Class 9 Science Chapter 9: Atomic Foundations of Matter

In a chemical reaction matter is neither created nor destroyed, so the total mass before equals the total mass after. Proposed by Antoine Lavoisier in 1789.

In an open vessel a gaseous product escapes and the balance appears to lose mass. Sealing the vessel catches the gas, and the reading holds.

Wherever a sample comes from, the elements inside a compound are present in one unvarying proportion by mass and no other. Proposed by Joseph Proust.

Any measurement carries an uncertainty of about one in the last digit, so a small variation in a balance reading is not evidence against a law.

An insoluble solid formed when two solutions react, as barium sulfate appears white when sodium sulfate meets barium chloride.

A beaker of water is weighed with salt added, and weighed again once the salt has dissolved. The solution weighs exactly what the water and the salt weighed before they were mixed. Dissolving therefore changes nothing measurable about the mass. The same holds for all physical changes, as tearing up a weighed sheet of paper also shows.

In the first, the flask is open, so the carbon dioxide produced escapes and the final reading falls short of the initial one. In the second, a balloon is fixed over the mouth of the flask with a thread before the soda is allowed to fall in. The gas inflates the balloon rather than escaping, and the final reading matches the initial one.

In a chemical reaction matter is neither created nor destroyed, so the total mass remains the same before and after. Antoine Lavoisier proposed it in 1789, and it applies to every chemical reaction. It rests on weighings such as the sealed vinegar and baking soda test, where the total mass before the reaction equals the total mass of the products after it.

No. The products of burning are gases, and in an open beaker they escape into the room rather than staying on the balance. Nothing has been destroyed; it has merely left. Repeat the burning in a closed system and the total mass will be found unchanged.

The reactants total $4.0 + 2.92 = 6.92$ g. The products total $1.76 + 0.72 + 4.44 = 6.92$ g. Since the mass of the reactants equals the mass of the products, the Law of Conservation of Mass is obeyed.

Whatever compound two or more elements make between them, they are present in it in one unvarying proportion by mass, and where the sample came from makes no difference. River, borewell or sea — purify the water from any of them. The hydrogen stands to the oxygen as 1 is to 8 by mass, every time; break up 9 g of it and you get 1 g of the one and 8 g of the other.

A compound has a fixed composition: its elements are present in one definite ratio by mass however the sample was obtained. A mixture has no such constraint, since its components may be put together in any proportion whatever. Fixed composition is precisely what distinguishes a compound from a mixture, so the law applies to the one and not to the other.

Yes. The ratio 8 : 2 reduces to 4 : 1, so both students in fact used the same proportion by mass. Their results agree with each other and with the Law of Constant Proportions. The lesson is to reduce a ratio to its simplest form before comparing it with another.

The reaction chosen is one that gives off a gas: vinegar with baking soda produces carbon dioxide together with other substances.

In the first set-up a dry conical flask and a balloon are placed on a balance and the reading is zeroed. About 20 mL of vinegar goes into the flask and about 2 g of baking soda into the balloon, and the initial reading is taken with both on the pan. The soda is then tipped into the flask, and both are returned to the balance. A brisk effervescence follows, and the final reading does not match the initial one.

That looks like a failure of the law, and the second set-up shows it is not. Everything is arranged as before, except that the balloon is fixed over the mouth of the flask with a thread before the soda is allowed to fall in. The effervescence now inflates the balloon rather than escaping, and this time the final reading matches the initial one exactly.

The conclusion is that the total mass of the vinegar and baking soda before the reaction equals the total mass of the carbon dioxide and other substances formed after it. The difference seen in the first set-up arose only because the gas produced escaped from the open flask.

So no chemical reaction brings matter into being, and none destroys any. That is the Law of Conservation of Mass, which Antoine Lavoisier set out in 1789, and no reaction is outside it. One caution goes with any such weighing: a measurement carries an uncertainty of about one in the last digit, so small variations lie within experimental error.

Not long after Lavoisier, Joseph Proust put it that whatever compound two or more elements make between them, they are present in it in one unvarying proportion by mass. Put the other way round, the elements in a compound have fixed proportions whatever its source.

Water is the standard illustration. Draw it from a river, from a borewell, from the sea; purify and analyse each; in every sample the hydrogen stands to the oxygen as 1 is to 8 by mass. So 9 g of purified water from any source whatever decomposes to give exactly 1 g of hydrogen and 8 g of oxygen.

The law goes by three names: the Law of Constant Proportions, the Law of Definite Proportions, and sometimes Proust's Law. A French chemist with a reputation for painstaking measurement, Proust showed that copper carbonate from any source and by any route keeps the same proportions by mass of copper, carbon and oxygen.

An older case makes the same point. Heating the red mineral known as hingula in India and cinnabar in Latin yields mercury and sulfur at about 86.22 and 13.78 per cent by mass, and grinding the two together in that ratio forms the mineral again.

One limit must be stated. The law holds for compounds and not for mixtures, because a mixture may be made up in any proportion at all. Fixed composition is exactly what makes a compound a compound.

