NH4+. If the solution is heated the solubility of ammonia falls and the gas is evolved as effervescence.

Ammonia can also be generated from the ammonium ions in a solid ammonium salt. The reaction which takes place when solid ammonium chloride is heated with sodium hydroxide solution is shown in Equation 26. Heating is not necessary for the reaction but it ensures that the ammonia is given off as a gas rather than remain in solution.

NH4Cl(s) + OH NH3(g) + H2O + Cl [Equation 26] Formation of complexes

Metallic ions can often combine with certain anions or neutral molecules to form a water-soluble species known as a complex. The anions or neutral molecules which take part in complex-formation are called ligands.

Species which often act as ligands are OH, F, Cl, CN and NH3. (CN is the cyanide ion).

The metallic elements most able to form complexes are the transition elements. The alkali and alkaline earth elements do not easily form complexes. In Periodic Group III, aluminium ions can form some complexes, especially with hydroxide ion.

(a) Hydroxocomplexes

If hydroxide ion is added to Al3+, the first observation is formation of a gelatinous white precipitate of Al(OH)3 (Equation 27).

Al3+ + 3 OH Al(OH)3(s) [Equation 27]
As more hydroxide is added, we see the solid dissolve:
Al(OH)3(s) + OH Al(OH)4(aq) [Equation 28]
The systematic name for this complex is tetrahydroxoaluminate. The “tetrahydroxo” signifies four OH ligands, and the “ate” ending means the species is negatively charged (an anion). The more common name is simply “aluminate ion”. The tetrahydroxoaluminate ion readily loses and regains water molecules, which is best expressed as equilibrium equation 29.
Al(OH)4 AlO2 + 2 H2O [Equation 29]

Not many metallic ions readily form hydroxocomplexes. Another commonly-encountered metallic ion which does so is Zn2+, which forms first the insoluble Zn(OH)2 and then tetrahydroxozincate, Zn(OH)4.

Hydroxocomplexes of aluminium and zinc, like the ions from which they are formed, are colourless.

(b) Fluorocomplexes

Fluoride ion is a powerful complexing agent with certain metallic ions such as iron(III), Fe3+ (Equation 30)

Fe3+ + 6 F FeF63 [Equation 30]

The number of ligand species present in the complex - the co-ordination number - and the charges on the original ions determine the charge on the complex (remembering that equations must be balanced in charge as well as in atoms).

The product is called hexafluoroferrate(III). The naming rules are as for tetrahydroxoaluminate, with the following extensions:

  1. When an element whose symbol is based on a Latin name appears in an anion, the stem of the Latin name precedes “ate”.
  2. When an element commonly occurs in more than one oxidation state, or is present in an uncommon oxidation state, the oxidation state is indicated by a bracketed Roman numeral written directly after “ate” (i.e. with no space).

Reaction 30 can be observed by a colour change. Iron(III) ions are yellow, and both fluoride and hexafluoroferrate(III) are colourless.Thus when sodium fluoride solution is added to iron(III) nitrate solution the yellow colour disappears.

(c) Chlorocomplexes

A typical chlorocomplex is the green tetrachlorocuprate(II), formed from blue copper(II) ions and colourless chloride ions (Equation 31).

Cu2+ + 4 Cl CuCl42 [Equation 31]

(d) Cyanocomplexes

Cyanide is a very strong ligand for a number of metals (meaning it forms a strong bond to the metal ion). Cyanocomplexes include:

  • dicyanoaurate(I), Au(CN)2, which is produced by treatment of gold with air and sodium cyanide solution (“cyanidation”),
  • hexacyanoferrate(II), Fe(CN)64 (often called ferrocyanide),
  • hexacyanoferrate(III), Fe(CN)63 (often called ferricyanide),
  • dicyanoargentate, Ag(CN)2 .

Dicyanoaurate(I) and dicyanoargentate are colourless, and the hexacyanoferrates are yellow.

(e) Ammine complexes

Complexes formed by the neutral molecule NH3 are called ammine complexes. It is important to spell this correctly, as amines (one “m”) are not complexes at all but a class of compound which includes the grouping NH2.

Addition of an excess of ammonia solution to a solution containing pale blue Cu2+ gives rise to a deep blue solution containing the complex ion tetraamminecopper(II), Cu(NH3)42+.

Note that the charge is +2 because ammonia molecules are electrically neutral, and that the Latin name for copper and the “ate” ending are not used because the complex is not negatively charged.

A number of other metal ions can form ammine complexes, such as Zn2+ (Zn(NH3)42+) and Ag+ (Ag(CN)2).

5.3 When it's acceptable to bend the rules

5.3.1 Equations involving intermediates

Often there are reasons to express in equation form the production or consumption of an intermediate species.

A case in point is oxidation and reduction half-equations. The intermediate species is the electron. When half-equations are appropriately combined we have a full equation which follows the for equations.

