Chemistry 14 Notes

Gabriel Christian V. Alava

2014

ii

Alava, G. C. V. (2014).Chemistry 14 Notes.Manila: Author.

For any corrections or revisions,you may contact the author at alavayou@icloud.com.

Syllabus in Chem 14

Course title Fundamentals of General Chemistry 1

Credit 3 hours (3 lecture hours)

Prerequisite Math 11 / Math 17

General objectives At the end of the course, the student should be able to:

1. Know chemical concepts and principles about matter.

2. Understand chemical concepts and principles about matter.

3. Apply chemical concepts and principles about matter.

Content

I. Atomic structure

A. Development of the different atomic models

B. The subatomic particles

C. Quantum mechanical model and quantum numbers

D. The periodic table

1. Periodicity of properties

II. The chemical bond

A. Ionic or electrovalent bond

B. The covalent bond

i. Theories on covalent bonds

a. Valence Bond Theory

b. Molecular Orbital Theory

First departmental exam

III. Changes in matter

iii

iv SYLLABUS IN CHEM 14

A. Nuclear changes

1. Nuclear versus chemical reactions

2. Types of radiation

3. Types of nuclear change

4. Radioactive disintegration

B. Chemical changes

1. Quantitative relations involving formulas and equations

a. Mole concept

b. Empirical and molecular formula

c. Stoichiometry and balanced equations % yield, % purity, lim-iting reactant

IV. Phases of matter

A. Intermolecular forces

B. Comparative descriptions of the states of matter

C. Phase changes and phase diagrams

D. The gaseous state

1. The Kinetic Molecular Theory

2. Ideal gas laws

3. Real versus ideal gases Van der Waals equation of state

4. Gas mixtures Daltons Law, Amagats Law

E. The liquid state properties of liquids

F. The solid state

1. Types of solids

2. Properties of solids

Second departmental exam

V. Solutions

A. The dissolution process

B. Factors affecting solubility

C. Types of solutions

D. Ideal versus non-ideal solutions: vapour pressure of solutions of com-pletely miscible liquids

vE. Concentration

1. Methods of expressing concentration

2. Dilution

F. Electrolytes and nonelectrolytes

1. Colligative properties

2. Acids, bases and salts

Third departmental exam

VI. Chemical thermodynamics

A. Basic concepts

B. First law of thermodynamics

1. Heats of reaction: heats of formation, Hess law

C. Second and third laws of thermodynamics

1. Entropy

2. Gibbs free energy

VII. Chemical kinetics

A. Theories on reaction rates

B. Factors affecting rates of reactions

VIII. Chemical equilibrium

A. Molecular equilibrium

1. Kinetic approach to equilibrium

2. Thermodynamic approach to equilibrium

3. Factors affecting equilibrium

B. Ionic equilibrium

1. Ionisation of strong and weak electrolytes

2. pH and pOH

3. Hydrolysis Concept

4. Neutralisation and titration

Fourth departmental exam

Course requirements Refer to Table 1.

vi SYLLABUS IN CHEM 14

Table 1: Course requirementsClass standing 2/3

Departmental examinations 80%Non-departmental 20%QuizzesRecitationAssignments / Problem sets

Final exam 1/3

Table 2: Grading scale90 1.0085 1.25 8980 1.50 8475 1.75 7970 2.00 7465 2.25 6960 2.50 6455 2.75 5950 3.00 5440 4.00 45

5.00 39

Exemption policies A student may be exempted from taking the final examprovided all of the following conditions are met:

1. All major exams are taken

2. No grade lower than 50% in any of the major exams

3. A class standing of 60% or better

4. Additional requirements by the professor or instructor

Absences Any student who failed to take a major exam due to illness maybe excused upon presentation of a medical certificate issued by the U.P. HealthService. The final exam may then be substituted for the missed exam. This canbe done for only one exam.

Scholastic integrity All forms of cheating merits a grade of 5.00 for thecourse. A student who is found guilty of cheating will not be allowed to dropthe course in order to avoid getting a grade of 5.00.

