Preview principles of physical chemistry by dr mahbubul haque, dr mohammad yousuf ali mollah

Preview Principles of physical chemistry by Dr. Mahbubul Haque, Dr. Mohammad Yousuf Ali Mollah Preview Principles of physical chemistry by Dr. Mahbubul Haque, Dr. Mohammad Yousuf Ali Mollah Preview Principles of physical chemistry by Dr. Mahbubul Haque, Dr. Mohammad Yousuf Ali Mollah Preview Principles of physical chemistry by Dr. Mahbubul Haque, Dr. Mohammad Yousuf Ali Mollah Preview Principles of physical chemistry by Dr. Mahbubul Haque, Dr. Mohammad Yousuf Ali Mollah

Huque and Nawab

Principles of

Physical Chemistry

Fully Revised by

Dr Muhammad Mahbubul Huque

Dr Muhammad Yousuf All Mollah

jumad Mahbubul Huque

Mohammad Yousuf A Mollah

Brothers' Publication

3/5 , Rafme Plaza

Mirpur Road, D hak a-1205

January, 2009

Fully R evised Edition : 2009 \

Fully Revised Edition-20\

(All rights reserved, no part o f this publication can be reproduced in any farm

w ithout the p rio r perm ission o f the authors.]

C o m p o se d by

A lka C om puter

B anglabazar, D h a k a -1100

Muhammad Mahbubul Hu que

M.Sc (Dhaka), Ph D (McGill, Canada)

Mohammad Yousuf All Moliah

M.Sc (Dhaka), Ph D (Macquarie, Australia) Professor

Department o f Chemistry cr"

Dhaka University, Dhaka

BROTHER’S PUBLICATIONS

3/5B RAFIN PLAZA MOBILE - 01674175433

FARHA N BOOK CEN TRE

Istamia Market, Milkhet

H e l p lin e

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01819440121,0] 720-579009, 01199-198703 0X711662823

Dedicated to the memory of

Late Professor M Ali Nawab

Professor M A Nawab was (he senior author o f the First Edition o f the book He was Professor o f the Department o f Chemistry o f Dhaka University Late Professor Nciiuab xoas the Chairman o f the Department o f Chemistry o f Dhaka University during 1973-Ĩ976

Professor Nawab expired on 23 A pril 1993.

The first edition o f 'Principles o f Physical C hem istry' was published in 196S and the third edition cam e in

1974 The authors did not make attem pts to bring out further editions o f the book as at th.ii tim e science texl books written in Bengali were preferred by the students W e had forgotten aboui ihe book Professor

M A Nawab, [he senior author expired in 1993 Then about three years back a form er student o f mine who was doing undergraduate studies in Pharm acy in a Private U niversity in Dhaka showed me a photocopy o f ihe original third edition o f the book which was being used as a text book This was described as a ‘fully revised edition’, A survey revealed that a large num ber o f students in different universities and colleges in Banzladesh were using this Tully revised edition’ as a text book o f Physical Chem istry As m entioned this was not a Revised Edition as the authors did not m ake any revision after Ihe third edition Professor M

Y ousuf A M ollah Professor o f Physical C hem istry at the Dhaka U niversity, persuaded me to prepare a revised edition I agreed on condition that he will be a co-author The book on Physical C hem istry being presented with !he sam e title as !he original one is (he result o f joint efforts o f Prof M Y ousuf A M ollah and me W e traced the printing house w hich had been m arketing ibe photocopies as 'fully revised edition’ They apologized for their action and agreed to publish the edition we have prepared.

