CHM 1101
Introductory
Chemistry

Dawn Fox
Medeba Uzzi
August, 2007
Compiled and edited by Medeba Uzzi

Authors’ Note
This document is an initiative by the authors in an attempt to deal with what they think may be one of the reasons contributing to the relatively high failure rate in the introductory Chemistry course (CHM 1101) at the University of Guyana. It was brought to our attention that many first year students taking CHM 1101 are unable to efficiently cope with the frenetic pace of the
Semester system and even less able to deal comprehensively with the large content in CHM
1101. It is hoped that by providing this paper, students will not need to make lots of notes in lectures and so they can focus on grasping the concepts taught.
The document is meant to be a guide to the topics covered in CHM 1101 and is by no means exhaustive. Students are still required to attend classes regularly and punctually and to engage meaningfully in lectures and tutorials. Further, supplemental reading of these topics in any good
General Chemistry text is expected.
Dawn Fox
Medeba Uzzi

2

SECTION 1 – Modules A – D: section deals with the foundation for chemistry. It introduces students to matter & its classification, Atom & its structure, Periodic table and chemical rxns.
Introduction to Science and Measurement
What is Chemistry? – Chemistry is the study of matter and its transformations
Natural sciences refer to the systematic study of the natural world (our earth, the universe and ourselves). The place of chemistry in the Natural sciences
What is matter?
Matter is anything occupying space and having mass.

Since chemistry is the study of matter there must be a logical way to go about studying nature or we will reap confusion. This is called the Scientific Method. The scientific method is a framework for gaining and organizing knowledge. It usually begins with a question to be answered or a problem to be solved. Consider this question; why do apples fall to the ground? To solve this question we must go through the following steps.
1. Making observations – An observation is something witnessed that can be recorded.
Observations are qualitative (does not involve measurements e.g. colour, texture and taste) and quantitative (involves measurements e.g. temperature, time, speed and length). In making observations we can gather facts. A fact is a singular truth – it has no predictive value e.g. water is a liquid, or water boils at 1000C.
2. Formulating Hypotheses – A hypothesis is a possible explanation for an observation. It needs to be tested to see if it is valid (holds true).
3. Performing experiments – An experiment is a logical, controlled gathering of information to test a hypothesis. This new information will tell the scientist whether or not the hypothesis is valid. That is, whether it is supported by the new information found through the experiments.
NB. Experiments produce new observations - this brings the process back to step 1.

3

When the steps have been repeated many times, eventually a set of hypotheses which agree with the observations is obtained. These hypotheses are assembled into a THEORY or MODEL – a set of tested hypotheses which explain a natural occurrence.
Theories usually change as more information becomes available. Theories have predictive value, that is, they can be extrapolated to other circumstances or situations
As scientists observe nature, they have seen that some observations apply to many different systems. E.g. After studying thousands of chemical reactions, it was observed that the mass before reaction = the mass after reaction. This general observation is expressed as a natural law.
[The law of conservation of mass states that the total mass of materials is not affected by chemical reactions]. Therefore we can say that a law summarises what happens generally and a theory is an attempt to explain why it happens.

Observation
Hypothesis

Apples fall because they are round

Prediction

Round things should fall but square or triangular things shouldn‘t fall

Experiment

Drop round things, square things and triangular things

New observation
Theory: Things fall because they have mass
Theory
(Model)
Prediction

Experiment

Law

Law: All things fall

New
Theory
Chemical properties are properties exhibited as matter undergoes changes in composition e.g. 2Mg + O2 → 2MgO
Physical properties are properties exhibited in the absence of any change in composition e.g. colour, density, hardness, m.p. and b.p
These properties can be further classified as extensive – dependent on the amount of material e.g. volume and mass or intensive – independent of the amount of material e.g. temperature, density, colour and m.p.
NB. All chemical properties are intensive

4

Properties of matter and its classification

Matter
Anything occupying space and having mass

Pure Substances

Mixture

Have a constant composition (e.g.
H2O) that is unchanged by physical processes e.g. boiling/freezing

A dispersion of two or more pure substances that retain their chemical identity. Can separate into compounds by physical changes (e.g. filtration)

Homogenous mixture

Heterogeneous mixture

Have visibly indistinguishable parts
(e.g. solutions)

Have visibly distinguishable parts (e.g. sand and water)

Compound
A chemical combination of two or more pure elements in fixed proportions.
Contains more than one type of atom

Element
Substance that cannot be decomposed into simpler substances by chemical means. Contains one type of atom only

Atoms
Characterized by a specific number of protons

Nucleus

Electrons

Contains protons and neutrons

Negatively charged particles

Protons

Neutrons

Positively charged particles Particles are neutral
(i.e. they have no charge)

5

Electromagnetic Spectrum
Electromagnetic radiation is one of the ways that energy travels through space. We are familiar with some examples of electromagnetic radiation – solar energy travels from the sun to heat and light the world; heat from a fire cooks food and x-rays create pictures of our bones.
All of these forms of energy show wavelike behavior and travel at the speed of light in a vacuum. Waves have three primary characteristics;


Wavelength (λ – lambda) is the distance between two consecutive peaks or troughs in a wave. Wavelength is measured in cm.



Frequency (υ – nu) the number of waves or cycles that pass a given point in space in one second. Frequency is measured in s-1 which is given the special name Hertz (Hz).



Speed (v) is the distance a wave travels in one second. Speed is measured in ms-1.

Wavelength and frequency have an inverse relationship;

λ = 1/υ

and λ υ = constant = speed of light (c) = 2.9978 × 108
The different types of radiation that we are familiar with are classified by their wavelengths or by their frequency. This range is called the electromagnetic spectrum.
Wavelength/m
radiation

10-12

10-10

10-8

Gamma rays X-rays

Ultraviolet

10-6

10-4

10-2

1

102

104

Infrared

Micro waves FM

Short wave AM

Visible spectrum
V I B G Y O R
4×10-7 5×10-7 6×10-7 7×10-7

NB. Energy and mass are not distinct. In fact, energy has mass and atoms show wavelike behavior. This is called the wave-particle duality of matter.

Units and Dimensions
In order to make quantitative observations, measurements are needed. Scientists all over the world have agreed to use specific measures in order to simplify and standardize reporting.

6

The système Internationale (SI); that is International system is a set of units that scientist agreed to use internationally in 1960. The system is still being used today; it is based on the metric system and has seven fundamental quantities.
Quantity
mass length time temperature electric current amount of substance luminous intensity

Unit kilogram metre second Kelvin ampere mole candela Symbol kg m s K
A
mol cd All derived units are combinations of the fundamental quantities
Derived quantity area volume density velocity/speed acceleration force pressure work

symbol
A
V ρ v a F p w

derivation length×length = m×m length×length×length = m×m×m

mass/volume = kg/m3 lenght/time = m/s velocity/time = ms-1/s mass×acceleration = kg×ms-2 force/area = kg ms-2/ m2 force×length = kg ms-2×m

SI unit m2 m3 kgm-3 ms-1 ms-2 kg ms-2 kg m-1 s-2 kg m2 s-2

Special name

Newton, N
Pascal, Pa
Joule, J

Prefixes used in the SI system include;
Prefix

Symbol

tera giga mega kilo hecto deka deci centi milli micro nano pico T
G
M k h da d c m µ n p Multiple of base SI unit
1012
109
106
103
102
10
10-1
10-2
10-3
10-6
10-9
10-12

7

Commensurate reporting in significant figures
Rules for determining the number of significant figures in a value
1. All non-zero digits are significant
2. Zeros before the first non-zero digit are not significant
3. Zeros after the last non-zero digit that lie after the decimal point are significant
4. Zeros in the middle of a number are significant.
5. Zeros after the last non-zero digit that lie before the decimal point may or may not be significant. In this case, express the value in scientific notation then every number is significant. 6. Infinite significance is assigned to defined quantities.
7. When adding or subtracting, the final answer cannot have more decimal places than any of the original numbers
8. When multiplying or dividing, the final answer cannot have more significant figures than nay of the original numbers.
Rules for rounding numbers
1. If the digit considered is less than 5, drop it.
2. If the digit considered is more than 5, round up 1.
3. If the digit is 5, round UP for odd numbers and round DOWN for even numbers.
Examples
 8.259 km – 4sf
 0.000661 g – 3sf
 5.2200 m – 5sf
 20.05 g – 4sf
 50,000 cm – 1 or 5sf; in scientific notation: 5×104 – 1sf OR
 7 days in one week – 7 has infinite significance
 3.18 + 0.0059 = 3.19 – (max. number of decimal places is 2)
 4.50 × 0.13 = 0.58 – (max. number of significant figures is 2)

5.0000×104 – 5sf

Report the following numbers to 3sf
1. 5.663105
2. 9.276052
3. 5.035071
Report the following numbers to 4sf
i) 4.7475

ii) 4.7465

8

There is always some uncertainty associated with the use of measuring instruments; here are some rules for determining the uncertainty of a measurement and; the accuracy of a value determined via the computation of measured values.
Taken from ―Notes on Estimating the Accuracy of a Measurement‖ © 2001 Alfred Bhulai

1.