The first law lets you check a reaction. Take calcium carbonate at 4.0 g against hydrochloric acid at 2.92 g; out come carbon dioxide at 1.76 g, water at 0.72 g, and calcium chloride at 4.44 g. The reactants total $4.0 + 2.92 = 6.92$ g and the products total $1.76 + 0.72 + 4.44 = 6.92$ g. The two sides agree, so the Law of Conservation of Mass is obeyed.

It also lets you predict. Carbon at 12 g takes up oxygen at 32 g to give 44 g of carbon dioxide, so a single gram of carbon yields $\frac{44}{12}$ g, and 2.4 g of it yields $\frac{44}{12} \times 2.4 = 8.8$ g. In the same way, 20 g of hydrogen reacting completely with 160 g of oxygen must give 180 g of water, since the products must total what the reactants totalled.

The second law works on ratios inside a compound. Sodium chloride holds sodium and chlorine at 23 : 35.5 by mass, so 46 g of sodium needs $\frac{35.5}{23} \times 46 = 71$ g of chlorine.

The method is always the same: scale both sides of the ratio by the same factor. A compound that is 40 per cent sulfur and 60 per cent oxygen has those elements at 2 : 3, so 20 g of sulfur goes with 30 g of oxygen. Carbon monoxide at 3 : 4 puts 12 g of oxygen with 9 g of carbon.

Taken together the two laws describe a great deal and explain nothing. The first says that in every chemical reaction the total mass before equals the total mass after, matter being neither created nor destroyed. The second says that the elements in any compound sit in one fixed ratio by mass, whatever the source of the sample. Both are firm experimental findings. Neither says why nature should behave so, and that gap is what Dalton's theory was proposed to fill. His answer came down to one idea: nothing splits an atom in a reaction; the atoms only change partners, and none is made or lost. See how that covers the first law. If the atoms present after a reaction are exactly the atoms present before, merely grouped differently, then nothing has been added or removed and the total mass cannot change. A rearrangement conserves whatever it rearranges. And see how it covers the second. If a compound is made of atoms joining in some definite grouping. Then each portion of that compound must contain the same kinds of atom in the same numbers, and since each kind of atom has its own mass the ratio by mass must come out the same in every sample. Nothing about where the sample was collected can touch it. So the two laws formed the basis of the theory, and the theory in turn gave them a reason.

A starting assumption taken as given, never proved, and used as ground for what follows. Dalton's theory is built of six.

An electrically neutral entity of more than one atom, capable of independent existence and showing all the properties of that substance.

The force that holds atoms together. It forms because the combined system has lower total energy than the separate atoms, and lower energy means greater stability.

An interaction between atoms through a shared pair of electrons. The pair attracts both nuclei, which is what holds the molecule together.

One shared pair makes a single bond, drawn as one line, as in H—H. Two shared pairs make a double bond, drawn as two lines, as in O=O.

A postulate is a starting assumption taken as given, never proved, and used as the ground on which the rest is built. Dalton held that everything material consists of exceedingly small particles, atoms, and that it is these that take part when substances react. That no reaction splits an atom, makes one or destroys one. That within an element the atoms agree in mass and in chemical behaviour, while across elements they differ in both. That the numbers in which they join to form a compound are small whole ones. And that any given compound always shows the same kinds of atom in the same proportions.

A molecule is an electrically neutral entity consisting of more than one atom, capable of independent existence and showing all the properties of that substance. A molecule of an element forms when atoms of one element combine, as two hydrogen atoms form a hydrogen molecule. A molecule of a compound forms when atoms of different elements combine, as one hydrogen and one chlorine atom form hydrogen chloride. Some elements such as helium exist only as atoms, their atoms being already stable.

An atom is stable with eight electrons in its valence shell, or two where the K shell is the outermost, and an atom falling short of that may share, gain or lose electrons to complete it. Atoms joined have less energy between them than the same atoms had apart, and that deficit is what makes the joined arrangement the steadier one. The force that holds the atoms together is called a chemical bond.

Hydrogen has atomic number 1 and so one electron in its K shell, and since that shell holds two it needs one more to become stable. Two hydrogen atoms therefore share one electron each. The shared pair attracts both the nuclei and makes the molecule stable, and this interaction through a shared pair is called a covalent bond. Since each atom shares one electron, they are joined by a single bond, written H—H.

A chlorine atom has seven valence electrons and needs only one more, so two chlorine atoms share one electron each, giving a single shared pair and hence a single bond, Cl—Cl. With six in its outer shell, an oxygen atom is two short of an octet, so a pair of them each put two into the sharing. That gives two shared pairs, which is a double bond, written O=O.

Hydrogen needs only one electron for a stable configuration while oxygen needs two, so a single hydrogen cannot satisfy an oxygen atom. The difficulty is met by using two hydrogen atoms, each sharing one electron with the same oxygen atom. The molecule formed is represented as $\text{H}_2\text{O}$, which records two hydrogen atoms and one oxygen atom.

The number of atoms of each element is indicated by a prefix system. The first element retains its regular name while the second ends in -ide. The prefixes are mono-, di-, tri-, tetra-, penta- and hexa- for one to six, and mono- is usually omitted for the first element but used for the second. Where a prefix ends in 'o' or 'a' and the element begins with a vowel the last vowel is dropped, giving monoxide and pentoxide, while a prefix ending in 'i' keeps it, giving dioxide and trioxide.