T his is a Fully Revised Edition with m ajor changes W hite rewriting this book we focused on !he syllabii o f undergraduate courses o r Physical C hem istry o f Public, Private U niversities and U niversity C olieges in Bangladesh The students o f Pharm acy, B iochem istry and Engineering will also be benefited from this book All through the book SI units have been used M any chapters have been rewritten with additional

m aterials A num ber o f chapters have been divided into sm aller chapters for the convenience o f the Students: For exam ple T herm odynam ics has been presented in three chapters with titles: Therm odynam ics I: the First Law, T herm ochem istry, T herm odynam ics II: [he S econd and the Third Law, The chapter on Solution has been divided into Solution and D ilute Solution E lectrochem istry has been divided into two chapters: Electrolytic C onduction and Electrolysis, Elecirochem ical cells T he chapter on Reaction Kinetics has been presented com pletely in a new form at A cids and Bases have been presented as a separaie chapter Solubility and Solubility Product form a new chapter As the m aterial presented in the chapter on Surface Chem istry and C olloids in the third edition is considerable, this has been split into two chapters: Surface Chem istry and C olloidal Slate In many chapters topics have been rew ritten with [he inclusion o f new materials and presented in a belter w ay: B rief discussion o f mass spectra, IR and N.M.R spectra and their applications are included in ihc chapter on Physical Properties and M olecular Structure End o f Chapter

Q uestions and Problem s have been revised, many new questions arid problem s with answers have been incorporated The form at o f the book has also been changed .

W e hope that the Revised Edition o f the book with its new look will receive the sam e acceptance by the students and teachers as the earlier editions.

Printing o f this book has been an arduous task The publishers are not well acquainted with printing a book

on science with a lot o f Figures and form ulae They have, however, m ade great efforts to keep the book free

o f printing m istakes W e thank the publishers fur [heir valiant efforts In spite o f their best intentions you will find som e errors W e hope to elim inate these in the future edition.

PREFACE TO THE SECOND EDITION

W e are gratified to see that the first edition o f the book has been well accepied by the students and teachers

in spite o f the num erous printing errors In the preparation o f second edition attem pt has been m ade lo increase the clarity of the presentation at several places The num ber o f num erical exam ples at the end o f [he chapters has been considerably increased Apart from these changes little has been altered in (he arrangem ent o f the material and the get up W e have also tried hard to keep the printing errors at the minimum.

We are indebted to m any o f our colleagues in the universities and colleges w ho have kindly sent their criticism s and pointed out the shortcom ings o f the first edition T hese have been o f great help in m aking

im provem ent in the clarity o f representation.

We are sorry, we could not make ihe book com pletely free o f m istakes in spite o f our best wishes.

January, 1971

Dhdka

M M H uque

M A N aw ab

PR EFA C E TO TH E FIRST ED ITIO N

P rinting o f an object by a hundred painters, or writing o f a hundred poetrv on tile same subject need no explanation, but writing on a book on a subject like Physical Chem istry calls for an explanation specially

w hen excellent books in English are available D ufing the last many years o f teaching Physical Chem isiry

10 the undergraduate students, we have always felt the necessity o f explaining the fundamental conccpls

W e believe that once the basic principles have been understood by the students, more than halt the battle IS won In this respect, there is a need for a book on Physical Chem istry for our students whose background is different from those for whom the available books are meant M any o f these books cover fields wider and

d eeper th jn what is needed for our undergraduates at the B Sc (Pass) level We, therefore, felt the necessity o f w riting a book on Physical C hem istry that would fully meet (he requirem ents o f the B Sc (Pass) students and ai the sam e tim e help in building a sound background for the Honours students, We alw ays tried, while writing the book, to explain the basic principles as clearly and elaborately as possible It

is uptu the teachers who leach the subject and the students w ho w ould read to ju d g e whether our aim s have been ÍU [filled.

In the book most portions deal with the kinetic theory, Iherm odynam ics and chem ical kinetics We have used i.ome final results and equations o f Q uantum Chem istry and did not go anywhere beyond it because

w e thought that o m n iu m C hem istry and Statistical M echanics should be treated at a higher level Although the approach - has been basically classical attem pts have been m ade to acquaint ihe students with therm odynam ic approach, tn many placcs both kinetic and therm odynam ic treatm ent have been used to show that identical results can be obtained Only the methodology and physical concept are different

Q uanlum mechanics! approach has been kepi to m inim um , only flashes appear here and there.