Grading scale Refer to Table 2

Contents

Syllabus in Chem 14 iii

I Coverage of the first departmental exam 1

1 The atom 31.1 Development of the atomic model . . . . . . . . . . . . . . . . . . 31.2 The subatomic particles . . . . . . . . . . . . . . . . . . . . . . . 41.3 Quantum numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 The periodic table 72.1 Groups and periods . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Periodicity of trends . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Chemical combination 113.1 Electron sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Writing Lewis structures . . . . . . . . . . . . . . . . . . . . . . . 133.3 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 The covalent bond 154.1 Valence Shell Electron Pair Repulsion Theory . . . . . . . . . . . 154.2 Hybridisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3 Molecular Orbital Theory . . . . . . . . . . . . . . . . . . . . . . 16

II Coverage of the second departmental exam 19

5 Phases of matter 215.1 Intermolecular forces . . . . . . . . . . . . . . . . . . . . . . . . . 215.2 The gaseous state . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3 The solid state . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 Nuclear chemistry 276.1 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

vii

viii CONTENTS

6.2 Nuclear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Part I

Coverage of the firstdepartmental exam

1

Chapter 1

The atom

Democritus (460-370 BC) suggested that matter was made up of tiny indivisibleparticles called atoms. His theory was rejected in favour of Aristotelean philos-ophy. John Dalton (1766-1844) however resurfaced Democritus suggestion anddrew up the following postulates1 in his own atomic theory:

1. Each element is composed of extremely small particles called atoms.

2. All atoms of a given element are identical, but the atoms of one elementare different from the atoms of all other elements.

3. Atoms of one element cannot be changed into atoms of a different elementby chemical reactions; atoms are neither created nor destroyed in chemicalreactions.

4. Compounds are formed when atoms of more than one element combine; agiven compound always has the same relative number and kind of atoms.

1.1 Development of the atomic model

Rutherfords nuclear model You will later on see that an electrons massis 0.05% of a protons mass. This disparity led J. J. Thomson to suggest thatthe electron similarly occupies a small volume in the atom. He proposed theplum pudding model wherein the atom was a sphere of positive charges whereinelectrons are embedded.

However, in Ernest Rutherfords -scattering experiment, in contrast to Thom-sons model, while most particles were not deflected by the gold foil thatstands in its way, some were by a degree or so and an even smaller percentageof those particles were deflected by larger angles.

1The following postulates are copied verbatim from [2].

3

4 CHAPTER 1. THE ATOM

This led him to draw up the nuclear model of the atom, where the all posi-tive charges are concentrated in a nucleus and the electrons inhabit the emptyperiphery of the nucleus.

Bohrs planetary model Having agreed upon the nuclear model, the nextquestion is where in the empty space around the nucleus the electron resides.Niels Bohr suggested that an electron move around the nucleus in orbits. Eachorbit has a corresponding principal quantum number n and energy E, givenby

E = RHn2

where the Rydberg constant RH = 2.18 1018 m1.Electrons may move from one orbit to another by absorbing or emitting energyE, but only in packets or quanta. E is given by

E = RH

(1

n2i 1n2f

)=hc

where Plancks constant h = 6.63 1034 J s, the speed of light c = 3.00 108 ms , and is the wavelength of the photon emitted by the electron.

Quantum mechanical model The quantum mechanical model refuted Bohrsproposition that the electrons orbit the nucleus in two-dimensional circularpaths. Instead, it suggested the existence of three-dimensional orbitals whereinthere is most probable to find an electron. It does not tackle the motion of anelectron around the nucleus since the Heisenberg uncertainty principle statesthat that cannot be precisely determined.

1.2 The subatomic particles

Table 1.1 summarises the properties of each of the three principal subatomicparticles. Note that

1 amu = 1.66054 1024 g1 g = 6.02214 1023 amu

J. J. Thomson is credited with the discovery of the electron by his discoveryof the cathode rays negative charge. James Cavendish is credited with thediscovery of the neutron and its location in the nucleus along with the protons,thus the name nucleon.

1.3. QUANTUM NUMBERS 5

Table 1.1: Subatomic ParticlesParticle Mass (g) Mass (amu) Charge (C)

Electron 9.1095 1028 0.000549 1.6022 1019Proton 1.67252 1024 1.007260 +1.6022 1019Neutron 1.67495 1024 1.008670 0

Atomic number, mass number, charge, and atomic weight The afore-mentioned terms are defined below.

Atomic number Z number of protons in an atom of an element. Atoms ofthe same element have the same atomic numbers while those of differentelements do not.

Charge number of protons minus number of electrons, represented as C in thisparagraph.

Mass number A number of protons and neutrons in an atom. This may varyeven among atoms of the same element.

Isobars atoms with the same mass number.

Isotones atoms with the same number of neutrons.

Isotopes atoms of the same element which have different numbers of electrons.

Atomic weight =

(isotope mass fractional isotope abundance)An atom of an element with symbol X may be written as AZX

C.