The assigned accuracy of an instrument is one half the unit of the smallest graduation. 2. Make your measurement and write it down to the nearest half of the unit of the smallest graduation (e.g. 40.0 ± 0.5 mm). The ± part is termed the absolute uncertainty. NB. It is by no means absolute but it serves to distinguish it from relative uncertainty.
3. Calculate the relative uncertainty. The relative uncertainty is often calculated in percent and is given by (AU/value) × 100%. (e.g. 40.0 ± {0.5/40.0 ×100%} = 40.0 ± 1.25%)
4. Absolute uncertainty can be determined from the relative uncertainty in the following manner; (RU/100%) × value.
(e.g. 40.0 ± 1.25% = {1.25%/100% × 40.0} = 40.0 ± 0.5 mm)
5.

When adding or subtracting measurements, their absolute uncertainties are added.

6.

When multiplying or dividing measurements, their relative uncertainties are added

7. If the dimensions of the thing to be measured are too small to be adequately resolved by the instrument, try measuring a large number of them; then simply divide the readings of the large number of objects by that large number such that an average reading for each object is found. When taking such an average, the absolute uncertainty is treated in the same way as the measured value and so the relative uncertainty remains constant.
(e.g. one hundred little beads of lead placed in a measuring cylinder of water raises the level of water by 14.5 ± 0.5cm3. The average volume of a lead bead is therefore;
(14.5 cm3 ÷ 100) ± (0.5 cm3 ÷ 100) = 0.145 ± 0.005 cm3.
This quantitative treatment of uncertainties dates back to the “Fehlerrechnung” of the
German mathematician, C.F. Gauss. The reasons for the procedures involve statistics and the calculus and are outside the scope of elementary courses. The simple treatment here is meant to be handy. Don‟t run away with the idea that this is all there is to it.
Truth is hard to measure.

9

Historical development of the Atomic theory; Electron configuration
Experiment

Observation

Inference

Priestlgy (1733-1804) isolated oxygen; Laoisier showed its importance to combustion. He combusted H2 (g) to form H2O
H2 (g) + ½O2 (g) → H2O(l)
Joseph Proust (1754-1826) measured the elemental mass composition of compounds using various samples

The mass of water formed = the mass of H2 and O2 consumed

Law of mass conservation
Mass is neither created nor destroyed in chemical reactions

Elements do not combine chemically in random proportions.
E.g. every sample of H2O had 1 part H2 and 8 parts O by mass

Law of definite proportions
Different samples of a pure chemical substance always contain the same proportion of elements by mass.
Dalton‘s Atomic theory
1. Elements are made up of tiny particles called atoms
2. Each element is characterized by the mass of its atoms; all atoms of same element have same mass but atoms of different elements have different masses 3. Chemical combination of elements to make different substances occurs when atoms join together in small whole number ratios
4. Chemical reactions only rearrange the way the atoms are combined. The atoms themselves are not changed.

1. An electric current flows through the tube from – to +
2. If the tube is not properly evacuated, the flowing current is visible as a ray called ― cathode rays‖
3. If the anode has a hole, the ray passes right through it and is visible as a bright spot of light

Cathode rays consist of negative particles called electrons

Dalton (1760-1844) studied the laws of mass conservation and definite proportions and tried to explain them with a theory.

Dalton‘s theory was used to predict the Law of Multiple Proportions
If two elements combine in different ways to form different substances, the mass ratios are small whole number multiples of each other.
J. J. Thompson (1856-1940) used cathode ray tubes; and applied a high voltage across the electrodes

Other scientists (1890s) brought magnets or electrically charged plates near the cathode ray tube
Different metals used as cathode

The cathode ray can be deflected toward a + plate

All different substances must contain electrons Substance must also contain + particles because matter is neutral
Thomson: Deflection of electron beam departed on;
1. strength of magnetic or electric field
2. size of the –ve charge on the electron
3. mass of electron

Cathode rays still produced

10

Thomson measured deflection buy electric and magnetic fields
Milliken (1868-1953) performed the
Oil drop experiment to determine the mass of an electron
Ernest Rutherford (1871-1937) searched for the positive particles.
He used alpha particles (from radioactive substances) and performed the gold foil experiment.
He knew that the particles were
+vely charged, had a magnitude of
2× the charge on an electron and were 7000 times heavier
During 1912-1930 Rutherford did further experiments. Chadwick also did similar scattering experiments.
He bombarded Be metal with alpha particles. Constant value for charge to mass ratio Charge ona oil drop was a small whole number multiple of e e = 1.602 177 × 10-19 C
Almost all particles passed through the gold foil undeflected, but a very small number were deflected at large angles

e/m = 1.758 819 × 108 C/g

Produced a very penetrating radiation which ionized Hydrogen gas The nucleus has neutral particles called neutrons that are similar in mass to the proton. Comparison of subatomic particles
Particle
Mass electron 9.109 390 × 10-28 g 5.485 799 × 10-4 amu
1.672 623 × 10-24 g 1.007 276 amu
Proton
1.674 929 × 10-24 g 1.008 664 amu neutron Mass number
M=N+Z

23

Therefore the mass of the electron is
1.602 177 × 10-19 C = 9.109×10-28 g
1.758 819 × 108 C/g
1. The atom was mostly empty space
2. Its mass is concentrated mostly in a tiny central core called the nucleus
3. Nucleus must be positively charged

Charge
-1.602 177×10-19 C
+1.602 177×10-19 C
0

-1
+1
0

Symbol: Sodium

Na

Atomic number or Proton no.
Z = # of protons
Z = # of electrons for a neutral atom Isotopes are atoms with the same number of protons (therefore atoms of the same element) but different number of neutrons. E.g.
Protium

Deuterium

Z = 1; M = 1; N = 0

Z = 1; M= 2; N = 1

Tritium

Z = 1; M = 3; N = 2

11

Radioactivity
Certain isotopes have unstable nuclei. The nuclei breakup (decay) spontaneously with the emission of certain types of radiation. This type of decomposition is a nuclear reaction which is different from a chemical reaction.

Nuclear reactions
Atom‘s nucleus changes producing a different element Different isotopes behave differently in nuclear reactions Rates of reaction are not affected by T, P or catalysts Energy change is very large

Chemical reactions
Only the outer-shell electron configuration of the atom changes; no new elements produced.
Different isotopes behave the same way in chemical reactions
Rates of reaction are affected by T, P and catalysts Energy change is relatively small
(106 times smaller than energy changes in nuclear reactions).

Types of Radiation/Nuclear emission
Process
Alpha radiation Beta radiation Gamma radiation Electron capture Positron capture Nature of particle He2+ nucleus

Symbol
4

2He

electron

0

-1β

Relative charge +2

Example of alpha emission:

238
92U

0
-

Electric field deflection A few sheets low of paper
A few mm of high plastic or Al
A few cm of lead
-

+1

→

0

-

high energy γ em radiation p → n by capturing e0
A positive
1e
electron

-1
0

or 0-1e

Relative mass 4

0

-

4

2He

+

Penetration

-

234
92Th

NB. Equation must be balanced by both mass and charge.

12

Electronic Structure and Quantum numbers
Q. How are electrons arranged in the atom? A. Electrons are arranged in atoms in energy levels.
The first evidence of this theory came from spectroscopy experiments. Spectroscopy is the study of how light and matter interact. We need to first understand the nature of light.
Wave-particle duality of light
Two models have been used to accurately describe the behaviour of light
1. Wave model

2. Particle model

It was found that one of them alone cannot accurately describe the behaviour, hence the theory, that light possesses both wave and particle characteristics, was accepted.
Wave characteristics
Particle characteristics
Different kinds of radiation have different Max Planck (1900) and Albert Einstein (1905) characteristics found that light is quantized; it is a stream of tiny packets of energy called photons.
All have the same speed in a vacuum
Energy of photons is linked fto frequency and
8
-1
(c = 2.99 × 10 ms ) hence to wavelength.
E=hc/λ
E=hυ
Frequency (υ) = # of cycles in 1 s h – Planck‘s constant (6.626 × 10-34 J/s) c=λυ Atomic spectra
Excitation: when electrons in atoms gain energy (from radiation/heat etc.) they get excited. The electrons move to higher energy levels than they occupy normally.
Relaxation: the electrons eventually ‗give off‘ the extra energy and return to their ―ground state‖ arrangement. They frequently emit radiation to lose the extra energy. We can analyse the emitted radiation by passing it through a prism or diffraction grating to give a series of (coloured) lines known as an emission spectrum – atomic emission spectrum.

Observation: When white light is passed through a prism we get a continuous spectrum i.e. all wavelengths are represented but when emitted radiation is diffracted, only specific lines are seen; a line spectrum is produced.
Reason: Atoms can only emit radiation of specific energies.