In several places we have gone a little beyond than what is expected to form the syllabus o f Pakistani Universities The idea is to point to the fact that im provem ents need be m ade as is constantly being done in

w estern countries This is further m eani to provide the mental food for [he more serious and above average students The average students may leave out the.sc portions on advanced treatment.

C ontrary to com m on practice we have not included a chapter on atom ic structure and radioactivity These

tw o topics generally form a part o f Inorganic C hem istry syllabus in our country and excellent treatm ent is available in text books o f Inorganic C hem istry W e therefore, thought it wise to leave oul the branches from the present volume This has considerably reduced (he size o f the book.

W c express our thanks to a num ber o f our colleagues who always inspired us during the writing o f (he book Thanks are specially due to Prof M H K hundkar Head o f the D epartm ent o f Chem istry, University

o f D haka, for his encouragem ent at various stages Mr A J M ahm ood Senior Lecturer in Chem istry

U niversity o f D haka, deserves special thanks for kindly going through a large portion o f the manuscript and

m aking valuable suggestions T hanks are also due to Mr A N, M Akhter, a student o f the Dhaka College, for draw ing a number o f original sketches and helping in m aking the design o f the dust cover We are indebted to Mr M esbahul Haque for preparing the index We must also thank Mr Sycd Md Fazlul Huq o f the S tudents' Publications for taking the task o f publishing the book Mr A K M Raja M eah deserves special m ention Cor his untiring efforts and hard work in the printing o f the book.

G ood printing is a challenging task and in spite o f our best efforts som e m istakes are still there We

ap ologise for this and hope to im prove in the next edition W e shall appreciate receiving com m ents from those w ho use the book, so that im provem ents can be m ade in future.

CONTENTS

S T A T E O F A G G R E G A T IO N O F M A T T E R IN T E R M O L E C U L A R F O R C E S

1.2 lnterm olecular Forces

2 9 T he Use o f the G as E quation in C a lc u la tio n s In v o lv in g G ases

10 D iffusion and E ffusion: G ra h am ’s L aw o t D iffusion

2 11 E q u atio n o f S tale o f a G as M ix tu re : D a lto n 's L aw OÍ P a rtia l P re ssu re

2.12 T he K inetic T h eo ry o f G ases

2.13 R o o i-m e an -sq u a re (r.m s.) V elocity

2.14 D eriv a tio n o f th e K in etic E q u atio n

2 1 5 D eduction o f the G as L aw s from the K inetic E quation

2.17 D istribution o f V elo cities

2.18 Average V elocity, r.m.s Velocity and M ost Probable V elocity

2.19 Mean Free Path

2.20 V iscosity o f G ases

2.21 M o le cu lar D iam ete r

2-22 Frequency o f C ollisions o f Gas M olecules

2.23 N um ber o f M o le cu les S trik in g a S u rfac e

2 25 The Kinetic T heory - a review: B row nian M ovem ent

f 26 B e h av io u r o f R eal G ases: T he A m agat s C u rv es

r 2 7 M odification o f the Ideal Gas Equation: van der W aals' Equation o f State

2 -’8 S ign ifican ce and L im itations o f van d er W aals E quation

2.29 O ther Equations o f S tate

2.30 Change o f State: G as-Liquid Transition

2.31 A ndrew s’ E x p erim en ts w ith C O ;

18 18

19

20

21 22

24

25

25 27 29 30 31 32 33 33 34 35 35 36 37

38

41 43 43

44

2.32 D ete rm in atio n o f C ritica l C o n sta n ts 46

2 33 van d e r W aals E q u atio n and the C ritic a l P h en o m en a 48

2 40 A bnorm al D en sitie s o f G ases; M o le c u la r A sso c iatio n and D isso c ia tio n 64