First, when hydrogen is the first element in a formula, no prefix is added before it however many hydrogen atoms there are, so $\text{H}_2\text{S}$ is hydrogen sulfide rather than dihydrogen sulfide. Second, a few binary compounds go by their common names alone: $\text{H}_2\text{O}$ would usually be hydrogen monoxide but is called water. $\text{NH}_3$ is really nitrogen trihydride but is called ammonia.

A postulate is a starting assumption taken as given, never proved, and used as ground for what follows. Dalton's postulates combined the experimental observations of his day and became the basis of modern scientific theory.

He held that everything material consists of exceedingly small particles, atoms, and that it is these that take part when substances react. That no reaction splits an atom, and that none makes one or destroys one. That within one element the atoms agree in mass and in chemical behaviour, while across elements they differ in both. That the numbers in which atoms join to form a compound are small whole ones. And that any given compound always shows the same kinds of atom in the same proportions.

The second postulate accounts for the conservation of mass. If the atoms present after a reaction are exactly those present before, merely regrouped, then nothing has been added or taken away and the total mass cannot change.

The fifth and sixth account for constant proportions. If a compound always contains the same kinds of atom in the same relative numbers, and each kind of atom has its own fixed mass, then the ratio by mass must come out the same in every sample, whatever its source.

Two examples show the atoms surviving. Hydrogen and oxygen combine to form water without the atoms being destroyed or changed into anything else, and burning magnesium in air gives magnesium oxide, showing magnesium atoms combined with oxygen atoms.

An atom is stable with eight electrons in its valence shell, or two where the K shell is outermost. An atom falling short may share, gain or lose electrons to complete that shell. Atoms joined have less energy between them than the same atoms had apart, and that deficit is what makes the joined arrangement the steadier one; what holds them so is a chemical bond.

Where the route is sharing, the result is a covalent bond: an interaction between atoms through a shared pair of electrons. The shared pair attracts both the nuclei, and that attraction is what makes the molecule stable.

Hydrogen has atomic number 1, so one electron in its K shell. That shell holds two, so it needs one more. Two hydrogen atoms share one electron each, forming $\text{H}_2$. Two atoms sharing one electron each are joined by a single bond, drawn as a single line: H—H.

Chlorine has seven valence electrons and so needs one more for a stable configuration. Two chlorine atoms likewise share one electron each, and the shared pair holds them together as Cl—Cl.

Oxygen has atomic number 8 and six valence electrons, so it needs two more to complete its octet. Two oxygen atoms therefore share two electrons each. Joined by two pairs of shared electrons, they are held by a double bond, drawn as two lines: O=O.

Take hydrogen chloride first. Hydrogen has atomic number 1 and so a single electron in its K shell, which needs one more to complete its duplet. Chlorine has atomic number 17 and the configuration 2, 8, 7, so it needs one more to complete its octet.

The counts match neatly. Both atoms need one electron each, so both share one electron each, and a molecule of hydrogen chloride is formed. Since the two atoms bond by sharing electrons, HCl is a covalent compound, and since they share one pair they are bonded by a single bond, written H—Cl.

Water is the more interesting case, because there the counts do not match. Hydrogen needs only one electron, while oxygen with its six valence electrons needs two. So how can oxygen share two electrons with an atom that requires only one?

The answer is to use two such atoms. Two hydrogen atoms each share an electron with one oxygen atom, and between them they supply the two that oxygen wants while each getting the one it wants itself.

That is exactly what the formula records. What results is written $\text{H}_2\text{O}$, the subscript announcing a pair of hydrogens against a single oxygen. The lesson generalises: where the counts do not match, the number of atoms in the formula adjusts until they do.

The name of a covalent compound says how many atoms of each element are in it, and a set of prefixes is what does that work.

Element one keeps whatever it is ordinarily called; element two is given an -ide ending. The prefixes run mono- for one, di- for two, tri- for three, tetra- for four, penta- for five and hexa- for six. The first element normally drops mono-; the second element keeps it.

Two rules handle awkward joins. If a prefix ends with 'o' or 'a' and the element starts with a vowel, the last vowel is dropped, which gives monoxide and pentoxide. If the prefix ends with 'i' it is kept, for the sake of pronunciation, which gives dioxide and trioxide.

Worked through: CO is carbon monoxide rather than monooxide; $\text{CO}_2$ is carbon dioxide rather than monocarbon dioxide; $\text{CS}_2$ is carbon disulfide; $\text{PCl}_3$ is phosphorus trichloride; $\text{SF}_6$ is sulfur hexafluoride; $\text{N}_2\text{O}_4$ is dinitrogen tetroxide rather than tetraoxide. And $\text{N}_2\text{O}_5$ is dinitrogen pentoxide.

Two exceptions remain. Where hydrogen stands first in a formula it takes no prefix at all, whatever its count, which is why $\text{H}_2\text{S}$ is hydrogen sulfide. And a few binary compounds are known only by common names: water would be hydrogen monoxide, and ammonia is really nitrogen trihydride.

A positively charged species formed when an atom loses one or more valence electrons, so that its protons outnumber its electrons. Sodium loses one to become $\text{Na}^+$.