1.3 Quantum numbers

To determine the location of an electron, we use quantum numbers, defined be-low, to describe the region where we will most probably find that electron.

The principal quantum number n {1, 2, 3, . . . } corresponds to the mainenergy level or electron shell and determines the distance of the electronfrom the nucleus, the size of the orbital it is in, and its energy, as discussedin Niels Bohrs model of the hydrogen atom.

The angular momentum quantum number l {0, 1, 2, . . . , n 1} corre-sponds to the sublevel or subshell and determines the shape of the orbital.While l may have numerical values, it may also take literal designationsas listed in Table 1.2

The magnetic quantum number ml {l,l + 1,l + 2, . . . , l 2, l 1, l}determines the orientation of the orbital.

6 CHAPTER 1. THE ATOM

Table 1.2: l valuesNumber Letter Shape

0 s

1 p

2 d3 f

The spin magnetic quantum number ms determines the spin of the elec-tron magnetic moment in a magnetic field. If the moment is against thefield, m = 12 and m = 12 if otherwise.

?The Pauli exclusion principle states that no two electrons in an atom can havethe same four quantum numbers.

The electron configuration of an atom describes how its electrons are ar-ranged. The following principles are applied when distributing electrons:

n+ l rule As n+ l increases, so too does E.

Aufbau principle The buildup of electrons in atoms results from continuallyincreasing the quantum number, starting with the lowest n, l, and mlvalues.

Hund?s rule of maximum multiplicity Electrons introduced into a subshellwill first occupy an empty orbital before sharing one with another electron.

Chapter 2

The periodic table

2.1 Groups and periods

First, let us define period and group. A horizontal row of elements is called aperiod and a vertical column is a group or family. We define s-block to be the

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8 CHAPTER 2. THE PERIODIC TABLE

set of elements whose last electron is in s sublevel and we define the p, d, andf -blocks in the same way. Note that the number of families in each block is thesame as the maximum number of electrons in each sublevel.

While the period number is simply the highest n-value of the elements electronconfigurations in that period, there are two systems followed in determininggroup numbers.

The U.S. convention splits the periodic table into two: A families, whichcomprise the s and p-blocks, and the B families, which comprise the d and f -blocks. The group number to which the letter A or B is affixed is correlated tothe number of valence electrons of that groups constituent elements as describedbelow, where n is the period number of the element.

A family group number = number of electrons in the ns subshell

+ number of electrons in the np subshell

B family group number = number of electrons in the ns subshell

+ number of electrons in the (n 1)d subshell

The IUPAC notation however simply numbers the families 1 to 18, butthere is still a correlation between the groups number and the valence electronsof its constituent elements. In fact the IUPAC notation applies the relationabove for the s and d-blocks. However, for the p-block, the group number isgiven below:

p-block group number = 10 + number of electrons in the ns subshell

+ number of electrons in the np subshell

The f-block Neither convention designates group numbers for the f -block.The number of valence electrons of an f -block element can be calculated as

A family group number = number of electrons in the ns subshell

+ number of electrons in the (n 1)d subshell+ number of electrons in the (n 2)f subshell

Since these elements vary only in the number of electrons in their inner mainenergy levels, their chemical properties are very similar, which is why neitherconvention bothers to give them group numbers.

2.2 Periodicity of trends

Atomic radius decreases through each period and increases down each group.The rest of the properties, defined below, increases through each period and

2.2. PERIODICITY OF TRENDS 9

decreases down each group. All of these trends are due to the increase in theeffective nuclear charge across a period and the increase in n down a group,which increases the distance between the most distant electron and the nucleus.Exceptions are also explained below.

Atomic radius is defined as half the distance between the two nuclei of eithertwo adjacent atoms as in the case of metals or two bonded atoms as in the case ofdiatomic molecules. Atomic radius decreases through each period and increasesdown each group. Cations are smaller than their parent atoms and anions arelarger. The larger the net charge, the smaller the atom.

Ionisation energy U is the minimum energy required to remove an electronfrom an atom or ion in its ground state, i.e.

Xn + U xn+ 1 + eThe first, second, third, and succeeding ionisation energies are related as de-scribed below:

A + U1 A1+ + eA1+ + U2 A2+ + eA2+ + U3 A3+ + e

and so on. When an electron is removed, the repulsion between electrons de-creases. Since the effective nuclear charge is constant, each ionisation energy isalways less than the succeeding ionisation energy, i.e. Un < Un+1.