5.7 Isothermal Reversible Expansion o f an [deai Gas: M axim um W ork 129

6.8 E ffect o f Tem perature on Heat o f Reaciion: The K irchhoff Equation 155

6.10 Heat o f N eutralization 158

T H E R M O D Y N A M IC S I I : S E C O N D AND T H IR D L A W S 171-201

8.13 Distribution o f a Solid between Two Immiscible Liquids : T he Distribution Law 216

8.15 A pplications o f D istribution Law

Q U ESTIONS AND PRO BLEM S

9 1 7

9 18 Relative Osmotic Pressure

9.19 Interrelation between the C olligative Properties

9.20 Abnormal M olecular M asses from C olligative Properties ’

9.21 Importance o f Osm osis Phenom enon

Q U ESTIONS AND PRO BLEM S

10 C H E M IC A L E Q U IL IB R IU M

10.1 Reversible Reactions

10.2 The Equilibrium Law: the Equilibrium C onstant

10.3 Gaseous Equilibria

10.4 Relation between K., and K,

10.5 Determ ination o f Equilibrium Constants

10.6 Criteria o f Chem icai Equilibrium

] 0.7 A ctivity and Activity C o-efficient

t o 8 Calculations Involving Chem ical Equilibrium

9.2 Ideal Solution

9 3 M olecular M ass from Low ering o f V apour Pressure

9-4 Derivation o f R aoult's Law •

9.7 Therm odynam ic D erivation o f Boiling Point Elevatiốn

9 8 Determ ination o f M olecular M ass from Boiling Point Elevation

9.9 Depression o f Freezing Point

9.10 Therm odynam ic D erivation o f the Freezing Point D epression

9 11 M easurem ent o f D epression o f Freezing Point

9 12 Osmosis and Osmotic Pressure

242 9.13 Sem i-perm eable M em brane

9 14 Determination o f O sm otic Pressure

9 15 Van't H o ffs Laws o f Osm otic Prer.i-Iire

9 16 D eterm ination o f M olecular M ass from Osmotic Pressure M easurem ents 246

9 17 Therm odynam ic D erivation of’ O sm otic Pressure Laws

250

252 252

226 228 228

229 231 233 235 237

238 240

255-283 255 257 260

261

262

2 6 2 263

264

264 269

10.12 Factors influencing Equilibrium : The Principle o t'L e C hạielier

10.13 A pplications o f the Principles o f Chemical Equilibrium 10

Reactions o f Industrial Im portance

10.14 Free Energy Change and Equilibrium Constant

10.15 Influence o f Temperature on Equilibrium C onstant: Thermodynamic Derivation QUESTIONS AND PROBLHM S

11.6 Sublim ation and Triple Point

11.7 Solid-liquid Equilibria: Eutectic Point

11.8 Liquid-Liquid System s

11.9 Fractionating Colum n

11.10 C om pletely M isibte Liquid Pairs Show ing D eviation from R aoult’s Law 11.11'D istillation o f Non-idea] Solutions : Azcofropic M ixture

11.12 L iquid-L iquid Equilibria in Partly M iscible System s :

Critical Solution T em perature (CST)