A negatively charged species formed when an atom gains one or more electrons. Chlorine gains one to become the chloride anion $\text{Cl}^-$.

The electrostatic force of attraction between oppositely charged ions, which holds them together. It follows transfer rather than sharing.

The regular, repeating three-dimensional arrangement of oppositely charged ions in an ionic compound. In sodium chloride each ion is surrounded by six of the other kind.

An ion formed when atoms of two or more elements combine, such as sulfate or ammonium. Their names generally do not end in -ide.

Sodium has atomic number 11 and only one electron in its valence shell, which it can lose to attain a stable electronic configuration. Once that electron has gone the atom has 11 protons against 10 electrons, so it is no longer neutral but carries a positive charge. Such a positively charged species is called a cation, and sodium's is written $\text{Na}^+$.

Seven in the outer shell leaves a chlorine atom one short, and taking that one from somewhere else settles it. Having gained that extra electron it acquires a negative charge, and is called the chloride anion, written $\text{Cl}^-$.

An ionic bond is the electrostatic force of attraction between oppositely charged ions, which holds them together. It differs from a covalent bond in that nothing is shared: an electron has been transferred outright from one atom to the other, leaving a cation and an anion, and the bond is simply the pull between their opposite charges.

Ionic compounds usually do not remain as single units but form three-dimensional crystals in which the ions are arranged in a repeating pattern. In sodium chloride each sodium ion is surrounded by six chloride ions and each chloride ion by six sodium ions. This regular, repeating three-dimensional pattern is the crystal structure, and it is represented as a crystal lattice with the ions shown as points or dots.

Magnesium can give two electrons to become $\text{Mg}^{2+}$, while chlorine can take only one to become $\text{Cl}^-$. One chloride ion therefore takes up only half of what magnesium sheds, so two chloride ions are needed for every magnesium ion, and the compound is $\text{MgCl}_2$.

Sulfur has six electrons in its outer shell and needs two more to complete its octet, becoming $\text{S}^{2-}$. Sodium has one valence electron to give and becomes $\text{Na}^+$. Since each sodium can supply only one electron, two sodium atoms are needed for one sulfur atom, so two $\text{Na}^+$ ions combine with one $\text{S}^{2-}$ ion to give $\text{Na}_2\text{S}$.

Put the cation's name down first and the anion's after it, and give a simple anion an -ide ending. Generally metals form cations and non-metals form anions, so ionic compounds generally arise when a metal combines with a non-metal, as in sodium chloride, calcium oxide and magnesium sulfide. Polyatomic ions, formed from atoms of two or more elements, generally do not take the -ide ending.

Because the compound does not exist as separate units. In a sodium chloride crystal each sodium ion is surrounded by six chloride ions and each chloride ion by six sodium ions, so no ion has a partner of its own. The formula NaCl therefore records that the two kinds of ion are present in equal numbers, rather than naming a pair that exists as a unit.

Begin with the rule that decides the route. If the valence shell of an atom has fewer than four electrons, it would generally donate those electrons to achieve a stable electronic configuration, while an atom with more than four usually gains or shares electrons to complete its octet.

Sodium has atomic number 11 and only one electron in its valence shell, so it is a donor. Losing that electron leaves it with 11 protons and 10 electrons, so it is no longer neutral but positively charged. Such a species is a cation, written $\text{Na}^+$.

Chlorine has seven valence electrons, so it is a receiver. Gaining one electron from another atom completes its octet and leaves it negatively charged. It is then the chloride anion, written $\text{Cl}^-$.

Cations and anions are together called ions. Once these two have formed, they are bound together by electrostatic attraction arising from their opposite charges, and that force is what is called an ionic bond.

The whole sequence is written $\text{Na} + \text{Cl} \rightarrow \text{Na}^+ + \text{Cl}^- \rightarrow \text{NaCl}$: transfer first, attraction second.

Notice what has not happened. No pair of electrons is shared here at all, which is what distinguishes this bond from a covalent one, and no proton has moved, which is why the ion is still sodium.

An ionic compound rarely sits about as separate units. It builds crystals in all three directions, the same arrangement of ions repeating over and over.

Sodium chloride is the standard case. In its crystal each sodium ion is surrounded by six chloride ions, and each chloride ion is surrounded by six sodium ions. These oppositely charged ions are arranged in a regular, repeating three-dimensional pattern, and that arrangement is known as the crystal structure.

To make the arrangement easier to picture, the crystal structure is represented as a crystal lattice, with the ions depicted as points or dots. Such a diagram is a map of where the ions sit rather than a picture of the ions themselves.

One consequence is worth drawing out. Since every ion is surrounded by six of the opposite kind, no sodium ion has a chloride partner of its own. The formula NaCl therefore records a ratio, saying that the two kinds of ion are present in equal numbers, rather than naming a pair that exists as a unit.

The reason for the pattern lies in the nature of the bond. An electrostatic attraction is not satisfied by a single partner: every ion attracts every oppositely charged ion near it, so the ions pack together as closely as their charges allow, and the repeating arrangement is what results.