13

The sequence of lines in a line spectrum is characteristic of each element and can be used to identify the element. Hydrogen was studied first. Johann Balmer (1885) discovered a pattern to describe line spectra. Upon relaxation four lines were seen.
Wavelength
Color
Energy level

656.3 nm red n=3

486.1 nm green n=3

434.0 nm blue n=3

410.0 nm
Indigo
n=3

He used trial and error techniques to calculate the λ of all four lines with;
1/λ = R [¼ -1/n2]

where n > 2

and

R = Rydberg constant = 1.097 × 10-2 nm-1

Other researchers discovered similar series in the no-visible region of the electromagnetic spectrum; Lyman Series (for UV0; Paschen/Brackett Series
Rydberg adapted the Balmer equation to a form which related λ and n for all series.
1/λ = R [1/m2 -1/n2] where n > m m – level of ground state
E.g. If m = 2; then m2 = 4

Rydberg Equation n – level of excited state

and

hence we have the Balmer series

Electronic configuration
The region in space where an electron is most likely to be found is called an orbital. These orbitals can be described by three quantum numbers


n = principal quantum number: describes the size and energy level of the orbital. As n increases, distance from the nucleus and energy level of the orbital increases. n is a positive integer {n = 1, 2, 3…}



l = angular momentum quantum number: describes the 3-D shape of the orbital l has values from 0 to n-1
(e.g. if n = 1, l = 0; [one shape] if n = 2, l = 1 and l = 0 [2 shapes]) – Therefore for the nth level there are n different orbital shapes.
Letter names are assigned to these shapes

l=0

l=1

l=2

l=3

l=4

s

p

d

f

g

14



ml = magnetic quantum number: defines the different orientations in space that an orbital of a given shape may assume. ml takes values from – l through 0 to +l.
e.g. if l=2, ml = -2, -1, 0,+1, +2 – So for any shape of orbital there are (2l +1) orientations
Summary

n

l

ml

Orbital notation Sub-orbitals
(# of orbitals of this type)

Total # of orbitals in level

Each sub orbital can accommodate two electrons. These electrons differ from each other by the direction of the ‗spin‘; i.e. they rotate either clockwise or anti clockwise about an axis. The spin quantum number (ms) is used to describe this direction of rotation of electrons (ms = +½ for ↑ and ms= -½ for ↓)
Therefore no two electrons in an atom have the same four quantum numbers – Pauli’s exclusion principle. The electron arrangement that we shall describe for each atom is called the ground state electron configuration (lowest energy). To determine these configurations, we use the Aufbau Principle as a guide: Each atom is „built up‟ by adding the appropriate numbers of protons and neutrons as specified by the atomic number and the mass number and by adding the necessary number of electrons into orbitals in the way that gives the lowest total energy for the atom.

15

Another guide that is employed when determining ground state electron configuration of atoms is Hund’s Rule: Electrons must occupy all the orbitals of a given sublevel singly before pairing begins. These unpaired electrons have parallel spins.

CHM 111 Worksheet # 2 & 3– Nuclear reactions & Electron configuration
1. Fill in the blanks in the chart below, you may round all atomic masses to the nearest whole number
# of neutrons # of electrons
Element
Atomic mass Atomic #
# of protons
Lithium
Oxygen
Chlorine
Calcium
Zinc

2. Balance the following nuclear reactions;
a) 21284Po

→

208
82Pb

+

X

b) 13755Cs

→

137
56Ba

+

Y

c) 2011Na

→

20
10Ne

+

Z

d) 105B

+

1

0n

→

4

2He

+

D

3. Write spectroscopic notation and electron in box diagram for the first 30 elements of the
PT
4. Use your electron in box diagram for the element Cr and identify the electrons that possess the following sets of quantum numbers n = 1, l = 0, ml = 0 and ms = +½ n = 2, l = 1, ml = -1 and ms = +½ n = 2, l = 0, ml = 0 and ms = -½ n = 3, l = 2, ml = +1 and ms = -½
5. Explain what is meant by an atomic orbital
6. Sketch the boundary surface of an s-orbital and a p-orbital
7. Starting with the previous noble gas, write the electron configurations of the following ions: a) Fe2+
b) Cl- and
c) Al3+
16

The Periodic Table – periodic trends

The periodic table is arranged in order of increasing atomic number. The earliest founder is
Dmitri Mendelev. Further arrangement includes groups of similar properties and periods of recurring properties.
The outer electron configuration of an atom tells the exact position of that element in the PT.
Tells group

Consider;

1s2 2s2 2p6 3s1

11Na

Tells block
Tells period

Na is therefore found in s – block, period 3, group 1.

13Al

2

2

6

1

1s 2s 2p 3s 3p

Tells period
Highest energy level
13Al

2

Tells group
# of electrons in highest energy levels

Tells block
Outermost occupied orbital

is therefore found in p – block, period 3, group 3

Determine the position of 23V 1s2 2s2 2p6 3s2 3p6 4s2 3d3

17

Periodicity of some chemical and physical properties
Atomic radii are estimated as ½ distance between two identical radii when covalently bonded.
Atomic radii increase down groups (due to electrons occupying larger and larger valence orbitals e.g. H 1s1; Li 2s1; Na 3s1; K 4s1) and decrease across periods (due to increasing nuclear charge – electrons feel a greater attraction to the nucleus since more electrons are added to the same valence shell).
NB. Diagonal relationships exist on account of the trends down a group and across a period e.g. which has the larger atomic radius, O or S?
Metallic character – Metals are hard, lustrous solids which conduct heat and electricity and tend to lose electrons easily. They are usually malleable, ductile and brittle. Metals are found to the left of the PT. Non-metals tend to be gases and liquids (only 5 solids) at room temperature.
They are not lustrous but may be brightly coloured. Non-metals are found to the right of the PT.
Metalloids are elements on either side of the zig-zag boundary between metals and no-metals.
Their properties are intermediate of metals and non-metals. Most are not lustrous but brittle.
They are poor conductors of heat and electricity.

B C N
Al Si P
Ga Ge As
In Sn Sb
Tl Pb Bi

O
S
Se
Te
Po

F
Cl
Br
I
At

Overall there is a gradual shift from metal to non-metal as we move across any row on the PT. Metallic character increases down groups and decreases across periods.

First Ionisation Energy is the energy required to remove one outer orbital electron from the neutral element and form a positive ion. First IE generally decrease down groups (due to electrons being further and further away from nucleus) and increase across periods (due to increasing nuclear charge).
Electronegativity is the ability of an atom to attract electrons to itself. Electronegativity decreases down groups (because atoms get larger, nucleus is more shielded) and increases across periods (due to increasing nuclear charge).
Exercise
Arrange the elements O, S, Cl in order of a) decreasing atomic radii, b) increasing electronegativity and c) increasing first IE.

18

Moles, Stoichiometry and Types of Reactions
One mole of any substance is the amount of substance which contains as many elementary units as there are atoms in 12 grams (exactly) of pure carbon-12.
The Avogadro Constant is the constant of proportionality between amount of substance and number of specified particles of that substance. It is represented by the symbol L, and has a numerical value of 6.023 x 1023; its unit is mol-1. In this context "specified particles" means molecules, atoms, ions, electrons, etc.
The importance of the mole
The mole has not become important by chance. Its importance stems from the following fact. If an element has a relative atomic mass (RAM) of X, one mole of its atoms (i.e. 6.023 x 1023 atoms) will have an actual mass of X grams. i.e. the molar mass is numerically equal to the
RAM. Thus oxygen has a relative atomic mass of 16, and 6.023 x 1023 (one mole) of its atoms has an actual mass of 16g, i.e. a molar mass of 16g.
Note that relative atomic mass and molar mass are not the same thing. However, they are numerically equal. Here are the relevant definitions, plus a definition of relative molecular mass:
The relative atomic mass of an element is the ratio of the average mass of its atoms to 1/12 of the mass of a carbon-12 atom;
The relative molecular mass of a compound is the ratio of the average mass of its molecules to
1/12 of the mass of a carbon-12 atom;
Molar mass is the actual mass in grams of 6.023 x 1023 (one mole of) specified particles of a substance (e.g. atoms of an element, molecules of a covalent compound etc.).
Molarity is a measure of concentration and should not be confused with the pure and simple mole. Nor should it be confused with another measure of concentration, gdm-3
Concentration in gdm-3 is the mass in grams of solute dissolved in 1dm3 of solution.
Concentration in moles dm-3 (molarity) is the number of moles of solute dissolved in 1dm-3 of solution. Note also that a solution with a molarity of 2 (i.e. containing 2 mol dm-3) is also known as a 2 molar, or 2M, solution.

NB. Other topics in this module will be treated in detail in class because of the complexity and working required.

19

SECTION 2 – Modules E – H: This section deals with types of bonding & structures of molecules, description and behaviour of gases, liquids, solutions and solids.

Structure and Bonding
Ionic bonding is the electrostatic attraction between oppositely charged ions which are arranged in a crystal lattice and which are formed by the transfer of electrons from one atom
(giving positive ions) to another (giving negative ions).
NB. We cannot define a single ionic bond in a lattice, because an ion is attracted to all the surrounding (oppositely charged) ions in the lattice.
Metallic bonding is the electrostatic attraction of positive ions (arranged in a lattice) for the mobile electrons surrounding the ions.
A covalent bond between two atoms is the electrostatic attraction of the two nuclei for a shared pair of electrons in a bonding orbital formed by the overlap of two singly occupied atomic orbitals (or, in the case of a dative covalent bond, sometimes known as a coordinate bond, formed by the overlap with a vacant orbital of an atomic orbital containing a pair of electrons).

Van der Waals bonds are very weak forces of electrostatic attraction amongst instantaneous dipoles and induced dipoles.
At a given moment in time, the electron cloud surrounding even an inert gas atom may not be perfectly symmetrical.
Thus one side will carry a relative positive charge and the other a relative negative charge. The separation of charge is called a dipole.
NB. Other topics in this module will be treated in detail in lectures.