11.13 Immiscible Liquid Pairs: Steam D istillation

Q U ESTIO N S AND PRO BLEM S

K IN E T IC S O F C H E M IC A L C H A N G E

12 i The Definition o f Rate o f a Reaction

12.2 Experim ental D eterm ination o f the Rate o f a Reaction

12.3 Factors A ffecting the Rates o f Reaction

12.4 Dependence o f Rate on C oncentration: T he Raie Law

12.5 Units o f Rate Constants

12.6 D eterm ination o f the Rate Law: D eterm ination o f O rder o f Reactions 12.7 Som e Typical R eactions

12.8 Com plex Reactions

12.9 Influence o f T em perature on Reaction Rates

12.10 C ollision Theory o f R eaction Rates

12 [Ỉ Transition State Theory

12.12 The Rate Law and M echanism o f R eaction

12.13 M oiecularity and O rder o f Reactions

i 2 14 U nim oiecular Reaction: Lindem ann's M echanism

12 15 T heory o f Absolute Reaction Rate

12 23 D eterm ination o f Q uantum Yield

12.24 Photosensitized R eaction

12 °6 Radiation Chem istry

I') 29 H eterogeneous Reactions in Solution

13 5 Prom oters and Catalytic Poisons

13.8 M e c h a n i s m o f A cid-Base C atalysis

13.10 M echanism o f E nzym e Catalysis

Q U ESTIO N S AND PRO BLEM S

14 4 T he M cchanism o f Electrolytic C onduction ,

14 7 The Conductance o f Electrolytic Solutions

14.9 Conducianee Ceil: Cell Constant

* 3 4 7

14.10 Conductivity W ater 390

15.13‘Effect o f C oncentration and Tem perature on Electrodc Potential: The Nernst Equation 426

( x v i i )

16.8 Dissociation o f w eak acids and weak bases: O stw ald’s D ilution L aw 465

16.10 pH o f solutions o f very weak acids

16.17 Buffer Solutions

16*18 Salt H ydrolysis

16.19 The pH o f Salt Solutions

17 SOLUBILITY ANDCOMPLEX-ION EQUILIBRIA «M-50S

17.2 Solubility and Common !on Effect

17.3 Predicting Precipitation

17.5 Equilibria o f Complex Ions

15.8 G ibbs' A dsorption Equation

15.9 Adsorption from Solution

State of aggregation o f m a tte r: Interm olecular forces 1

1 STATE OF AGGREGATION OF MATTER

ỈNTERMOLECULAR FORCES

1.1 M atter: States of Aggregation

Under ordinary conditions all material bodies exist in one of the three states of aggregation-solid, liquid or gaseous Apart from these well known states matter is also found to exist in three other states, e.g liquid crystals, giass and an unusual state under special conditions called the plasma state Each state is characterized by some specific properties For example, solids have definite shape and size and these are incompressible

On the other hand, liquids do not possess any definite shape or size It takes the shape of the container in which it is placed Liquids are also only slightly compressible Gases are highly compressible When placed in a container a gas completely fills it, that is to say, gases do not have a definite volume A common characteristic o f solids, liquids and gases

is that these expand when heated at constant pressure, but the amount of expansion is much more ill Ihe case o f a gas than in the case of a liquid or a solid

ĩn describing the nature of matter Ihe atomic molecular theory of matter has been universally accepted According to this Iheory the smallest particle of all elements is culled atom Atoms o f the same element have the same characteristic structure and properties The structures and properties of atoms of different elements are different The molecule is defined as the smallest particle of matter which can exist independently.Molecules of most substances are composed o f two or more atoms of the same or

different elements Examples are molecules of nitrogen, N 2 , or carbon dioxide, CŨ 2 -

Molecules of the rare gases like helium, argon etc and those of mercury are made up of one atom and hence are called monatomic The physical and chemical properties o f a substance are the sum of the properties of all the molecules of which it is composed

A substance may exist in all the three states o f aggregation under different conditions o f temperature and pressure, but it has the same molecules The effect o f heat on a oiece o f ice may be taken as an example When heated, ice melts to form liquid water On heating further liquid water is converted into steam or water vapour Heat is a form o f energy and ever since the days of Count Ruml'ord heat energy has been related to motion When motion is increased more heat is produced or, conversely, when heat energy is added to a substance, i.e., the substance is heated motion increases The question is motion o f what increases as a result o f heating? ]n trying to answ er this question it was soon realized that it must be the motion o f the molecules that increases on h e a tirg ■’ hodv Thi’ k’i'=vtic rrtoleculi!" theory o f matter

look ils birlh The molecules may execute any one or more of the three possible types

o f motion, namely, translational, rotational and vibrational (Figure 1.1) Translational motion consists in movement from one position to another For rotational and vibrational motion displacem ent o f the molecule is not necessary Rotation of the molecule may take place around any of the different axes, whereas vibration o f the molecule may take place around a mean position