A possible break in the trend between the s and p-blocks is due to the higherenergy associated with the p-sublevel. Likewise, a possible break in the trendin the middle of the p-block may arise due to the repulsion of the electron tobe added when moving from Group 15 to 16. Also note that the ionisationenergy of a Group 12 is higher than that of a Group 13 element from the sameperiod.

Electron affinity is the energy released or absorbed when an electron is addedto an atom, i.e.

A + e A

Note that this is not simply the opposite of ionisation energy. Our sign conven-tion here will be that, if the system released energy, the electron affinity mustbe positive.

Electron affinity generally increases through the period but a break in Groups2 and 18 may be explained by the fact that these elements are already stableand would rather give electrons away rather than receiving them, which takesmore energy because they will have to place it in the next sublevel.

10 CHAPTER 2. THE PERIODIC TABLE

Electronegativity is the tendency of an atom to attract electrons whenbonded.

Metals and nonmetals Using the information above, we can classify ele-ments as either metals or nonmetals. Metals, occupying the left side of the pe-riodic table, have larger atoms, lower ionisation energies, and lower electronega-tivities than their nonmetallic counterparts. In between are the metalloids. Wewill also observe that metallic properties decrease across the period.

Chapter 3

Chemical combination

We have learned from the previous lessons that an atom whose orbitals are com-pletely filled probably will not react and we can see this in Group 18 elements.Those that have partially filled orbitals will tend to combine with another atomto either fill them up or give away the electrons in them. This is the basis ofthe octet rule.

Atoms also have two modes of combination: electron sharing and electron trans-fer. The mode by which they will combine is determined by the difference intheir electronegativities, which we will represent here as |A B |.

Electron transfer If the difference |A B | > 1.7 or if one of the two atomstend to gains electrons and the other tends to lose, the two atoms combinethrough electron transfer. An electrostatic or ionic bond is established betweenthem. Take for example NaCl.

Na + Cl Na+[

Cl]

The less electronegative atom becomes a cation and gives up its electron(s) tothe more electronegative ion, which will take it and become an anion. Note thatthe electron given up is farthest one from the nucleus, not the last electron weassign.

3.1 Electron sharing

When neither atom is willing to give or if |A B | < 1.7, the two atoms form amolecule held together by covalent bonds, each one formed by a pair of electronsshared by the two atoms.

11

12 CHAPTER 3. CHEMICAL COMBINATION

Polarity These covalent bonds are further divided into two: nonpolar andpolar covalent bonds. For non polar bonds, |A B | 0.4. For polarbonds, 0.5 |A B | 1.7. Beyond that, the chemical bond is classifiedas ionic.

In polar bonds, the shared electron pair is shared unequally. The more elec-tronegative atom naturally gets the larger electron density than the less elec-tronegative atom. The molecule possesses a dipole moment.

If the dipole moments within the molecule balance out or if the molecule issymmetrical, the molecule is nonpolar. However, this is different from the polarbonds within the molecule.

Bond dissociation energy or bond energy, the energy required to break a bondin one mole of a gaseous molecule, increases with polarity, along with the bondorder or number of bonds between two atoms in the molecule.

and pi bonds bonds are formed by the overlap of atomic orbitals betweenthe nuclei of the two bonding atoms. Sigma bonds are formed by an s, p, andhybrid orbitals and another one of those orbitals.

Additional pibonds may be formed by the sideways overlap of additional p or-bitals alongside a bond to form a double or triple bond.

Covalency number The number of covalent bonds that a nonmetal or ametalloid can form is called its covalency number. If the central atom followsthe octet rule, its covalency number is eight minus the number of its valenceelectrons. If not, its covalency number is simply the number of its valenceelectrons.

Coordinate covalent bonds While a covalent bond is formed by a pair ofelectrons shared by the two atoms, there are cases in which only one atom con-tributes both of the electrons that form the bond. Take for example NOCl3.

Cl N

Cl

Cl + O Cl N

O

Cl

Cl

In this case, N shared its electrons to to form Os octet even though N alreadyhad a complete octet and did not need to do so.

Formal charge is the apparent charge an atom would have if it were to shareelectrons equally with the other atom it is covalently bonded to. Formal charge

3.2. WRITING LEWIS STRUCTURES 13

may be computed using the formula

Formal charge = number of valence electrons in a neutral atom

lone electrons lone pairs 2 number of bonds

Charge of molecule =

[Formal charges]

This preference for minimal formal charges often overrides the octet rule andgives rise to expanded octets, which may only occur for elements where n 3.Note that in these cases, the maximum possible number of valence electrons ofthe central atom in the compound is twice the number of valence electrons inthe free atom.