20

GASES
Matter exists in three physical states: solids, liquids and gases. Liquids and gases are called fluids because they flow freely. Solids and liquids are referred to as condensed states because they have much higher densities than gases. The table below provides some evidence of this;

Water
Benzene

Density (g/mL)
Solid
Liquid
0.917
0.998
0.899
0.876

Gas
0.000588
0.00255

This data implies that molecules must be far apart in gases and much closer together in liquids and solids. Further, gases are easily compressed and they completely fill any container in which they are present. This tells us that the molecules in a gas are far apart compared to their sizes and that interactions among them are weak. All substances that are gases at room temperature may be liquefied by cooling and compressing them. Volatile liquids are easily converted to gases at room temperature or slightly above. The term ‗vapor‘ refers to a gas that is formed by evaporation of a liquid or sublimation of a solid; it is commonly used when some of the liquid or solid remains in contact with the gas.
The study of gases is important because many important chemical substances are gases, the earth‘s atmosphere is a mixture of gases and particles of solids and liquids. All gases are miscible, that is they mix completely unless they react with each other. Several scientists notably
Torricelli (1643), Boyle (1660), Charles (1787) and Graham (1831) laid an experimental foundation upon which our understanding of gases is based. Their investigations showed that;


Gases can be compressed into smaller volumes.



Gases exert pressure on their surroundings and so pressure must be exerted to confine gases. 

Gases expand without limits.



Gases diffuse into each other.



The amounts and properties of gases are described in terms of temperature, pressure, the volume occupied and the number of molecules present.

21

Pressure
Pressure is defined as force per unit area (e.g lb/in2).
Pressure may be expressed in many different units; the SI unit is the Pascal (Pa) defined as the pressure exerted by a force of one newton acting on an area of one square metre. [1Pa = 1N/m2].
By definition the Newton (N) is the force required to give a mass of one kilogram an acceleration of one metre per second [1N = 1kgms2].
Other units of pressure include;
Unit
Atmosphere

Symbol atm Millimeter mercury
Torr

mmHg torr Equivalent
1 atm = 101,325 Pa
1 atm = 101.325 kPa
1 atm = 760 mmHg
1 torr = 760 mmHg
1 torr = 101,325 Pa

Boyle‘s Law
In the 17th century, Robert Boyle conducted experiments on the behaviour of gases by trapping a sample of gas in a U-tube and allowing it to come to constant temp., he then recorded the volume of the gas and the difference in height of the two Hg columns. Addition of more Hg to the tube increases the pressure by changing the height of the Hg column. As a result the gas volume decreases. Using the results of several such experiments Boyle showed that; for a given sample of gas at constant T, the product (PV) always has the same number.
At constant T, the volume, V occupied by a definite mass of a gas is inversely proportional to the applied pressure, P.

V α 1/p at constant n, T

If a sample of gas at a given T occupies volume V1 then its resulting pressure P1 is related to volume by;

P1V1 = k

If the same sample is then compressed so that its volume changes to V2 then the resulting pressure P2 is related to volume by; P2V2 = k
Therefore;

P1V1 = P2V2 for a given amount of gas at constant pressure.

This form of Boyle‘s law is useful for calculations involving P and V changes.

22

Charles‘Law
About 1800, two French Scientists – Jacques Charles and Joseph Gay-Lussac began studying the expansion of gases with increasing temperature. Their results showed that the rate of expansion with increasing temperature was constant and was the same for all the gases they studied as long as pressure remained constant. Lord Kelvin, a British Physicist noticed that an extension of different temperature-volume lines back to V=0 yields a common intercept at -273.15 0C on the temperature axis. Kelvin named this temperature absolute zero, and since the scale is uniformed,
00C corresponds to 273.15 K. Therefore temp. in unit K = 0C + 273.15
At constant pressure, the volume occupied by a definite mass of gas is directly proportional to its absolute temperature.

V α T at constant n, P

Converting this proportionality to an equality gives V/T = k. If we let subscripts 1 and 2 represent values for the same sample of gas at two different temperatures we obtain;
V1/T1 = V2/T2 for a definite mass of gas at constant pressure.
NB. This expression is only valid when temperature is expressed in K.
Standard Temperature and Pressure
We have seen that both temperature and pressure affect the volumes (and therefore the densities of gases). It is often convenient to choose some standard temperature and pressure as a reference point when discussing gases. Standard temperature and pressure (STP) are, by international agreement, 0 0C (273.15 K) and 1 atm.
Avogadro‘s Law and the standard molar volume
In 1811, Amedeo Avogadro postulated that; at the same temperature and pressure, equal volumes of all gases contain the same number of molecules. Many experiments have demonstrated that
Avogadro‘s hypothesis is accurate to within about ±2%, and the statement is now known as
Avogadro‘s Law.
At constant temperature and pressure, the volume occupied by a gas sample is directly proportional to the number of moles of gas.

V α n at constant P, T.

For two different samples of gas at the same temperature and pressure, the relation between volumes and numbers of moles can be represented as;

V1/n1 = V2/n2 at the same T and P.

NB. The volume occupied by 1 mole of gas at STP is referred to as the standard molar volume.
This volume is nearly constant for all gases and is taken as 22.414 L/mol for an ideal gas.

23

Summary of Gas Laws – The Ideal Gas Equation
An ideal gas is one that obeys Boyle‘s law, Charles‘ law and Avogadro‘s law exactly. Many real gases show slight deviations from ideality, but at normal temperatures and pressures the deviations are usually small enough to be ignored.
We can summarize the behaviour of ideal gases as follows;
Boyle‘s law; V α 1/p at constant n, T
Charles‘ law; V α T at constant n, P
Avogadro‘s law; V α n at constant P, T
Summarizing therefore gives; V α nT/p with no restrictions. Writing this proportionality as an equality gives;
V = R(nT/p); which rearranges to

pV = nRT

This relation is called the ideal gas equation or the ideal gas law where R is the universal gas constant. R has values of 8.314 J K-1 mol-1; 8.314 kPa dm3K-1mol-1 and 0.08206 L atm K-1mol-1.
Dalton‘s Law of Partial Pressures
Many gas samples, including our atmosphere, are mixtures that consist of different kinds of gases. The total number of moles in a mixture of gases is ntotal = nA + nB + nC + … where nA and nB and so on represent the number of moles of each kind of gas present.
Using the ideal gas equation PTotal = nTotal R T

and substituting ntotal = nA + nB + nC + …

V gives PTotal = PA + PB + PC + ……. (constant V and T) PA = nART/V

this is called Dalton‟s

Law of Partial pressures – the total pressure exerted by a mixture of ideal gases is the sum of the partial pressure of each gas. Dalton‘s law is useful in describing real gas mixtures at moderate pressures because it allows us to relate total measured pressures to the composition of mixtures.
We can describe the composition of any mixture in terms of the mole fraction of each component. The mole fraction of component A, χA in a mixture is defined as χA = nA/nT.
NB. χA is a dimensionless quantitiy.
The sum of all mole fractions in a mixture equals 1; that is χA + χB + χC + …. = 1 for any mixture
Recall that χA = nA/nT;

therefore χA = PAV/RT

and so χA = PA/PT

PTV/RT
This equation can be rearranged to give another statement of Dalton‘s Law; PA = χA PT

24

The Kinetic Molecular Theory
The basic assumptions of the kinetic molecular theory for an ideal gas are;
1. Gases consist of discrete molecules of negligible size
2. The gas molecules are in continuous, random, straight-line motion with varying velocities. 3. The collisions between gas molecules and with the walls of the container are elastic
(no net energy gain or loss)
4. Between collisions, the molecules exert no attractive or repulsive forces on one another instead each molecule travels in a straight line with constant velocity.
Kinetic energy (k.e.) is the energy a body possesses by virtue of its motion. It is ½mv2; where m is the body‘s mass (kg) and v is its velocity (ms-1). The assumptions of the kinetic-molecular theory can be used along with the ideal gas equation to relate temperature and molecular k.e. average v = √(3RT/M)
The average kinetic energy of gaseous molecules is directly proportional to the absolute temperature but inversely proportional to the molecular weight of the sample. The average kinetic energies of molecules of different gases are equal at a given temperature. For instance, in samples of H2, He, CO2 and SO2 at the same temperature all the molecules have the same average k.e. but the lighter molecules H2 and He have much higher average velocities than do the heavier molecules CO2 and SO2.
Real Gases – Deviations from ideality
Under ordinary conditions most real gases do behave ideally, their P and V are predicted by the ideal gas laws. However, under some conditions most gases can have pressures and/or volumes that are not accurately predicted by the ideal gas laws. Nonideal gas behaviour is most significant at high pressures and low temperatures i.e. near the conditions under which the gas liquefies.
Johannes van der Waals studied deviations of real gases from ideal behavior. In 1867 he empirically adjusted the ideal gas equation; PidealVideal = nRT

to take into account two

complicating factors:



Reduction of volume in which the molecules livebecause they cannot approach closer than a certain distance due to repulsive forces



V → V-nb

Pressure is reduced due to attractive forces slowing the molecules down and so they cannot collide with as much force, the P is reduced by a factor of

a(n/V)2
25

Including these two factors into the ideal gas equation gives;

P = nRT/(V – nb) - a(n/V)2

This is called the van der Waals equation in which ‗a‘ and ‗b‘ are constants.

