Formulae, Equations and Amount of Substance

Formulae, Equations and Amount of Substance

1. Formulae

2. Formulae of ionic compounds

3. Relative molecular mass

4. Chemical equations

5. Further chemical equations

6. Ionic equations

7. The mole

8. Calculating masses and Mr values

9. Calculating formulae

10. Mass equations

11. Calculations on gas volumes

12. The volumes of gases involved in reactions

13. Quantitative chemistry with solutions

14. Finding an unknown concentration by titration

15. Key words and ideas

16. Questions

17. Marking schemes

1 Formulae

Introduction

Every pure chemical has a formula. Chemical reactions are often described using balanced chemical equations of various types. In order to find out what is the correct formula of a substance, or what is the correct equation to describe a chemical reaction, measurements of the amounts of various substances involved can be made. This booklet is intended to provide an independent learning scheme to help you understand how formulae and equations are decided upon, and how to handle the mathematical methods that are inevitable when measurements have been made. The booklet includes worked examples to show how the methods work and a variety of questions so you can practice the methods for yourself.

The Ar values used are those on the OCR Data Sheet for Chemistry.

Compounds are made of different atoms in fixed proportions

A substance made of one type of atom is called an element. There are currently 115 known elements. However, most of the substances on this planet are made of more than one type of atom, chemically combined together. Such substances are called compounds. ‘Chemically combined’ means that two (or more) different types of atom are bonded (held) to each other by forces called chemical bonds. The different types of atom a compound is made of are always present in set, fixed, proportions. For example, water is a compound of hydrogen atoms and oxygen atoms, and every drop of water contains twice as many hydrogen atoms as oxygen atoms. This is because water is made of small groups of atoms called molecules. One water molecule consists of two hydrogen atoms and one oxygen atom, chemically bonded together. Since every water molecule is made thus, any drop of water (which will contain many billions of molecules) contains twice as many hydrogen atoms as oxygen atoms.

The molecular formula of a compound tells you about the atoms in its molecules

The molecular formula of a compound tells you two things:

• It tells you which elements the compound is made of.

• It tells you how many atoms of each element are in one molecule of the compound.

The molecular formula of water is H2O. The 2 means that one water molecule contains two hydrogen atoms. The lack of a number after the O means that a water molecule contains one oxygen atom.

Question 1

What is the molecular formula of each of the compounds whose molecules are drawn below? (These drawings are called displayed formulae.)

a. b. c. d.

e. C=O f. g.

2 © Cambridge University Press 2005 Formulae, equations and amount of substance

An empirical formula tells you the simplest ratio of the numbers of each type of atom in a compound

Chemists have more than one way to express the formula of a compound. Instead of using a molecular formula, a chemist may describe a compound using an empirical formula. The empirical formula of a compound gives the information about the elements it contains in their simplest ratios. We can take the compound hydrogen peroxide as an example, the molecules of which are H–O–O–H. Its molecular formula is H2O2 but its empirical formula is HO, since the ratio of hydrogen atoms to oxygen atoms is 1:1. For most, but not all, compounds the molecular formula and the empirical formula are the same. For water, for example, both are H2O, and for carbon dioxide both are CO2.

Question 2

Copy and complete the table below.

Name of / Molecule (displayed / Molecular formula / Empirical formula
compound / formula)
Ethane / H / H / C2H6 / CH3
H / H
C / C
H / H
Ethene / H / H
C / C
H / H
Propane
H / H / H
H / H
C / C / C
H / H / H
Propene / H / H
C / C
H / C / H
H / H
Benzene / H
H / C / H
C
C
H / H
C / C
C
H
Phenol / H
H / C / O – H
C
C
H / H
C / C
C
H
Lactic acid / H / H
O
H / C
C / C
O / H
H / OH

[12]

Formulae, equations and amount of substance © Cambridge University Press 2005 3

Many non-metal elements are molecular

The empirical formula of an element is simple. A sample of any element contains one type of atom only, so there is no ratio to calculate. For example, the empirical formula of oxygen is O, sulphur is S and magnesium is Mg.

In a sample of a metal the atoms are packed as individual atoms in a vast array called a lattice, so for a metal the molecular formula is also that of the single atom, e.g. sodium’s is Na.