3.2 Writing Lewis structures

The procedure below enumerates the steps to draw a Lewis structure.

1. Count the available valence electrons.

2. Write down the atoms as they are connected. The central atom usuallyhas the highest covalency number, the largest size, or the lowest elec-tronegativity. The following tips may also help:

(a) If one atom is unique, its probably the central atom. Hydrogen andoxygen are not probable candidates.

(b) If there are two unique atoms, the one with the larger atomic numberis probably the central atom.

(c) Carbon family elements usually form four bonds. Nitrogen familyelements form three. Oxygen family elements form two. Halogensusually form one.

(d) When oxygen and hydrogen are in the same molecule, they usuallyform the combination HOX where X is the other atom in themolecule.

(e) Three-membered rings are unlikely for most molecules. Larger ringsare possible but nevertheless uncommon.

3. Fill the octets of the peripheral atoms and, if there are still electrons,assign them to the central atom.

4. If there arent enough electrons to fill the central atoms octet, try multiplebonds.

14 CHAPTER 3. CHEMICAL COMBINATION

3.3 Resonance

In molecules with double bonds, the location of the double bonds is arbitrary,allowing for more than one Lewis structure. However, when all of the bonds areexamined, all of them are identical, hybrids of single and double bonds. Thisphenomenon is called resonance.

When choosing a resonance structure, we try to minimise formal charges andassign the negative formal charges to the more electronegative atoms. It is alsoadvisable that should there be formal charges with opposite signs, they are toalternate signs across the adjacent atoms.

Chapter 4

The covalent bond

4.1 Valence Shell Electron Pair Repulsion The-ory

Each single bond, multiple bond and lone pair affiliated with an atom comprisesan electron domain. The VSEPR Theory posits that the molecule arranges itselfby maximising the distance between the electron domains of the central atom tominimise the repulsion between them. Table 4.1 summarises the possible shapesof a molecule.

Bond angles Repulsion between lone pairs is greater than repulsion betweenbonding pairs, and repulsion between a lone pair and a bonding pair is some-where in between. Additionally, repulsion by multiple bonds is stronger thanthat of a single bond but still smaller than that of a lone pair. This results insmaller bond angles and larger angles between lone pairs and bonding pairs inmolecules which have lone pairs.

This is because a bond pair, being attracted by two positive nuclei, is stretchedalong the line connecting the two nuclei, reducing its volume. Lone pairs, on theother hand, are attracted by only one nucleus, to which it becomes closer.

Likewise, the sizes of a molecules constituent atoms affects its bond angles.As the central atoms size increases, the overall electron-electron repulsion de-creases. However, as the size of a surrounding atom increases, so too does thebond angle.

Bond angle decreases with the increase in the central atoms size because thatincrease in size increases the distance between the nucleus and the surroundingelectron pairs and between the electron pairs themselves.

15

16 CHAPTER 4. THE COVALENT BOND

Table 4.1: Molecular geometriese domains Hybridisation Bonding

domainsLonepairs

Molecular geometry

2 sp 2 0 Linear

3 sp23 0 Trigonal planar2 1 Bent

4 sp34 0 Tetrahedral3 1 Trigonal pyramidal2 1 Bent

5 sp3d

5 0 Trigonal bipyramidal4 1 Seesaw3 2 T-shaped2 3 Linear

6 sp3d26 0 Octahedral5 1 Square pyramidal4 2 Square planar

4.2 Hybridisation

More often than not, the electron configuration of an atom will not allow anotheratoms electrons to interact with its own because of energy differences. For thisreason, two or more atomic orbitals may undergo hybridisation to form thesame number of degenerate hybrid orbitals, i.e. hybrid orbitals of the sameenergy.

Table 4.1 likewise details the hybridisation necessary to make each moleculargeometry possible. Likewise, you may calculate the number of hybrid orbitalsproduced by adding the number of the central atoms lone pairs and its bonds,counting double or triple bonds as only one.

4.3 Molecular Orbital Theory

Where the Valence Bond Theory falls short, the Molecular Orbital Theory com-pensates. Rather than associating orbitals with atoms, it associates orbitalswith the molecule as a whole.

A pair of atomic orbitals combine to form a more stable bonding pair withlower energy and a less stable antibonding molecular orbital with higher en-ergy. As their names state, the bonding molecular orbital keeps the moleculetogether while the antibonding molecular orbital destabilises it. There are alsononbonding electrons which do not significantly affect the bonding.