26

LIQUIDS
Shearing force – Force exerted in a direction parallel to parallel planes such that adjacent planes tend to slide over each other. For example, if a rectangle is subjected to a shearing force parallel to one side it becomes a parallelogram.
Shear stress – the shearing force divided by the area over which it is acting.
Shear rate – the rate at which the velocity of a fluid under shear changes through its thickness.
Newtonian liquids are liquids in which the viscosity varies with temperature but is independent of shear rate eg. water.
Non-newtonian liquids are liquids in which the viscosity varies with shear rate. There are various types of non-newtonian fluids including; pseudo-plastics (viscosity decreases with increasing shear rate e.g. honey), dilatant fluids (viscosity increases with increasing shear rate
e.g. starch solution) and Bingham solids (materials that show little tendency to flow until a critical stress is reached e.g. toothpaste).

Solutions
Solutions are common in nature and are extremely important in all life processes, all scientific areas and many industrial processes. The body fluids of all forms of life are solutions. Variations in their concentrations, especially those of blood and urine, give physicians valuable clues about a person‘s health.
Solutions include many different combinations in which a solid, liquid or gas acts as either solvent or solute. Usually the solvent is a liquid e.g. sea water is an aqueous solution of many salts and some gases such as CO2 and O2. Carbonated water is a saturated solution of CO2 in water. Examples of solutions in which the solvent is not a liquid include air (a solution of gases with variable compositions), dental fillings (solutions of liquid mercury dissolved in solid metals) and alloys (solid solutions of solids dissolved in a metal). A solution is defined as a homogenous mixture of substances in which no settling occurs.

Dissolution of solids in liquids
The ability of a solid to go into solution depends most strongly on the strength of attraction among the particles making up the solid. The smaller the magnitude of the solute-solute

27

interactions, the more readily dissolution occurs. Less energy must be supplied to start the dissolution process. Nonpolar solids such as naphthalene do not dissolve appreciably in polar solvents such as water because the two substances do not attract each other significantly. This is true despite the fact that solute-solute interactions in solids consisting of nonpolar molecules are much smaller in magnitude than those of ionic solids. Napthalene dissolves readily in nonpolar solvents such as benzene because there are no strong attractive forces between solute molecules or between solvent molecules. These observations help to explain the theory that ―like dissolves like‖. Dissolution of liquids in liquids
Miscibility is the ability of one liquid to dissolve in another. The mixing process is often exothermic for miscible liquids. Polar liquids tend to interact strongly with and dissolve readily in other polar liquids. Methanol, CH3OH; ethanol, C2H5OH; acetonitrile, CH3CN and sulphuric acid, H2SO4 are all polar liquids that are soluble in most polar solvents such as water. Nonpolar liquids that do not react with the solvent generally are not very soluble in polar liquids because of the mismatch of intermolecular forces. However, nonpolar liquids are quite soluble in other nonpolar liquids. The weak London forces between nonpolar molecules (even if they are not similar) are easily overcome therefore when two nonpolar liquids are mixed their molecules just
―slide between‖ each other.

Dissolution of gases in liquids
Based on the previous discussions it is expected that polar gases are most soluble in polar solvents and nonpolar gases are most soluble in nonpolar liquids. Although CO2 and O2 are nonpolar gases they do dissolve slightly in water. CO2 is somewhat more soluble because it reacts with water to some extent to form carbonic acid, H2CO3.
NB.The only gases that dissolve appreciably in water are those that are capable of hydrogen bonding (such as HF), those that ionize (such as HCl, HBr and HI) and those that react with water (such as CO2).

28

Effect of temperature and pressure on solubility
Solubility is defined as the mass of a substance that dissolves in 100 g of water at a given temperature. The solubilities of solids in liquids usually increase as temperatures increase.
Conversely the solubilities of many liquids and gases decrease as temperature increases.
Pressure changes have no significant effect on the solubilities of solids and liquids in liquids.
However the solubilities of gases in all solvents increase as the partial pressures of the gasess increase. For example, Carbonated water is a saturated solution of CO2 in H2O under pressure.
When a can of carbonated beverage is opened, the pressure on the surface of the beverage is reduced to atmospheric pressure, and much of the CO2 bubbles out of solution. Henry‘s Law applies to gases that do not react with the solvent in which they dissolve. It is usually stated as:
The pressure of a gas above the surface of a solution is propotional to the concentration of the gas in the solution (Pgas = kCgas). where Pgas is the pressure of the gas above the solution k is Henry‘s constant that is specific for a given gas and solvent at a particular T.
Cgas is the concentration of dissolved gas expressed as molarity or mole fraction.
NB. The relationship is only valid at low concentrations and low pressures.
Vapour pressure and Raoult’s law
Concept of vapour pressure – due to the equilibrium process between a liquid and its vapour
X(l) ↔ X(v)
At the surface of the surface of the liquid, some particles will possess sufficient energy to escape the liquid phase and enter the vapour phase. The gaseous/vapour particles may lose some energy and some of them condense and return to the liquid. In the process, just above the surface of the liquid, an equilibrium process is set up between the liquid and vapour particles. This equilibrium gives rise to a vapour pressure – the force exerted per unit area by the vapour particles above a liquid onto the surface of the liquid. Vapour pressure is characteristic of the liquid and directly related to the number of particles in the vapour phase. The number of particles that enter the vapour phase depends on the intermolecular forces holding the particles in the liquid state, the temperature, atmospheric pressure and the presence of impurities. Liquids with strong intermolecular forces would have low vapour pressures because the particles would be held strongly in the liquid state.

29

Vapour pressure increases with temperature since at higher temperatures, more particles will possess the required energy to change to the vapour phase. Vapour pressure therefore increases with temperature up to a maximum at the boiling point of the liquid. At this temperature, all the particles have sufficient energy to change to the vapour phase and the equilibrium vapour pressure will be equal to the atmospheric pressure (usually 101.3kPa, 760mmHg or 1 atm). NB.
Above this temperature, all particles will be in the vapour phase and there will be no equilibrium with the liquid phase.
Surface area does not affect vapour pressure since vapour pressure is defined per unit surface area (P = F/A). However a larger surface area does increase the rate of evaporation.
The presence of an impurity lowers vapour pressure by occupying sites at the surface of the liquid such that there are now less sites occupied by the liquid particles and thus less of them can escape the liquid phase. The vapour pressure of the liquid then becomes a function of the liquid / impurity ratio. This ratio is expressed as a mole fraction ratio, X, defined as
XA =

nA _ nA + nB

where A represents the pure liquid and
B represents the impurity

(Mole fraction has a maximum value of one and for a binary mixture, XA + XB = 1, or
XB = 1 - XA.)
Raoult’s Law
The vapour pressure of a volatile liquid is directly proportional to the mole fraction of that liquid in an ideal mixture.
This may be expressed as PA



XA and could be reduced to the equation, PA = kXA where

k is the constant of proportionality.
For the pure liquid A, XA = 1 and the vapour pressure is that of the pure liquid, PAo.
Substituting gives,

PAo = k . 1. Or k = PAo.

The equation thus reduces to

PA = PAoXA

That is the vapour pressure of a volatile liquid in a mixture is equal to the product of the vapour pressure of the pure liquid by the mole fraction of that liquid in the mixture.

30

Graphically this may be represented as

(Note the double vertical vapour pressure axes. This comes in very useful when dealing with mixtures of two volatile liquids.)

PAo
V.P.

0

XA

1

Ideal Mixtures of Two Volatile Liquids
Each liquid is considered as independently as obeying Raoult‘s Law. Therefore for a mixture containing volatile liquids, A and B, the vapour pressures due to these components are;
PA = PAoXA and PB = PBoXB respectively. The total vapour pressure of the mixture, PT, is defined by

PT = PA + PB

Also, since it is a binary mixture

Dalton‘s Law

Or

XB + XA = 1,

or

Therefore the total pressure can be given as;

PT = PAoXA + PBoXB
XB = 1 - XA,

PT = PAoXA + PBo(1 - XA)

Graphical representation of the ideal mixture of two volatile liquids is given below
PAo
PT = P A + PB

(Note how useful the double vertical vapour pressure axes are when dealing with mixtures of two volatile liquids. Also note the contradictory changes in XA and XB. Often only one of the two mole fractions is used on the x-label since one implies the other for binary mixtures.)

V.P.
PBo
PA
PB

0
1

XA
XB

1
0

31

Vapour Composition
The vapour that is in equilibrium with a mixture of two volatile liquids will not have the same composition as the liquid mixture. E.g. for an equimolar mixture (XA = 0.5), the more volatile liquid will contribute more particles to the vapour phase. This results in an equilibrium vapour that is richer in the more volatile component. Since PA α nA (Avogadro‘s Law), the vapour pressure of the more volatile liquid is greater than that of the other liquid in the mixture.
The composition of the vapour (YA) may be calculated using the partial pressures.
YA =
But

PA



nA(v) _ nA(v) + nB(v)

nA(v) (Avogadro‘s Law)
YA =

PA _
PA + PB

Due to difference in composition for the liquid and vapour in equilibrium, different vapour pressure curves are observed.
PAo

vapour pressure – liquid composition
A

B

P1

V.P.
PBo
vapour pressure – vapour composition

X1

0
1

XA
XB

X2

1
0

Note the vapour pressure – vapour composition curve is always below the vapour pressure – liquid composition curve. Thus, for an observed vapour pressure, e.g. P1, the mole fraction of A, the more volatile liquid, is greater in the vapour composition, X2, compared to the liquid composition, X1.