Figure 1.1 (a) Rotation of molecules; (b), (c) and (d) Different types of vibration

Based on the atomic molecular and kinetic molecular theory of matter the characteristics of the three states of matter may be summarized as follows

ỉn the solid state the molecules or ions are fixed in a uniform manner in definite mean positions in the solid state There are strong intermoỉccular (or inter-ionic) forces which keep the molecules (ions) in their positions in (he lattice The only type of movement that the molecules may undergo is vibration around their fixed mean positions The resulting

structure is a fairly rigid one, having a definite shape and a definite volume, which

strongly resists compression, expansion and distortion

In the liquid state the molecules or ions have more energy They have sufficient energy to overcome ihe forces which hold the particles in their positions in the solid state

As a result ths molecules or ions possess translational motion but within a limited range,

as the energy is not so high as to enable them to overcome the attractive forces altogether The liquid state is, therefore, such that in this state it has a definite volume but not a definite shape As ihc molccules (or ions) cannot escapc far from each other the compressibility o f a liquid is high In the liquid state the molecules (ions) also possess rotational and vibrational energy

When the molecules have sufficient energy which enables them to completely overcome the attractive forces the molecules form Ihe gaseous state o f matter In the absence o f the attractive forccs molecules can move about in a random manner within the container at high speeds As a result, they distribute themselves uniformly throughout the whole volume o f the container A gas, therefore, has no definite shape or volume In the gaseous state the molecules are far apart from one another, and the volume within which the gas is confined is almost empty space This explains why the gases are so highly compressible When pressure is exerted the volume of the gas decreases, i.e., the molecules get closer In addition to translational energy molecules in the gaseous state also possess rotational and vibrational motion

The conversion of solid to liquid and that of liquid to gas takes place on the application of heat The reverse process o f converting a gas into a liquid may be accomplished by compressing the gas (so that the molecules are very close) and cooling

so that the molecules have lesser energy than required to overcome the forces OÍ repulsion On further cooling, the translational energy may be decreased to such an extent that the attractive forces will hold the molecules in fixed positions, i.e., the solid state is reached Ill solids, therefore, the particles are very d o s e to each other, in liquids they are close but not very close, but in gas they are widely apart This is shown in Figure 1.2 as a pictorial representation

State o f aggregation o f m a tte r: Interm olecular forces 3

SolidFigure 1.2 Schematic representation of gas, liquid and solid

It should be noted that solids may also be converted to the gaseous state w ithout passing through the interm ediate liquid state by application o f heat Such a process

is known as sublim ation The above argum ents may be given for such transformation C hanges o f states are, therefore, reversible p rocesses as sho w n inFigure 1.3

Solid

Figure 1.3 Reversibility between three states of matter

W hen solids are converted into liquids, intermediate phases possessing some of the molccular order characteristic of crystalline solids are sometimes obtained These

intermediate phases are called liquid crystals (Section 4.14.1) bccause they possess some

of the properties of both solids and liquids

G lasses are amorphous substances which have the properties o f a solid but the

structure of a liquid Although apparently solid, structurally they resemble liquids as their constituent particles are found Lo be randomly Arranged Glasses are amorphous, meaning without shape* These are, in fact, liquids coolcd below their freezing points without crystallization taking place These arc regarded as supercooled liquids and are considered

Plasm a is an ionized gas formed when high temperature strips electrons from atoms

Plasma is an electrically neutral mixture o f electrons and positive ions It exists in the sun where nuclear fusion takes place Over 99% o f the matter in the universe, in stars and galaxies, seems to exist in the form o f plasma The sun and stars consist o f matter in the form ot highly ionized plasmas formed at verv high temperatures