An ionic compound as a whole carries no charge, so the total positive charge contributed by the cations must exactly balance the total negative charge contributed by the anions. That single requirement fixes the ratio in which the two ions combine.

Take sodium chloride. Sodium gives one electron to become $\text{Na}^+$ and chlorine takes one to become $\text{Cl}^-$. One of each balances, so the formula is NaCl.

Now magnesium chloride. Magnesium gives two electrons to become $\text{Mg}^{2+}$, while chlorine can take only one to become $\text{Cl}^-$. A single chloride ion takes up only half of what magnesium sheds, so two chloride ions are needed for every magnesium ion, and the formula is $\text{MgCl}_2$.

The reverse case is sodium sulfide. Sulfur has six outer electrons and needs two, becoming $\text{S}^{2-}$, while each sodium can supply only one. Two sodium atoms are therefore needed for one sulfur atom, giving $\text{Na}_2\text{S}$.

And where the two valencies match, no multiplying is needed at all: magnesium gives two and sulfur takes two, so magnesium sulfide is simply MgS.

The method is always the same. Find the charge each ion carries, then choose the smallest numbers of each that make the totals cancel.

To name an ionic compound, put the cation's name down first and the anion's after it, giving a simple anion an -ide ending. Generally metals form cations and non-metals form anions, so ionic compounds generally arise when a metal combines with a non-metal, as with sodium chloride, calcium oxide and magnesium sulfide.

The common monoatomic cations fall into three groups by valency. At valency 1 are sodium $\text{Na}^+$, lithium $\text{Li}^+$, potassium $\text{K}^+$, silver $\text{Ag}^+$ and cuprous copper $\text{Cu}^+$. At valency 2 are calcium $\text{Ca}^{2+}$, barium $\text{Ba}^{2+}$, ferrous iron $\text{Fe}^{2+}$, cupric copper $\text{Cu}^{2+}$, magnesium $\text{Mg}^{2+}$ and zinc $\text{Zn}^{2+}$. At valency 3 are ferric iron $\text{Fe}^{3+}$ and aluminium $\text{Al}^{3+}$. Iron and copper each appear twice, with different valencies.

The common monoatomic anions are fluoride, chloride, bromide and iodide at valency 1, and oxide and sulfide at valency 2. Every one of those six names ends in -ide.

Where an ion is built out of atoms drawn from several elements at once, it is called polyatomic. Their names generally do not end in -ide. Hydroxide, nitrate, hydrogencarbonate and ammonium have valency 1, while carbonate and sulfate have valency 2. Ammonium is the only positively charged ion among them.

Write the symbols, write the valencies or charge numbers beneath them, then cross each over to become the other's subscript.

A chemical formula gives the simplest ratio of the elements present, so subscripts obtained by crossing over are divided by any common factor.

The positive and negative charges in an ionic compound must balance exactly, so that the overall structure is neutral. That is what the crossing over achieves.

Used when two or more polyatomic ions of the same type appear. $\text{Al(OH)}_3$ means three hydroxide ions; $\text{AlOH}_3$ would mean something else entirely.

Where a valency comes out as one after criss-crossing, that subscript is simply not written. HCl carries no ones.

First write the symbols of the constituent elements. Second write their valencies beneath them. Third, swap each atom's valency onto the other symbol and set it there as a subscript. For hydrogen sulfide, hydrogen has valency 1 and sulfur 2, so sulfur's 2 crosses to hydrogen and hydrogen's 1 crosses to sulfur where it is dropped, giving $\text{H}_2\text{S}$.

First write the symbol of the cation followed by that of the anion. Second write the charges under the symbols rather than as superscripts. Third cross over the charges, taking only the numbers. Fourth, since a chemical formula gives the simplest ratio of the elements, divide the subscripts by a common factor if there is one.

Calcium is $\text{Ca}^{2+}$ and chloride is $\text{Cl}^-$, so crossing the numbers gives a 2 on chlorine and a 1 on calcium, which is not written. The formula is $\text{CaCl}_2$, meaning two chloride ions for each calcium ion. The reason is that the positive and negative charges must balance each other so that the overall structure is neutral.

They must be reduced when they share a common factor, because a formula gives the simplest ratio. Magnesium oxide crosses over to $\text{Mg}_2\text{O}_2$, and both subscripts divide by 2, so it is written MgO. Aluminium oxide crosses over to $\text{Al}_2\text{O}_3$, and since 2 and 3 share no factor nothing is reduced and the formula stands as it is.

Brackets are used when two or more polyatomic ions of the same type appear in a formula, and are not required when only one is present. Magnesium hydroxide has two hydroxide ions for each magnesium ion and so is written $\text{Mg(OH)}_2$. Calcium carbonate has only one carbonate ion and so is written $\text{CaCO}_3$ without brackets.

OH inside a bracket with 3 after it says that one aluminium ion is holding three hydroxides. Written as $\text{AlOH}_3$ the subscript would attach to the hydrogen alone rather than to the whole hydroxide group, which would describe something quite different.

Sodium hydrogencarbonate is $\text{NaHCO}_3$, since both ions carry a single charge. Sulfur dioxide is $\text{SO}_2$. Ferric chloride is $\text{FeCl}_3$, since ferric iron carries three positive charges against chloride's one. Cuprous oxide is $\text{Cu}_2\text{O}$, since cuprous copper carries one positive charge against oxide's two negative.