32

An application of the differing compositions that a mixture has in the liquid and vapour phases is
Fractional Distillation. This is a separation technique for miscible liquids based on their diferent bfoiling temperatures.
Boiling Point – Composition Graphs
The boiling point of a liquid is the temperature at which its vapour pressure equals the applied pressure on its surface (for open containers this is atmospheric pressure).
Thus more volatile liquids achieve this pressure more readily upon application of heat and have lower boiling points. Or, liquids with higher vapour pressures have lower boiling points.
ToB boiling point – vapour composition

B.P.
ToA

boiling point – liquid composition

0

XA

1

Note the boiling point of liquid B, ToB, is higher than that of liquid A, ToA. Liquid A was previously described as more volatile than Liquid B. Also, the liquid composition curve is now below the vapour composition curve.
Non-ideal Mixtures – Deviation from Raoult’s Law
Raoult‘s Law applies for ideal mixtures (mixtures in which intermolecular forces before and after mixing are approximately the same). In many mixtures, non-ideal behaviour is observed. In some cases the observed vapour pressure is greater than that predicted by Raoult‘s Law. This is a positive deviation. Here intermolecular forces are less than those before mixing allowing more particles to enter the vapour phase than was predicted.

33

observed vapour pressure
V.P.

predicted vapour pressure

0

XA

1

A negative deviation describes the state in which the vapour pressure is lower than predicted by
Raoult‘s Law. Here the intermolecular forces after mixing are stronger than those before mixing.
Less particles are allowed to escape into the vapour phase and the vapour pressure is lower than predicted. predicted vapour pressure
V.P.

observed vapour pressure

0

XA

1

Colligative properties of solutions
Physical properties of solutions that depend upon the number, but not the kind, of solute particles in a given amount of solvent are called colligative properties. Colligative (tied togther) properties include; 1. vapour pressure lowering
2. boiling point elevation
3. freezing point depression
4. osmotic pressure
These properties of a solution depend on the total concentration of all solute particles, regardless of their ionic or molecular nature, charge or size. For most of our discussions we shall consider

34

non-electrolyte solutions i.e. substances which dissolve to give one mole of dissolved particles for each mole of solute.
Boiling point elevation
The boiling point of a liquid is the temperature at which its vapour pressure equals the applied pressure on its surface (for open containers this is atmospheric pressure).
We have seen that the vapour pressure above a solvent is at a given T is lowered by the presence of a nonvolatile solute in it. This solution would therefore require a higher temperature than the pure solvent to cause the vapour pressure of the solvent to equal atmospheric pressure.
The boiling point elevation of a solvent is given by ∆Tb = Kbm where

∆Tb is the elevation of

the boiling point of the solvent
Kb is the proportionality constant called the ebullioscopic constant and m is the molal concentration of the solute
Freezing point depression
The freezing point of a liquid is the temperature at which the forces of attraction among molecules are just great enough to overcome their kinetic energies (bring molecules closer together) and thus cause a phase change from the liquid to the solid state. When a dilute solution freezes it‘s the solvent that begins to solidify first, leaving the solute in a more concentrated solution. Due to the presence of solute particles, solvent molecules in a solution are further apart from each other than they are in the pure solvent. Consequently the temperature of a solution must be lowered below the freezing point of the pure solvent to freeze it. The freezing point depression of a solvent is given by
∆Tf = Kfm

;

where ∆Tf is the depression of freezing point of the solvent
Kf is the proportionality constant called the cryoscopic constant and

Diagram showing the phase diagrams of pure water and that of an aqueous salt solution
Commercial application: Ethylene glycol is the major component of antifreeze. It is added to automobile radiators so as to lower the freezing point and raise the boiling point of water. The result is that the solution remains in the liquid phase over wider ranges of temperature than does pure water, this protects against both freezing and boil-over.

35

SOLIDS
Solid matter is either crystalline or Amorphous.
Amorphous solids – particles are randomly arranged and have no ordered long-range structure
e.g. glasses and plastics.
Crystalline solids – particles have an ordered arrangement extending over a long range.
Crystalline solids are divided into various groups:


ionic crystals (ions bonded by electrostatic forces e.g. NaCl);



molecular crystals (separate molecules held together by intermolecular forces e.g. sucrose and ice);



giant covalent networks (atoms covalently bonded to form one very large molecule e.g. diamond and SiO2) and



metallic crystals (atoms with delocalized electrons e.g. Au and Li).

Crystal systems
Each ‗crystal‘ is made up of small repeating units called unit cells. The unit cell is the smallest sub-division of the crystal which is representative of the entire crystal. The unit cell is a convenient division of space, it provides a scheme where every single atom, molecule or ion in the crystal can be accounted for in a lattice. Mathematicians have shown that there are only 230 different shapes, which can pack 3-D space without a gap. These shapes can all be classified under fourteen different lattice types and even more generally into seven crystal systems: cubic
(3), tetragonal (2), hexagonal (1), trigonal rhombohedric (1), rhombi (4), monoclinic (2) and triclinic (1).
We will only focus on the simplest crystal system, the cubic system. There are three kinds of cubic lattices;
1) Simple cubic (CUB)

2) Body centred cubic (BCC)

3) Face centred cubic (FCC)

Summary of some characteristics of the cubic srystals
Structure
CUB
BCC
FCC

Stacking a-a-a a-b—a-b a-b-c---a-b-c Coordination #
6
8
12

Radius & length r = l/2 r = √3l / 4 r = √2l / 4

NB. The coordination number refers to the number of closest neighbours that an atom/molecule or ion has in a specific crystal lattice.

36

Physical and chemical combinations of matter

Matter
Everything that has physical existence

Pure Substances

Mixture

One chemical substance

A dispersion of two or more pure substances that retain their chemical identity

Compound

Element

A chemical combination of two or more pure substances in fixed proportions

A pure substance that cannot be further decomposed by chemical means

Homogenous mixture

Heterogenous mixture

Uniform throughout in composition Inconsistent composition e.g. sand and water

Suspension

Colloid

Solution

Homogenous mixture where the dispersed particles are larger than those of a solution, but smaller than those of a suspension. Homogenous mixture in which the dispersed phase are ions or molecules

Heterogenous mixture where the solid particles are seen with the naked eye or under a light microscope

There are various types of colloids, these are summarized in the table below;

Gas
Gas

Dispersing Medium
Liquid
Foam

Solid
Foam

e.g. shaving cream, whipped cream

Solid

Aerosol

Emulsion

Gel

e.g. fogs, clouds, aerosol can spray

Liquid

e.g. foam rubber, sponge e.g. mayonnaise, milk, face cream

e.g. Jelly, cheese, butter Aerosol

Sol

Solid sol

e.g. smoke, car exhaust, e.g. gold in water, milk Alloys of metals airborne viruses of magnesia, river silt
e.g. steel, brass
NB. This table indicates that all combinations of solids, liquids and gases can form colloids except nonreacting gases (true solutions). The type of mixture formed (solution, colloid or suspension) depends upon the size of the solute-like particles as well as solubility and miscibility.

37

SECTION 3 – Modules I, J & K
This section deals with the possibility for change (energetics); the extent of change (equilibria) and the rate of change (kinetics)

ENERGETICS (Energy of chemical systems)
Energetics tells us why chemical reactions occur and also if they will occur. Chemical reactions tend to move towards greater stability
High Energy

→

Low Energy

Reactive (unstable)

unreactive (stable)

System: the part of the universe under study for energy content (e.g. reactants and products)
Surroundings: ―everything else‖ in the universe e.g. reaction vessel, the lab, the building....
Universe: System

+

Surroundings

Systems are classified in 3 groups;


Open system: matter and energy can be transferred between system and surrounding
(e.g. a titration experiment).



Closed system: No matter, only energy can be transferred between system and surrounding (e.g. a covered beaker with hot water).



Isolated system: Neither matter nor energy may be transferred between system and surrounding (e.g. Thermos flask).

State function vs. Path function
State function is a function or property whose value depends only on the present state (condition) of the system and not on the path taken (e.g. temperature).
Path function is a function or property whose value depends on the path taken (e.g. cost).
NB. State functions are reversible i.e. ∆State function = Final state value – Initial state value

Heat, Work and Energy
Work is the distance traveled against an opposing force.
Energy is the capacity to do work.
Heat is the transfer of energy that makes use of disorderly molecular motion.

38

In chemical systems: we encounter ‗expansion work‘ occurring as a result of the change in volume of a system. E.g. Consider a reaction that produces gases causing an increase in volume w=F×d w=P×A×d since the distance changed between the initial and the final states we refer to the change as Δd.
Therefore; w = P × A × d which is simplified to; w = P ΔV

Sign convention of work
When work is done by system on the surroundings, final energy will be less than initial energy so the change is negative. Therefore w = -p∆V
When work is done on the system by the surroundings, final energy is greater than initial energy so the change is the change is positive. Therefore w = p∆V
When the energy of a system changes because of a temperature difference, there has been a heat flow. Containers that allow the flow of heat are diathermic and those that do not are adiabatic.
There are two ways in which a system can exchange energy with the surroundings;
1. heat transfer
2. work
The law of conservation of energy states that energy can neither be created nor destroyed; merely changed from one form to another.
The First law of thermodynamics states that the energy of the universe is constant.
If we are able to truly isolate a chemical system then the first law can be stated as;
The total internal energy of an isolated system is constant.