Many non-metal elements are different, as their atoms form small groups (molecules) held together by chemical bonds. Oxygen atoms bond together to form molecules consisting of two atoms so the molecular formula of oxygen is O2.

Question 3

Copy and complete the table below.

Name of / Molecule (displayed / Molecular formula / Empirical formula
element / formula)
Oxygen / O / O / O2 / O
Nitrogen
N / N
Fluorine / F / F
Hydrogen / H / H
Sulphur / S / S
S / S
S / S
S / S
Phosphorus / P
P
P / P
Iodine / I / I

[12]

Not all non-metal elements have a structure with the atoms in small groups. Both carbon and silicon have their atoms bonded in a lattice, so their formulae are just given as C and Si. The gases helium, neon, argon, krypton, xenon and radon consist of totally independent single atoms not bonded to any other, so their formulae are also given as He, Ne, etc.

The substances whose molecules are drawn on these pages all have a simple molecular structure. The bonds that hold the atoms together within the molecules are covalent bonds. These pages include examples of single, double and triple covalent bonds. The next section discusses compounds held together by a very different type of chemical bond – the ionic bond.

Total: / 31 Score: %

4 © Cambridge University Press 2005 Formulae, equations and amount of substance

2 Formulae of ionic compounds

The particles in some compounds are ions

The compounds whose formulae you have studied on these pages up to now are all covalent compounds with simple molecular structures. Many compounds, however, have their components held together by ionic bonds. Such compounds usually consist of a metal element combined with one or more non-metal elements:

• The metals are present as positive ions – atoms that have lost one or more electrons.

• The non-metals are present as negative ions – atoms or small groups of atoms that have gained one or more electrons.

The positive and negative ions in a sample of the compound do not form a structure consisting of small, distinct groups. The structures formed are vast arrays of ions called giant lattices. The constituent ions are present in fixed proportions, so an ionic compound also has a formula.

Ions can be positive or negative, simple or compound

Most positive ions are simple ions – this means that they consist of single atoms that have lost one or more electrons. Examples of simple ions that you will have come across are the sodium ion, Na+, and the copper ion, Cu2+. The most important exception is the ammonium ion. Each ammonium ion consists of four hydrogen atoms bonded covalently to one central nitrogen atom, and since this group of five atoms has always lost one electron from its constituent atoms it has a single positive charge – a ‘one plus’ charge. The ammonium ion is a compound ion, and is shown as NH4+. The table below includes many of the positive ions whose names and charges you need to know.

Name / Symbol / Charge / Name / Symbol / Charge
Lithium / Li+ / 1+ / Zinc / Zn2+ / 2+
Sodium / Na+ / 1+ / Copper(I) / Cu+ / 1+
Potassium / K+ / 1+ / Copper(II) / Cu2+ / 2+
Magnesium / Mg2+ / 2+ / Cobalt(II) / Co2+ / 2+
Calcium / Ca2+ / 2+ / Iron(II) / Fe2+ / 2+
Barium / Ba2+ / 2+ / Iron(III) / Fe3+ / 3+
Aluminium / Al3+ / 3+ / Tin(II) / Sn2+ / 2+
Hydrogen / H+ / 1+ / Lead(II) / Pb2+ / 2+
Ammonium / NH4+ / 1+ / Manganese(II) / Mn2+ / 2+
Silver / Ag+ / 1+ / Chromium(III) / Cr3+ / 3+

Assignment 1

Learn the table of positive ions above.

• Copy the table onto a blank sheet of paper and fill in the ‘Name’ columns only, using the table.

• Cover this page and complete the ‘Symbol’ and ‘Charge’ columns from memory. Repeat until you get it right every time.

• See if you can still complete the assignment successfully in an hour’s time, and again tomorrow. Put it in your diary to be redone once a week between now and your Module 1 exam. Use a copy of the Periodic Table to help you at first.

• Note that the Group I elements all form simple ions with a 1+ charge, and the Group II elements all form simple ions with a 2+ charge. You could also include rubidium, caesium, beryllium and strontium in the assignment.

Negative ions can also be simple, consisting of single atoms that have gained one or more electrons. However, many important negative ions are compound ions, consisting of small groups of covalently bonded atoms that have gained one or more electrons. There are many different compound negative ions, most of which contain oxygen atoms and some of which contain metal atoms, so metals in compounds are not found exclusively as positive ions. The table below includes many of the negative ions whose charges you need to know.