The first is $\text{Fe(OH)}_3$, since three hydroxide ions are needed to balance three positive charges, and brackets are used because the group is repeated. The second is $\text{K}_2\text{CO}_3$, since two potassium ions are needed to balance two negative charges, and no brackets are required because only one carbonate ion is present.

Formulae can be written by finding the number of electrons shared or transferred, but there is a quicker route, and it takes three steps.

First, write the symbols of the constituent elements of the compound. Second, write the valencies of those elements underneath. Third, swap each atom's valency onto the other symbol and set it there as a subscript.

A small rule attaches to that third step: a subscript of one is left off after the swap.

Hydrogen chloride comes first. Hydrogen has valency 1 and chlorine has valency 1. Crossing over would give a 1 on each, and since ones are not written the formula is simply HCl.

Hydrogen sulfide is next. Hydrogen has valency 1 and sulfur has valency 2. Sulfur's 2 crosses to hydrogen, and hydrogen's 1 crosses to sulfur where it is dropped. The formula is $\text{H}_2\text{S}$.

Carbon tetrachloride is the third. Carbon has valency 4 and chlorine has valency 1. Carbon's 4 crosses to chlorine and chlorine's 1 crosses to carbon and is dropped, giving $\text{CCl}_4$, a formula whose name announces the four chlorine atoms it contains.

The pattern to notice is that the larger the valency of one element, the more atoms of the other are needed, which is just what combining capacity means.

Four steps are involved.

First, let the cation's symbol lead, with the anion's coming after it. Second, write the charges under the symbols rather than as superscripts. Third, cross over the charges, taking only the numbers, to obtain the formula. Fourth, a formula is meant to show the elements in their lowest terms, so take out any common factor the subscripts share.

One note applies throughout: a compound's formula carries no sign of what charges its ions bore.

Calcium chloride shows the first three steps. Calcium is $\text{Ca}^{2+}$ and chloride is $\text{Cl}^-$, so the 2 crosses to chlorine and the 1 crosses to calcium, where it is dropped, giving $\text{CaCl}_2$. There are therefore two chloride ions for each calcium ion. The reason is that the two kinds of charge have to cancel exactly, leaving the whole thing without any.

Magnesium oxide shows why the fourth step exists. Magnesium is $\text{Mg}^{2+}$ and oxide is $\text{O}^{2-}$, so crossing over gives $\text{Mg}_2\text{O}_2$. That formula balances the charges perfectly well, but it is not the simplest ratio, so both subscripts are divided by 2 and it is written MgO.

Aluminium oxide shows the opposite case. Crossing $\text{Al}^{3+}$ with $\text{O}^{2-}$ gives $\text{Al}_2\text{O}_3$, and since 2 and 3 share no common factor nothing is reduced.

The criss-cross method works for compounds of metals with polyatomic ions just as it does for simple ones, provided the polyatomic ion is treated as a single unit that crosses over whole.

Magnesium hydroxide shows the point. Write the cation $\text{Mg}^{2+}$ first and then the anion $\text{OH}^-$, and criss-cross the numbers only. Two hydroxide ions are needed for each magnesium ion, and the formula is $\text{Mg(OH)}_2$.

The rule it illustrates is that brackets go in whenever a formula carries more than one polyatomic ion of the same kind, and are left out when there is only the one.

Calcium carbonate is the case where they are not needed. Calcium is $\text{Ca}^{2+}$ and carbonate is $\text{CO}_3^{2-}$, so crossing over gives $\text{Ca}_2(\text{CO}_3)_2$, which reduces since the valencies are the same. Written as $\text{CaCO}_3$ it carries only one carbonate ion, so the brackets go too.

Aluminium hydroxide shows why brackets matter rather than merely tidying. The bracket around OH with a subscript 3 indicates three hydroxide ions bound to one aluminium ion. It is $\text{Al(OH)}_3$ and not $\text{AlOH}_3$, because without the bracket the subscript would attach to the hydrogen alone.

Aluminium sulfate combines everything: $\text{Al}^{3+}$ with $\text{SO}_4^{2-}$ crosses over to $\text{Al}_2(\text{SO}_4)_3$, with brackets because the sulfate group repeats three times.

Ferric hydroxide first. Ferric iron is $\text{Fe}^{3+}$ and hydroxide is $\text{OH}^-$. Crossing the numbers gives three hydroxide ions for each iron ion, and since the group repeats the formula takes brackets: $\text{Fe(OH)}_3$.

Potassium carbonate next. Potassium is $\text{K}^+$ and carbonate is $\text{CO}_3^{2-}$. Crossing over gives two potassium ions for each carbonate ion, and since only one carbonate ion is present no brackets are needed: $\text{K}_2\text{CO}_3$.

Ammonium sulfate is the interesting one, because both ions are polyatomic. Ammonium is $\text{NH}_4^+$ and sulfate is $\text{SO}_4^{2-}$, so two ammonium ions are needed for each sulfate ion. The repeated group is the ammonium, so it takes the brackets: $(\text{NH}_4)_2\text{SO}_4$.