1,2 Interroofecular Forces

In the above paragraphs mention has been made o f intermolccular (or inter-ionic) forces One might ask ‘what is the origin of these forces'? We have to remember that atoms and molecules are made up OÍ only protons, electrons and neutrons O f these, prnlons in the nucleus are positively charged, electrons are negatively charged and neutrons do not carry any charge These are particles with very small mass As the effect

o f gravitational attraction between particles of such small mass is extremely small and negligible, one can only think that the forces between particles must be electrical in nature The melting point and the boiling point o f a substance are measures o f the strength oi such forces The higher Ihe melting and boiling points stronger must be the attractive forces between particlcs, i.e ions or molecules

From the study o f the nature of these forces it has emerged that there are different types o f forces between particles These forces arc listed below :

(a) Ionic interactions

(i) P ip o ie -d ip o le interactions

(ii) Dipole-induced rtipple interactions

(iii)Dispersion forces (instantaneous dipole-induced - induccd dipole interaction)(ivjHydrogen bonding

As an approximation the relative strengths of these forces can he summarized as follows:

T ab le 1.1 Relative s tre n g th s of in te r-p a rtic le forcesType o f interaction Relative strength

State o f aggregation of matter : Interm olecular forces 5

(a) Ionic Interactions

Electrostatic interactions occur between ions resulting in the form ation of strong ionic bonds These bonds are formed when metals atom s tran sfer their valcnce electrons to non-metal atoms forming positively charged metal ions (cations) and negatively charged non-metal ions (anions) The oppositely charged ions attiact each other forming a three dim ensional giant rigid structure in the solid state Ionic com pounds have high melting and boiling points as large am o u n t oi energy IS required to overcom e the electrostatic forces o f attraction betw een the charged ions

In the m olten state they are good conductors o f electricity as the ions becom e free and mobile

In cases where a small cation with large charge combines with an anion having a large size the resulting compound may have some covalent characters Examples are,

aluminum chloride) of compounds between metals and non-metals which are completely covalent

Metal atoms are held together by strong m etallic bonds.

(b) van der W aals Forccs

(i) Dipole - dipole interactio n s : Dipole-dipole interactions were first described by Willem Hendrick Keesom in 1921

These are the forces that occur between two polar m olecules w ith perm anent dipole m om ents D ipole-dipole attractions are electrostatic in nature like the ionic bonds but are w eaker because only partial charges are involved An ex am p le o f this type o f interactions can be seen in the hydrogen chloride m olecules In a H Cl molecule there is large difference in electronegativity b etw een H atom and Cl atom

(C l is much more electronegative than H ) and the electron pair between these tw o

atoms in h i Cl molecule is attracted more strongly by Cl atom than by the H atom

This unsym m etrical (unequal) distribution o f the electron pair b etw een the

com bining atoms give rise to partial positive charge (5+) on the H atom and partial negative charge (S') on the Cl atom As a result a dipo le is form ed, and the m olecule

is called po la r W hen two polar H C l molecules are close to ge th er a structure sim ilar

to the one shown below is formed

Ò + Ó

-H— Cl -H— Cl

In a polyatomic molecule if the bond polarities do not cancel each other then the molecule has an overall polarity This can happen because the symmetry in shape of the

molccule Examples are H 2 O and B F j molecules Water is polar, but BF3 is non-polar as shown b e l o w :

F S “

Figure 1.4 Shapes of H ;0 and BFj molecules

As can he seen, the bond polarities in BFi cancel each other, because o f the symmetrical planar shape o f the motccule In water, however, o - H bond polarities do

not c a n e d as the molecule has a he 111 shape

(H) D ipole-iw lticttl d ip o tc in te ractio n s : Dipole-induced dipole interaction involve (he attraction belwcen temporarily induced dipoles in non-polar molecules This pof dilution can be induced either (a) by a polar molecule or (b) by the repulsion of Ihe negatively charged electron clouds in a norvpolar molecule An example of the former is chlorine dissolving in water

( Í + ) < £ - ) (d+> ■ tử’- ) <Sy)

[Perm anent dipole] H - o - H - Cl - Cl [Induced dipole]

This is an example o f interaction between the permanent dipole of water molecule and iiO induced dipole on chlorine molecule The dipole in non-polar chlorine molecule is induced by the electric field offered by (he permanent dipole of water molecule This

permanent diooJe -induced dipole interaction is referred to as induction (or polarization)

interaction and is to be distinguished from London dispersion interaction.