∆U = q + w
Enthalpy
Heat change at constant pressure is referred to as enthalpy change, ∆H (see justification).
H = U + pV

Justification
Recall ∆U = q + w
When the system does work; w = -p∆V
Therefore ∆U = q - p∆V
And so q = ∆U + p∆V
Consider a reaction taking place in an open vessel then P is constant at 1 atm
Therefore,
qp = ∆U + p∆V
Where qp is given the special symbol ∆H

39

But H is a state function so ∆H = Hfinal - Hinitial
Hence for chemical reactions; ∆H = Hproducts - Hreactants
When Hproducts > Hreactants ∆H is positive (endothermic rxn)
Hproducts < Hreactants ∆H is negative (exothermic rxn)
Since enthalpy is a state function then the overall enthalpy change for a reaction is equal to the sum of the individual steps in the reaction, this statement is known as Hess’s law.

Enthalpy measurements made under standard conditions (1 atm, 298 K and 1 M soln.) are called standard enthalpies (∆H0). Standard enthalpy of reaction (∆H0rxn) refers to the enthalpy change that occurs when reactants at standard state change to products at standard state. The enthalpy of reaction may be determined by the following equation;
∆H0rxn = Σ m ∆H0products – Σ n ∆H0reactantss where m and n are stoichiometric coefficients
Therefore for the hypothetical reaction;

aA + bB → cC + dD

∆H0rxn = {c ∆H0C + d ∆H0D} – { a ∆H0A + b ∆H0B}
The term enthalpy of reaction may be modified to suit the specific type of reaction. For example, when reactants are the pure elements, it is called Standard enthalpy of formation (∆H0f).
E.g.

C(s, graphite) + O2 (g) →

CO2 (g)

∆H0f = -393.5 kJ/mol

NB. Standard enthalpies of formation of elements are zero for all temp. (∆H0f (elements) = 0)

40

EQUILIBRIA
Consider the chemical reaction;
2 Na(s) + 2 H2O(l)

→

2 NaOH(aq) + H2 (g)

The reaction goes to completion at the ―end‖ of the reaction that is, at least 99.9 % of the reactants have been converted to products. However not all reactions go to completion; in fact the vast majority of reactions do not. They react to an extent then appear to stop. We have observed that the reaction does not really stop, to demonstrate this observation, consider the reaction; N2O4 (g)

2 NO2 (g)

At the beginning if we have N2O4, then the forward reaction is dominant producing products – the backward reaction is negligible. As time progresses, more product molecules are formed and they begin to react and reform the reactant molecules – the backward reaction becomes significant. At some point (characteristic of each reaction), the rate of the forward reaction will be equal to the rate of the backward reaction, that is, products are being formed just as fast as reactants are being replaced; it therefore appears as if no further change occurs. The reaction is said to have reached equilibrium.
NB. This does not mean that the concentration of products and reactants are the same.
Chemical equilibria are dynamic; although the concentrations of products and reactants do not change, the actual molecules are continuously changing.
The equilibrium state is the aim of all reversible chemical reactions since it is the state of minimum free energy ∆G = 0
Important notes
The equilibrium state may be approached from either side of a reversible reaction
Regardless of the starting conditions the same equilibrium state is reached.

41

The law of mass action
Consider a general reaction;

aA + bB

cC + dD

The equilibrium constant expression for this reaction is given as;
KC = [C]c [D]d
[A]a [B]b

where KC is called the equilibrium constant and [ ] represent molar conc.

This expression is an approximation of the law of mass action which was proposed by Guldberg and Waage in 1864:
K = (aC)c (aD)d
‗a‘ refers to the activity of… and is a truer
(aA)a (aB)b

measure of concentration

Points to note


The activity of a pure substance is 1



K is temperature specific and is usually stated with ‗temperature measured at..‘



Solids and liquids are omitted from the equilibrium constant expression since their concentrations do not change during the course of chemical reaction

Where reactants and products are gaseous; the equilibrium constant Kp may be used.
E.g.

N2 (g) + 3H2 (g)
Kp =

2 NH3 (g)

(PNH3)2
(PN2)2 (PH2)2

For the general reaction;
Kp = KC (RT)∆n

aA + bB

cC + dD

It can be shown that;

where ∆n = (c + d) – (a + b)

Using and Interpreting the equilibrium constant
The equilibrium constant may be used to;


Judge the extent of reaction (that is, decide whether reactants or products are favoured)



Predict the direction of change



Calculate equilibrium concentrations of reactants and products

Judging the extent of reaction; if K = [products] >> 1
[reactants]

then products are favoured.

In other words, at equilibrium, the concentration of products is greater than the concentration of reactants. If K = [products] [prod])

42

Predicting the direction of change
The reaction quotient, QC = [C]c [D]d
[A]a [B]b

can be used to determine if equilibrium has been achieved If QC = KC

the reaction mixture is at equilibrium and no net reaction occurs.

If QC < KC

the reaction mixture has less products than at equilibrium and reaction will proceed in the forward direction (from left to right) until equilibrium is attained.

If QC > KC

the reaction mixture has more products than at equilibrium and reaction will proceed in the backward direction (from right to left) until equilibrium is attained.

Changing the state of equilibrium
Le Chatelier‘s principle governs the way in which that state of equilibrium (that is, the equilibrium position) is changed.
Le Chatelier’s principle states that if a stress is applied to a reaction mixture at equilibrium, the reaction proceeds in the direction that relieves that stress.
By ‗stress‘ we mean;


Change in concentration of reactants or products



Pressure (volume) change



Temperature change

NB. The addition of a catalyst does not change the state of equilibrium; it only increases/decreases the rate at which the equilibrium state is attained.
Relationship between ∆G and K
The free energy available from a reaction is linked to the equilibrium constant by the following expression; ∆G = -RT ln K

43

Acid –Base Equilibria
According to Arrhenius; acids are defined as proton generators (they dissociate to give H+)
HA

H+(aq) + A-(aq)

(aq)

and bases are defined as OH- generators (they dissociate to give OH- ions)
OH-(aq) + H+(aq)

MOH (aq)

The Bronsted-Lowry definitions for acids and bases are;
Acids are proton donors
HA
acid

+

B base BH+ acid +

Abase

H3O+ + acid Abase

Conjugate acid-base pairs
Conjugate acid-base pairs

Bases are proton acceptors
HA
acid

+

H2O base Conjugate acid-base pairs
Conjugate acid-base pairs

Below is a list of some Bronsted-Lowry acids and bases
Acids

Bases

HCl

NH3

What are the acids for these bases? Write the formula and give the names of each.

HNO3

OH-

OH-

HF

H2O

NH4

+

HSO4-

-

F

NO2-

CO32NH2-

HCO3Write balanced equations for the dissociation of H2SO4, HSO4-, and H3O+ in water.

44

Acid and Base strength
Strong acids and bases are those that are almost completely dissociated in water.
E.g.

HCl(aq)

+

H3O+(aq)

H2O(l)

+

Cl-(aq)

Weak acids and bases are only partially dissociated in water.
E.g.

CH3COO-(aq) +

CH3COOH(aq)

H3O+(aq)

the mixture contains undissociated acid plus some CH3COO- and some H3O+

Acids
HClO4
HCl
H2SO4
HNO3
H3O+

Strong acids Weak acids

Very weak acids Bases
ClO4ClHSO4NO3H2O

H3PO4
HSO4HF
H2O
OHNH3
H2

H2PO4
SO42FOHO2NH2H-

Very weak bases Weak bases

Strong bases NB. The stronger the acid, the weaker is its conjugate base and the stronger the base the weaker is its conjugate acid.

Dissociation of H2O and pH
Consider the autoionisation of H2O:

H2O

+

H2O

KW = [H3O+] [OH-]

[H3O+] = 1.0×10-7

OH-

where KW is the ion product constant for water

For water at 250C;

H3O+ +

and

therefore KW = (1.0×10-7)( 1.0×10-7) = 1.0×10-14

[OH-] = 1.0×10-7
(water is largely undissociated)

However, when acids are added to water, [H3O+] increases.
E.g.

HA

+

H2O

H3O+ +

A-

On the other hand, when bases are added to water [OH-] increases.
E.g.

B

+

H2O

BH+

+

OH-

45

So in acidic solution;

[H3O+] > [OH-]

In basic solution;

[H3O+] < [OH-]

And in neutral solution;

[H3O+] = [OH-]

The pH scale is the logarithmic way of writing [H3O+]

pH = - log [H3O+]

where pH is referred to as the power of hydrogen

and so [H3O+] = antilog (- pH)
Typical pH value of some common substances encountered daily
Nature of solution acidic neutral

basic

pH
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

substance
1.0 M HCl
Stomach acid (pH = 1.5)
Soft drinks
Tomatoes
Black coffee
Pure water
Baking soda (pH = 8.5)

Cleaning ammonia
1.0 M NaOH

Exercises
Calculate the pH of i) acid rain with [H3O+] = 6.0×10-5 and ii) sea water with [OH-] = 1.58×10-6
Human blood has a pH of 7.40. Calculate the concentrations of H3O+ and OH- in human blood.