4.3. MOLECULAR ORBITAL THEORY 17

With this, we can also compute for the bond order using the equation

Bond order =1

2 [(bonding electrons) (antibonding electrons)]

Two factors are considered in forming molecular orbitals: the symmetry ofatomic orbitals and the difference in the energies of the two atomic orbitals.The following equations will detail which molecular orbitals are formed fromatomic orbitals:

+ * = s+ s

= pz + pz

pi + pi* = px + px= py + py

Note that these equations are not real and are just representations.

The energy level diagram of a diatomic molecule of an element whose Z 8 isdrawn below.

1s

2s

2p2p2p

1s

2s

2p2p2p

1s

1s

2s

2s

2pz

2pz

pi2px

pi2px

pi2py

pi2py

For a diatomic molecule of an element whose Z 7, where there is signifi-cant 2s-2p interaction, the pi2px and pi2py orbitals switch energy levels with 2pzorbital.

18 CHAPTER 4. THE COVALENT BOND

Part II

Coverage of the seconddepartmental exam

19

Chapter 5

Phases of matter

Table 5.1 summarises the properties of the three phases of matter.

A phase diagram like Figure 5.1 contains the vapour pressure, sublimation,and melting curves. Each curve bounds two phases and is the set of conditionswhere the two phases coexist in equilibrium and where the transition betweenthe two phases occurs.

The triple point, the intersection of the three curves, details the conditionswhere the three phases coexist in equilibrium. The critical point, the endpointof the vapour pressure curve, details the conditions where the liquid and gasphases are identical.

5.1 Intermolecular forces

The following properties of substances are indicators of strength of intermolec-ular forces:

Heat or enthalpy of fusion, vaporisation, or sublimation heat requiredto undergo the phase change, increases with the strength of intermolecularforces

Melting or boiling point temperature required to undergo the phase change,increases with the strength of intermolecular forces

Normal melting or boiling point melting or boiling point at 1 atm.

Viscosity measure of a fluids resistance to flow, increases with the strength ofintermolecular forces

21

22 CHAPTER 5. PHASES OF MATTER

Table 5.1: Properties of matterProperty Gas Liquid Solid

Volume Assumes the vol-ume of the con-tainer

Has definite volume

Shape Assumes the shape of the container Has definiteshape

Density Low HighCompressibility Very compress-

ibleSlightly com-pressible

Virtually incom-pressible

Diffusion Rapid Slow Very slowlyFlow Flows readily Does not flow

Particles move freely move freely rela-tive to each other

virtually dontmove

Figure 5.1: A generic phase diagram

5.1. INTERMOLECULAR FORCES 23

Vapour pressure pressure exerted by gas molecules on the surface of the liq-uid with which it is in equilibrium, decreases with the strength of inter-molecular forces

Surface tension amount of energy required to increase the surface of a liquidby a unit area, increases with the strength of intermolecular forces

Solubility maximum amount of solute that will dissolve in a given solvent orsolution at a given temperature, increases with the strength of intermolec-ular forces between solute and solvent.

Intermolecular forces are classified into the following categories, arranged in in-creasing strength. Note that intermolecular forces are simply a result of chargesand their attraction or repulsion in accordance with Coulombs law.

London dispersion forces are forces that exist between nonpolar substances.Instantaneous dipoles arise when electrons are concentrated at a certain locationat an infinitesimal duration, and these in turn repel the electrons of a neigh-bouring molecule, making an induced dipole. The strength of London dispersionforces increases with atomic size because a larger electron cloud allows electronsto move within a larger space.

When a polar molecule and a nonpolar molecule are present, the polar moleculemay induce polarity in the nonpolar molecule, thus the dipole-induced dipoleforce. The presence of an ion also has the same effect on a nearby nonpolarmolecule, thus the ion-induced dipole force.

Dipole-dipole forces are forces that exist between polar substances as aresult of permanent dipoles. Since the dipoles are permanent, the attractionsand repulsions of these dipoles are more constant, making this type of forcestronger than London dispersion forces. The strength of dipole-dipole forcesincreases with polarity.

Hydrogen bonding is a type of dipole-dipole force that exists between a hydrogenatom bonded to an atom of nitrogen, oxygen, or fluorine to another atom ofnitrogen, oxygen, or fluorine. Hydrogen bonding is much stronger than otherdipole-dipole forces.