Name / Symbol / Charge / Name / Symbol / Charge
Fluoride / F– / 1– / Sulphate(VI) / SO42– / 2–
Chloride / Cl– / 1– / Sulphate(IV) / SO32– / 2–
Bromide / Br– / 1– / Thiosulphate / S2O32– / 2–
Iodide / I– / 1– / Nitrate(V) / NO3– / 1–
Oxide / O2– / 2– / Nitrate(III) / NO2– / 1–
Sulphide / S2– / 2– / Manganate(VII) / MnO4– / 1–
Hydroxide / OH– / 1– / Manganate(VI) / MnO42– / 2–
Silicate / SiO32– / 2– / Dichromate(VI) / Cr2O72– / 2–
Carbonate / CO32– / 2– / Chromate(VI) / CrO42– / 2–
Hydrogencarbonate / HCO3– / 1– / Phosphate(V) / PO43– / 3–

Assignment 2

Learn the table of negative ions above, using the method given in Assignment 1. Note that the Group VII elements form simple ions with a 1– charge and the Group VI elements form simple ions with a 2– charge. Note also how the names change, for example from ‘chlorine’ for the element to ‘chloride’ for the ion.

It is essential that you know the charges on these ions and the formulae of the compound ions in order to be able to work out the formulae of ionic compounds.

The amount of plus charge must equal the amount of minus charge in one formula unit of an ionic compound

All ionic compounds consist of positive ions and negative ions arranged in a lattice. The name of the compound gives the positive ion first, e.g. zinc oxide, ammonium carbonate, iron(III) nitrate. Every ionic compound has a formula; the small group of particles represented by the formula is called the formula unit of the compound. For example the formula of common salt (sodium chloride) is NaCl, therefore one formula unit of common salt consists of one sodium ion and one chloride ion.

The formula of an ionic compound tells you the relative amounts of the two types of ion present in one formula unit of the compound. These relative amounts are such that the amount of plus charge and the amount of minus charge in one formula unit are always the same.

Worked examples

1 Zinc oxide The zinc ion is Zn2+. The oxide ion is O2–. One Zn2+ ion has two units of plus charge, one O2– ion has two units of minus charge; these amounts are the same. Therefore for every one Zn2+ ion in the zinc oxide formula unit there is one O2– ion. The formula is ZnO.

2 Ammonium carbonate The ammonium ion is NH4+, the carbonate ion is CO32–. One NH4+ ion has one unit of plus charge, one CO32– ion has two units of minus charge. Therefore for every one CO32– ion in the ammonium carbonate formula unit there are two NH4+ ions. The formula is (NH4)2CO3.

Note the use of brackets in the formula of ammonium carbonate. This is necessary on occasions with compound ions. (NH4)2 means two of the NH4 units. NH42 would cause obvious confusion.

3 Iron(III) nitrate(V) The iron(III) ion is Fe3+, the nitrate(V) ion is NO3–. One Fe3+ ion has three units of plus charge, one NO3– ion has one unit of minus charge. Therefore for every one Fe3+ ion in the formula unit there are three NO3– ions. The formula is Fe(NO3)3.

These three examples are summarised in this table.

Compound / Positive ion / Negative ion / Number of each / Formula of
present / present / to balance charges / compound
Zinc oxide / Zn2+ / O2– / 1 / × Zn2+ and / ZnO
1 / × O2–
Ammonium / NH4+ / CO32– / 2 / × NH4+ and / (NH4)2CO3
carbonate / 1 / × CO32–
Iron(III) nitrate(V) / Fe3+ / NO3– / 1 / × Fe3+ and / Fe(NO3)3
3 / × NO3–
Question 1
What is the formula of each of the following compounds?
a / sodium chloride
b / lithium oxide
c / lead(II) nitrate(V)
d / ammonium dichromate(VI)
e / potassium manganate(VI)
f / potassium manganate(VII)
g / aluminium oxide
h / sodium phosphate(V)
i / copper(I) chloride
j / copper(II) hydroxide
k / iron(III) sulphate(VI)
l / sodium sulphate(IV)
m / calcium carbonate
n / calcium hydrogencarbonate / [14]
Total: / / 14 / Score: / %