Cuprous oxide last. Cuprous copper is $\text{Cu}^+$ and oxide is $\text{O}^{2-}$, so two copper ions balance one oxide ion, giving $\text{Cu}_2\text{O}$. The name matters here: cupric copper would give CuO instead.

What all four share is a single requirement. The compound must come out with no charge overall, and every step of the method exists to secure that: crossing over balances the charges, reducing removes any needless multiple, and brackets make sure a subscript counts whole ions rather than single atoms.

Ionic compounds dissolve in water but not in kerosene or petrol. Most covalent compounds do the opposite, dissolving in those solvents but not in water.

Its ions are held in fixed positions by strong forces. Conduction needs ions that are free to move, which dissolving in water provides.

Sugar dissolves readily in water yet supplies no ions to the solution, so the bulb stays dark. Solubility alone does not make a conductor.

The total mass of a molecule, found by adding the atomic masses of every atom in its formula. It applies only where molecules exist.

In an ionic compound the simplest whole number ratio of ions is a formula unit, and the sum of the atomic masses in it is the formula unit mass.

Sodium chloride and copper sulfate behave as ionic compounds usually do: water takes them up, while kerosene or petrol leaves them untouched. Most covalent compounds, such as camphor and naphthalene, show the opposite pattern: insoluble in water but soluble in kerosene and petrol.

In the solid its ions are held in fixed positions by strong forces, and since nothing charged can move, no current can flow. To conduct electricity the ions must be free to move, and that happens once the compound is dissolved in water, so the solution conducts while the solid does not.

Conduction requires free ions, not merely a dissolved substance. Sugar is a covalent compound, and although it is soluble in water it does not provide ions in solution, so there is nothing to carry the current and the bulb stays dark.

An ionic compound would, because melting frees its ions from the fixed positions they occupy in the solid, and free ions can carry a current. A covalent compound would not, since it has no ions for melting to release.

Ionic compounds generally have high melting and boiling points, because of the strong attractions between their ions, which take a great deal of energy to overcome. Covalent compounds usually have low melting and boiling points by comparison.

With two valence electrons M loses them to become $\text{M}^{2+}$, while oxygen with six valence electrons gains two to become $\text{O}^{2-}$. The charges match, so the formula is MO. A metal combining with a non-metal by transfer gives an ionic bond, and the aqueous solution conducts electricity because dissolving frees the ions to move.

Molecular mass is the total mass of a molecule, found by adding the atomic masses of all the atoms that make it up. Formula unit mass adds together the atomic masses of every atom in one formula unit, a formula unit being the collection of the simplest whole number ratio of ions. Both terms are needed because ionic compounds form three-dimensional crystals rather than molecules, so no molecule of them exists to be weighed.

Work the bracket first. One nitrate group is $14 + (16 \times 3) = 14 + 48 = 62$ u. There are two such groups, giving $62 \times 2 = 124$ u. Adding calcium's 40 u gives a formula unit mass of 164 u.

Samples of camphor, sodium chloride, copper sulfate, sugar and naphthalene are taken, and each is tried separately in water, kerosene and petrol. For the second part, two carbon or metal electrodes are fixed through holes in a piece of cardboard and connected to a 9 V battery and a bulb, and each sample is tested first as a solid and then dissolved in water.

Safety matters here. The electrodes must not be touched while connected to the battery, a low voltage battery is used to avoid the risk of shock, and kerosene and petrol are both flammable.

The solubility results divide the samples in two. Ionic compounds such as sodium chloride and copper sulfate are generally soluble in water but insoluble in kerosene and petrol, while most covalent compounds such as camphor and naphthalene are insoluble in water but dissolve in those two solvents.

The conductivity results divide them again, and in the same way. Solid, an ionic compound will not carry a current, its ions being pinned where they stand by strong forces; carrying a current asks that the ions be able to travel. Dissolving in water frees them, so those solutions do conduct.

The covalent samples never conduct. Sugar is soluble in water but provides no ions in solution, while camphor and naphthalene neither dissolve nor supply ions.

One further difference completes the picture: ionic compounds generally have high melting and boiling points from strong inter-ionic attractions, while covalent compounds usually have low ones.

The requirement for conduction is a single one: charged particles that are free to move. Everything in the topic follows from it.

A solid ionic compound contains plenty of charged particles, since it is made of nothing else. But they are held in fixed positions by strong forces, and a charge that cannot move cannot carry a current. So the bulb stays dark.

Dissolve that same compound in water and the picture changes entirely. The ions are released from their positions and can move through the solution, so the bulb glows. Nothing has been added to the compound; only the freedom of its ions has changed.

The same reasoning answers the question about the molten state. Melting also frees the ions from their fixed positions, so a molten ionic compound conducts as well.

Covalent compounds fail the requirement at the first step rather than the second. Sugar dissolves perfectly well in water, but it does not provide ions in solution, so there is nothing charged to move and no current flows. Camphor and naphthalene do not even dissolve in water, and have no ions in any case.

So a substance that will not conduct as a solid but conducts once dissolved has ionic bonding, and that pair of results is its signature.

For a covalent compound the formula already says which atoms are present and how many of each, so the mass of the molecule is found by simply adding up the masses of those atoms.