Ion-dipole forces are forces that exist between ions and polar substanceswhere an ion attracts an oppositely-charged pole of a polar molecule. Thisinterparticle force is stronger than dipole-dipole forces because of the permanentcharge of the ion.

Ionic bonds are forces that exist between ionic species. Since both specieshave permanent charges, their attractions are much stronger than ion-dipoleforces.

24 CHAPTER 5. PHASES OF MATTER

5.2 The gaseous state

The Kinetic Molecular Theory explains the macroscopic properties ofmatter as a result of the behaviour of its constituent molecules. The theorycomprises the following postulates1:

1. A gas is composed of a very large number of extremely small particles(molecules or, in some cases, atoms) in constant, random, straight-linemotion.

2. Molecules of a gas are separated by great distances. The gas is mostlyempty space. (The molecules are treated as so-called point masses, asthough they have mass but no volume.)

3. Molecules collide only fleetingly with one another and with the walls oftheir container, and most of the time molecules are not colliding.

4. There are assumed to be no forces between molecules except very brieflyduring collisions. That is, each molecule acts independently of all theothers and is unaffected by their presence, except during collisions.

5. Individual molecules may gain or lose energy as a result of collisions. In acollection of molecules at constant temperature, however , the total energyremains constant.

The gas laws We will use the following variables to refer to each property ofa gas or its container:

P = pressure

V = volume

n = number of moles

T = temperature

M = molar mass

= density =PM

RT

Z = compressibility factor =PV

RT

R = 0.08205L atmmolK = 8.3145

J

molKurms = root-mean-square speed =

u2 =

3RT

M

The equation below details how the different units of pressure are related.

1 atm = 760 mmHg = 760 torr = 101, 325 Pa = 1.01325 bar

1The following postulates are copied verbatim from [1].

5.3. THE SOLID STATE 25

STP or standard temperature and pressure is defined as T = 273.15 K and,according to IUPAC, P = 1 bar, although this used to be P = 1 atm.

The following laws predict the properties of an ideal gas:

P 1V

(Boyles law)

V T (Charles law)PV = nRT (Ideal gas law)PiViniTi

=PfVfnfTf

(General gas equation)

rate of effusion = urms 1M

(Grahams law)

V n (Avogadros law)

Avogadros law also states that, at STP where P = 1 atm, a mole of gas occupies22.414 L. If P = 1 bar, V = 22.711 L.

The van der Waals equation of state takes into account the intermolecular forcesbetween gas molecules and the volume of the gas, which the Kinetic MolecularTheory treats as negligible. The van der Waals equation of state predicts thenonideal behaviour of gases. Given the correction a for intermolecular forcesand the excluded volume per mole b,(

P +an2

V 2

)(V nb) = nRT

Gas mixtures For a mixture of gases in a single container, the total pressurein the container is equal to the sum of partial pressure of each gas according toDaltons law of partial pressures. Likewise, the total volume in the container isequal to the sum of the partial volume of each gas according to Amagats lawof partial volumes.

The mole fraction is the ratio of the number of moles of a gas to the totalnumber of moles of gas in a container. The mole fraction is also the ratio of thepartial pressure of a gas to the total pressure or its partial volume to the totalvolume, i.e.

A =nAntot

=PAPtot

=VAVtot

Note that 1 = A + B + . . . .

5.3 The solid state

Solids may be classified according to the arrangement of its constituents:

26 CHAPTER 5. PHASES OF MATTER

Crystalline solids have a regular pattern all throughout the solid.

Amorphous solids have almost no orderly arrangement at all.

Polycrystalline solids are aggregates of crystalline structures.

Likewise, solids may be classified according to the bonds that hold it together:

Ionic and covalent solids are held together by their respective chemicalbonds. These chemical bonds give these solids their hardness and high meltingpoints. However, their structures are fragile and will break all throughout oncethe structure is distorted, making it brittle.

Covalent solids lack the ions to carry charges through it and therefore cannotconduct electricity. Ionic solids cannot conduct electricity either because theions are held in place by ionic bonds. However, in liquid form, ions are free tomove and can therefore conduct electricity.

Molecular solids comprise molecules bound together by intermolecular forces,which are much weaker than the chemical bonds, making them softer and giv-ing them much lower melting temperatures. They also lack the ions to conductelectricity.

Metallic solids comprise positive metal ions in a sea of electrons coming fromthe ionised metals. The electrons of the metal atoms are insufficient to fill eachothers orbitals and, as a result, they are delocalised and shared by many atoms,enabling the solid to conduct electricity.