A species which is strictly an intermediate but is often treated for convenience as an initial or final species is the proton, H+. For example, when nitric acid is added to water it dissociates, transferring a proton to water. This can be divided into two (half) equations:

HNO3     NO3 + H+ [Equation 32]
H+ + H2O H3O+     [Equation 33]

HNO3 + H2O NO3 + H3O+ [Equation 34]

Equation 32 is very often used as an abbreviation for Equation 34, and is generally acceptable, as are redox equations in which H+ is involved. The formula H3O+ is used when there are reasons to draw attention to the fact that a proton is transferred to a molecule of water. (In fact, the formula H3O+ does not tell the whole story. The proton is believed to be associated with several water molecules, not just one, at any given time).

5.3.2 Doubt about major species

Consider the reactions of the following acids with dilute sodium hydroxide:

  1. dilute hydrochloric acid (HCl), which is essentially a solution of H+ and Cl (abbreviating the more formal H3O+(aq))
  2. dilute acetic acid, which is essentially a solution of HOAc (i.e. CH3COOH)
  3. very dilute hydrofluoric acid, in which about half the HF remains as HF molecules and half has dissociated into H+ and F.

There are no problems about writing the equations for (i) and (ii). In (i), H+ and OH are the major species which change, giving water. The reaction is as in Equation 12:

H+ + OH H2O   [Equation 12]
In (ii), the major species present which are changed in the reaction are HOAc and OH, and the major species formed are H2O and OAc:
HOAc + OH H2O + OAc [Equation 35]

In (iii), however, both HF and H+ are major species which change as a result of reaction with OH. In such a case (and there are many like it) one may choose either Equation 12 or an equation like Equation 35.

5.3.3 Equations used in tracing quantities

An equation is often used as a basis for calculating quantities of chemicals produced or required in a process. When this is the case it is usually convenient to write the equation in a way which shows the quantities of ingredients.

For example, if an excess of ammonia, in water-solution, from an industrial process is neutralised with sulphuric acid, and the product (ammonium sulphate) sold as a fertiliser, the neutralisation reaction would be as shown in Equation 36, using the abbreviated form for the hydrated proton.

NH3 + H+ NH4+ [Equation 36]
Sulphate is a spectator ion and is present in the solution throughout. After neutralisation the ammonium sulphate would be recovered by evaporation of the water:
2 NH4+ + SO42 (NH4)2SO4(s) [Equation 37]
However, the company carrying out this process is likely to want to know how much sulphuric acid to buy and how much ammonium sulphate will be produced. A form of equation directed to this end would be
H2SO4 + 2 NH3 (NH4)2SO4 [Equation 38]
It is important to recognise that this equation is appropriate only to the special purpose described. For the neutralisation reaction itself, Equation 36 and not Equation 38 is appropriate. If emphasis on the proton-transfer aspect is required this could be shown as in Equation 39.
NH3 + H3O+ NH4+ + H2O [Equation 39]

In your reading you may well see references to such species as “NaOH(aq)”. These references are almost always incorrect. Sodium hydroxide solutions contain hydrated Na+ and OH, and only in very concentrated solutions would NaOH(aq) be present in more than ultratrace concentrations.

5.3.4 Equations with fractional coefficients

Normally an equation containing fractional coefficients should be multiplied through by an appropriate number to clear the fraction. Sometimes, however, there may be a purpose served by not doing so.

For example, the combustion of ethane (C2H6) requires 7 atoms of oxygen for each molecule of ethane. Since oxygen consists of O2 molecules, 7 atoms of oxygen require 3 molecules of oxygen:

C2H6 + 3 O2 2 CO2 + 3 H2O [Equation 40]

Multiplying both sides by 2 gets rid of the fraction, but Equation 40 could be left as it is if, for instance, it was desired to focus attention on a single molecule of ethane or a single mole of ethane as in enthalpy of combustion tables.

5.3.5 Reaction outlines

It is common, especially in organic chemistry, to write an outline that shows the formula of the organic starting material joined to the formula of the desired organic product by an arrow on which is written the formulae of any substances with which the starting material is treated. Conditions such as temperatures and pressures are also sometimes included. The formulae of non-organic products may or may not be included depending on what is to be emphasised.

The conversion of ethanol (C2H5OH) into acetic acid (CH3COOH) using dichromate (Cr2O72) in acid solution provides an example:

  Cr2O72 /H+    
C2H5OH CH3COOH [Equation 41]
It might be desired to represent the fact that heat is required for the reaction to proceed at a convenient rate. Equation 41 becomes
  Cr2O72 /H+    
C2H5OH CH3COOH [Equation 42]
When this reaction occurs the dichromate, which is orange, is converted into chromium(III), Cr3+, which is blue-green. If the reaction is meant as a test for ethanol, with the blue-green colour as the observation to show that the result is positive, the equation might be extended further:
  Cr2O72 /H+        
C2H5OH CH3COOH + Cr3+ [Equation 43]

Equations 41, 42 and 43 are not strictly equations, as the term “equation” implies balance, but are usually referred to as such.