Water is the simplest case. With H at 1 u and O at 16 u, its molecular mass is $(1 \times 2) + (16 \times 1) = 18$ u. Carbon dioxide works the same way: with C at 12 u and O at 16 u, its molecular mass is $(12 \times 1) + (16 \times 2) = 44$ u. Notice that a subscript multiplies rather than adds.

But the calculation cannot simply be carried across to ionic compounds, because their ions form three-dimensional crystals and such compounds do not form molecules at all. There is no molecule of sodium chloride whose mass could be taken.

What exists instead is a formula unit: the collection of the simplest whole number ratio of ions. Weigh that set and what you have is the formula unit mass.

Sodium oxide shows it worked: with Na at 23 u and O at 16 u, the formula unit mass is $(23 \times 2) + (16 \times 1) = 62$ u. Where a bracket appears, the group inside must be worked out first and then multiplied. Calcium nitrate gives one nitrate group as $14 + 48 = 62$ u, doubled to 124 u, plus calcium's 40 u, giving 164 u.

The arithmetic is identical throughout. Only the name changes, and it changes because the thing being weighed is different.

Every one of the four results points the same way, and together they identify ionic bonding.

The solubility comes first. Ionic compounds as a rule are taken up by water and left untouched by kerosene or petrol, and that is exactly the pattern the results show. A covalent compound would have behaved the other way about.

The two conductivity results are the signature. As a solid it does not conduct, because its ions are held in fixed positions by strong forces and a charge that cannot move cannot carry a current. Dissolved in water it does conduct, because the ions are then free to move. Notice that this pair of results distinguishes it not only from camphor, which fails both tests, but from sugar, which dissolves and still fails the second.

The melting point completes the case. Ionic compounds generally have high melting and boiling points, because the attractions between their ions are strong and a great deal of energy is needed to overcome them. Covalent compounds usually have low ones.

As for the mass, the molecular mass calculation does not apply. In an ionic compound the ions form a three-dimensional crystal and no molecules exist, so what must be calculated is the formula unit mass: the sum of the atomic masses of all the atoms in the simplest whole number ratio of its ions.

A beaker of water is weighed with salt added, and weighed again once the salt has dissolved. The solution weighs exactly what the water and the salt weighed before they were mixed. Dissolving therefore changes nothing measurable about the mass. The same holds for all physical changes, as tearing up a weighed sheet of paper also shows.

In the first, the flask is open, so the carbon dioxide produced escapes and the final reading falls short of the initial one. In the second, a balloon is fixed over the mouth of the flask with a thread before the soda is allowed to fall in. The gas inflates the balloon rather than escaping, and the final reading matches the initial one.

In a chemical reaction matter is neither created nor destroyed, so the total mass remains the same before and after. Antoine Lavoisier proposed it in 1789, and it applies to every chemical reaction. It rests on weighings such as the sealed vinegar and baking soda test, where the total mass before the reaction equals the total mass of the products after it.

A postulate is a starting assumption taken as given, never proved, and used as the ground on which the rest is built. Dalton held that everything material consists of exceedingly small particles, atoms, and that it is these that take part when substances react. That no reaction splits an atom, makes one or destroys one. That within an element the atoms agree in mass and in chemical behaviour, while across elements they differ in both. That the numbers in which they join to form a compound are small whole ones. And that any given compound always shows the same kinds of atom in the same proportions.

A molecule is an electrically neutral entity consisting of more than one atom, capable of independent existence and showing all the properties of that substance. A molecule of an element forms when atoms of one element combine, as two hydrogen atoms form a hydrogen molecule. A molecule of a compound forms when atoms of different elements combine, as one hydrogen and one chlorine atom form hydrogen chloride. Some elements such as helium exist only as atoms, their atoms being already stable.

An atom is stable with eight electrons in its valence shell, or two where the K shell is the outermost, and an atom falling short of that may share, gain or lose electrons to complete it. Atoms joined have less energy between them than the same atoms had apart, and that deficit is what makes the joined arrangement the steadier one. The force that holds the atoms together is called a chemical bond.

Sodium has atomic number 11 and only one electron in its valence shell, which it can lose to attain a stable electronic configuration. Once that electron has gone the atom has 11 protons against 10 electrons, so it is no longer neutral but carries a positive charge. Such a positively charged species is called a cation, and sodium's is written $\text{Na}^+$.

Seven in the outer shell leaves a chlorine atom one short, and taking that one from somewhere else settles it. Having gained that extra electron it acquires a negative charge, and is called the chloride anion, written $\text{Cl}^-$.

An ionic bond is the electrostatic force of attraction between oppositely charged ions, which holds them together. It differs from a covalent bond in that nothing is shared: an electron has been transferred outright from one atom to the other, leaving a cation and an anion, and the bond is simply the pull between their opposite charges.

First write the symbols of the constituent elements. Second write their valencies beneath them. Third, swap each atom's valency onto the other symbol and set it there as a subscript. For hydrogen sulfide, hydrogen has valency 1 and sulfur 2, so sulfur's 2 crosses to hydrogen and hydrogen's 1 crosses to sulfur where it is dropped, giving $\text{H}_2\text{S}$.