46

Electrochemistry
Electrochemistry is the area of chemistry which deals with the relationship between chemical reactions and electricity (the flow of electrons). Electrons flow by way of Redox reactions i.e. reactions where reduction and oxidation occurs simultaneously. Reduction is defined as the gain of electrons by a species resulting in a decrease in oxidation state. Oxidation is defined as the loss of electrons by a species resulting in an increase in oxidation state.
The reduction and oxidation reactions that comprise a redox process are called half-reactions. If the two half-reactions are physically separated (i.e. allowed to occur in separate containers) but remain in electrical contact, an electrochemical cell is obtained where the flow of electrons
(electricity) can be measured and used to do work.
For example;
Zn(s)

→

Zn2+(aq) + 2e-

(oxidation half reaction)

Zn(s) has been oxidized and is therefore the reducing agent (the species that aids in the reduction of another species).
Cu2+(aq) + 2e-

→

Cu(s)

(reduction half reaction)

Cu2+(aq) has been reduced and is therefore the oxidizing agent (the species that aids in the oxidation of another species).
There are two kinds of Electrochemical cells;


Galvanic cells – those in which spontaneous reactions are exploited and their flow of electrons is made to do work.



Electrolytic cells – those in which a voltage is applied to a cell in order to drive a nonspontaneous reaction.
Galvanic cells

47

This cell can be described using abbreviated cell notation (short hand notation). The notation is as follows;
Zn(s) / Zn2+(aq) // Cu2+(aq) / Cu(s)
When the redox reaction involves a non-metal, an inert metal is used as the electrode.
For example; the abbreviated cell notation for the reaction:
Cu(s) + Cl2 (g) → Cu2+(aq) + 2Cl-(aq) is written as; Cu(s) / Cu2+(0.1M) // Cl-(0.1M) / Cl2 (1 atm) / Pt(s)
Cell Potentials
The driving force of a cell is called the electromotive force (emf) or cell potential or cell voltage.
The emf depends on the tendency of a species to gain electrons and the other to lose electrons.
Emf of galvanic cells is positive.
Cell potentials measured under standard conditions (1 atm, 298 K, 1M) are called standard cell potentials (E0). E0 can be calculated using a list of standard reduction potentials.
E0cell = E0cathode + E0anode
In this list, the tendency of a species to gain or lose electrons was measured against hydrogen in a Standard Hydrogen Electrode.
Important notes
1. Half reactions are written as reductions
Cu2+(aq) + 2e-

→

Cu(s)

E0 = 0.34 V

2H+(aq) + 2e-

→

H2(g)

E0 = 0.00 V (reference)

Zn2+(aq) + 2e-

Eg.

→

Zn(s)

E0 = -0.76 V

2. Those half reactions with positive values tend to occur as written (reduction) while those with negative values tend to occur in the reverse direction (oxidation).
3. When writing the potential for a reaction in reverse, change the sign.
Eg. calculate the standard cell potential of the reaction:
Zn(s) + Cu2+(aq)

→

Cu(s) + Zn2+(aq)

48

∆G and cell potential
We wish to harness the electricity of a galvanic cell to do work (∆G = wmax)
It can be shown that; where ∆G = -nFE

n – no. of moles of electrons transferred
F – Faraday‘s constant (the electrical charge on 1 mol of e-) {96,500C/mol}
E – cell potential

NB.

1J = 1C × 1V

E.g Calculate the free energy available in the galvanic cell:
Zn(s) + Cu2+(aq) →

Cu(s) + Zn2+(aq)

It can therefore be seen that if;
E is +ve ; ∆G is –ve and reaction is spontaneous
E is -ve ; ∆G is +ve and reaction is non-spontaneous

49

CHEMICAL KINETICS
Kinetics deals with reaction rates (how fast reactions occur) and the sequence of steps by which reactions occur.
Reaction rates
Reaction rate can be measured by the rate of change in concentration of a reactant or product:
Rate = concentration change time Consider the reaction;

2N2O5 (g)

→

4NO2 (g) + O2 (g)

The rate is either given as increase in concentration of product (+ve) per unit time or decrease in concentration of reactant (-ve) per unit time.
Rate = ∆[O2] = [O2]final - [O2]initial
∆t
tf - ti
Now consider that for every 1 mol of O2 which forms, 4 mol of NO2 form, and 2 mol of N2O5 decompose…..therefore rate of formation of NO2 is 4 times the rate of formation of O2.
We can therefore state that;
Rate of O2 formation = ¼ Rate of NO2 formation = ½Rate of N2O5 decomposition
∆[O2] =
∆t

1∆[NO2]
4 ∆t

=

-1∆[NO2]
2 ∆t

→

products

Rate Laws and Reaction Orders
Consider a reaction;

aA + bB

The dependence of the reaction rate on concentration of reactants is given by the rate law. The rate law has the form; rate = k [A]m [B]n where m and n indicate the influence of [A] and [B] respectively over reaction rate. They are called the ―order‖ of the reaction with respect to the species. e.g.

if m = 1, then the reaction is first order w.r.t. A if n = 3, then the reaction is third order w.r.t. B

NB. If the concentration of a reactant does not affect the rate, the reactant does not appear in the rate law. However, until experiments prove otherwise, all reactants are placed in the rate law.
The values of m and n can only be determined experimentally.
Overall order of the reaction is the sum of the individual orders.

50

For example, the reaction:

aA + bB

→

products

has rate law; rate = k [A][B]2

therefore the reaction is 1st order w.r.t. A; 2nd order w.r.t. B and 3rd order overall.

Experimental determination of rate law
Consider the reaction;

2 NO(g)

+

O2 (g)

2 NO2 (g)

Four experiments were done using various concentrations of reactants and initial rates were determined. The following data were obtained; determine the rate law for this reaction.
Expt #
1
2
3
4

Initial [NO]
0.015
0.030
0.015
0.030

Initial [O2]
0.015
0.015
0.030
0.030

Initial rate (Ms-1)
0.024
0.096
0.048
0.192

Half-life
The half-life of a reaction (t½) is the time required for the reactant concentration to drop to half of its initial value (this may be a few seconds to millions of years).
Exercise
The half-life for the decomposition of A is
2 mins. If the initial concentration of A is
24 M, what concentration of A remains after 10mins?

51

Factors affecting rate of reaction
Rates are dependent on;
1. concentration of reactants
2. surface area (sub-division of solids)
3. temperature
4. addition of catalyst
The collision theory offers an explanation for these effects.
Collision theory: A bimolecular reaction occurs when two properly oriented reactant molecules collide with sufficient energy necessary for bond breakage. Therefore any factor that serves to increase the kinetic energy of molecules or the frequency of collisions will increase the probability of successful collisions occurring and ultimately increase the rate of reaction.
NB. Bond breakage requires energy and bond formation releases energy.
The collision theory is supported by the activated complex theory.
Activated complex theory
→

AB + C

When A and BC collide we get;

A + B-C

Consider

A + BC

→

A….B…C (transition state)

A…B…C is a high energy compound referred to as the activated complex.
When molecules approach each other, their eclouds repel each other. Hence for reaction to occur the collision must be sufficiently energetic to overcome the repulsions. The energy barrier to reaction is called the activation energy (Ea). The activation energy is defined as the minimum amount of energy necessary to initiate the reaction. NB. The higher the Ea the slower the reaction.

All the energy for the reaction must be provided by the kinetic energy of the colliding molecules.
If the colliding E < Ea; the molecules n\bounce apart after collision and no reaction occurs

52

If colliding E > Ea; the reacting molecules can surmount the Ea barrier and be converted to products. Hence, not all collisions result in a reaction. By way of experiment it has been deduced that only a small fraction of molecules collide with sufficient energy to cause a reaction.
This fraction is given by;

ƒ = e -Ea/RT

where ƒ – fraction of molecules with sufficient energy
R – ideal gas constant and T – absolute temperature (i.e. temperature in K)

Diagram showing how ƒ varies with temperature

At higher temperatures, a greater fraction of collisions have sufficient energy to overcome the Ea
If Z = total number of collisions then ƒZ = number of collisions with sufficient E

Steric effects
The number of collisions which result in reaction are further reduced by the incidence of molecules not having the proper orientation for reaction.
E.g. Consider the reaction;

2 NO2

NO

+

NO3

The two NO2 molecules must collide with a particular orientation for the reaction to occur.

53

The fraction of colliding molecules with the correct orientation is called the steric factor, p.
Therefore for a reaction between A and B;

reaction rate = p ƒ Z [A] [B]

But previously we saw that the rate law is given by;

reaction rate = k [A] [B]

Therefore k = p ƒ Z
This gives;

=pZe

k=Ae

-Ea/RT

-Ea/RT

where p Z is called the frequency factor, A

-- Arrhenius equation (it shows the temperature dependence of K)

Catalysis
A catalyst is a substance that increases/decrease the rate of reaction without being consumed in the reaction. It provides an alternative path for the reaction that has a lower/higher Ea than the previous path.
E.g.

2 KClO3 (s)

2 KCl (s)

+

3 O2 (g)

This reaction is catalysed by MnO2, the reaction proceeds much faster in the presence of MnO2.
NB. Biological catalysts are called enzymes.

Energy profile diagram of a catalysed and uncatalysed reaction

54