The sea of electrons attracts the positive metal ions, giving the solid a highmelting point. The smaller distance between the metal ions gives the solidhigher density. Unlike the brittle ionic and covalent solids, metallic solids aremalleable and ductile because distortion will not break the metallic bonds thathold the solid together.

Chapter 6

Nuclear chemistry

The concept of chemical reactions is more familiar to us since it abounds innature. Only valence shell electrons are involved in chemical reactions, unlike innuclear reactions where particles in the nucleus are involved. Chemical reactionssimply makes and breaks bonds between the reacting atoms. Nuclear reactionscan create new elements or isotopes. The energy involved in nuclear reactionsdwarf those involved in chemical reactions.

6.1 Radioactivity

Radioactivity is the spontaneous emission of particles or ionising radiation byunstable nuclei of heavier elements. Radioactive nuclei are called radionuclidesand atoms which have these nuclei are called radioisotopes. These nuclei un-dergo radioactivity to lose energy and make themselves stable.

The stable nuclei, when plotted with the number of protons on the y-axis andthe atomic number on the x-axis, form a belt of stability, printed in Figure 6.1in blue.

Below is a summary of the three kinds of radiation, , , and , in additionto two more nuclear changes a nucleus can undergo, + emission and electroncapture.

AZX A 4Z 2Y + 42 ( radiation)AZX AZ + 1Y + 01 ( radiation)AZX AZX + ( radiation)AZX AZ 1Y + 0+1 (+ emission)

01e +

AZX AZ 1Y (e capture)

27

28 CHAPTER 6. NUCLEAR CHEMISTRY

Figure 6.1: The belt of stability

The mass and atomic numbers on a reaction are not simply balanced to followthe rules. The equations below explain how 0-1 and

01e emission and

0-1e capture

occur:

11n 11p + 01e ( radiation)11p 10n + 01e (01e emission)

11p +

01e 10n ( 0-1e capture)

The rate of decay A of a substance is directly proportional to the numberof atoms present N , i.e.

A = N

where is the decay constant of the substance. The decay constant is also usedin the formula for the half-life t 1

2of a substance

t 12

=ln 2

6.2 Nuclear equations

Nuclear reactions are not limited to the generic equations above. Nuclei caneven undergo fission or fusion, although fission usually happens to an atomwhose mass number is greater than 200. Nuclear equations follow a rule similar

6.2. NUCLEAR EQUATIONS 29

to the law of conservation of mass: the sums of the mass and atomic numberson each side must be equal to each other.

Mass-energy conversions may also occur in a reaction. Given the masschange m and the speed of light c, the energy change is given by

E = mc2

While the equation usually gives the energy change in joules, the energy changemay also be expressed in mega-electron volts (MeV) using the equation

1 MeV = 1.6022 1013 J

Nuclear transmutation is the process by which a nucleus is bombarded witha neutron or another nucleus to experience change. The shorthand notation fornuclear transmutation is as follows:

Original nucleus (Bombarding particle,Resulting particle) Resulting nucleus

A nuclear chain reaction is a self-sustaining sequence of nuclear fissionreactions. This reaction occurs only when the amount of fissionable materialis equal to or greater than the critical mass, the minimum amount of materialrequired to generate a self-sustaining nuclear chain reaction. 1

Radioactive series As mentioned earlier, there are nuclei which are unstableand undergo nuclear reactions to become more stable. There are elements whichundergo a succession of these nuclear reactions to go from unstable to stable,and this is called a radioactive series. There are three radioactive series innature, the 23892U series which ends with

20682Pb, the

23692U series which ends with

20782Pb, and the

23290Th series which ends with

20882Pb.

1This definition is copied verbatim from [3].

30 CHAPTER 6. NUCLEAR CHEMISTRY

Bibliography

[1] Bissonnete, C, Herring, F. G., Madura, J. D., & Petrucci, R. H. (2010).General Chemistry: Principles and Modern Applications. Toronto: PearsonCanada Inc.

[2] Brown, T. L., Bursten, B. E., LeMay, H. E., Murphy, C. J., & Woodward, P.M. (2012). Chemistry: The Central Science. Upper Saddle River: PearsonEducation, Inc.

[3] Engle, H. L. & Ilao, L. V. (2008). Learning Modules in General Chemistry1. Manila: University of the Philippines Manila.

[4] Logronio, A. J. (2011). Chemistry 14: The Fundamentals of General Chem-istry I. Manila: Author.

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