Oil) Induct'd dipole-i ml u m l dipule fore© (London forces or dispersion forces)

The above ideas o f intcrmoỉecuiar forcc are unable to explain why molecules which

do not have dipoles and noble gases like argon, xenon etc can be liquefied and solidified Strong attractive forces must exist between the molecules or atoms (in case o f noble gases) to keep the particles together in these states

l.ef us take the ex am ple o f a Xenon atom The electron distribution about the

nucleus o f a Xe utom is perfectly spherical However, the electrons are constantly in motion and it is possible that at any given instant in some o f the X e atoms all the

electrons may be positioned on one side o f the nucleus, temporarily giving rise to partial positive charge ai one end o f the atoms and a partially negative charge on the

other side As a result an instantaneous dipole is formed in these Xe atoms During

this transitory existence the instantaneous dipole is likely to induce a dipole in a

neighbouring atom and the two instantaneous dipoles attract each other A schematic diagram o f this situation is depicted in Figure 1.5.

<5+ - a - Ổ+ -Ỗ—

State o f aggregation o f m atter : Interm olecular forces 7

Figure 1.5 London forces as the instantaneous dipole in A forms, it induces a dipole in atom B Forces between transitory dipoles are called instantaneous dipole-induced dipole

fo r c e s , or alternately, London fo rc e s or dispersion fo r c e s after Fritz London who first

proposed them We will refer £ữ them as dispersion fo rces It should be realized that in

u one gram sample o f any substance the number o f particlcs (atoms or molecules) is so large that if a small fraction o f such particles are oriented in the manner described the attractive force between the particles will be significant It is these forces that are responsible for (he liquefaction and/or solidification o f substances whose molecules do not possess permanent dipole moments For example, dry ice or solid carbon dioxide The carbon dioxide molecule is linear and has no overall dipole moment Similarly, carbon tetrachloride, with perfectly tetrahedral mọlecules and no net dipole moment, is

a liquid at room temperature, and iodine, which consists o f iodine molecules, is a solid

at room temperature

Dispersion forces depend on two aspects o f molecular (or atomic) structure

• First, they increase in magnitude with the size and number of electrons and protons in the interacting particles and hence with their molecular masses (or atomic masses) Examples are: (a) the boiling points o f the noble gases increase from helium to xenon; (b) fluorine and chlorine arc gases at loom temperature and

1 atm pressure, bromine is a liquid, and iodine is a solid; (c) large polymers which are electrically neutral are solids with low transition temperatures from solid to liquid Only dispersion forces arc operative in these substances

• Second, dispersion forces depend upon molecular shape via the surface area over which two molccules can be in contact When the molecules are close to each other lying side by side there arc more sites of interaction; the molecules are able

to come in contact over a large portion of their length At each region o f contact

of the surface of a molecule distortion of the electron distribution may take place

and temporary dipoles may be created which will lead to dispersion forces in each region The larger the surface area of contact the stronger the dispersion forces Examples are: large polymers with linear structure which are neutral solids have low transition temperatures from solid to liquid.

If the molecule is not linear but has branched chains the number of contact points between the molecules is less and the strength of dispersion forccs is also less For

example, n- p en tnne and 2,2-diinethyỉpropa.ne have the same molecular mass but the boiling point o f n-peiitane is higher by 27°c than that of the other isomer.

It is important to realize that dispersion forces operate between all molecules, whether

or not other forces also operate Molecules of chloroform, CHCỈ3, are attracted by a

combination of dipole-dipole and dispersion forces Dispersion forces are generally weaker than dipole-dipole forces, having values in the range 0.1 to 5.0 kJ mol-

1.3 Hydrogen bonding

Strong forces of attraction exist between molecules containing a hydrogen atom bonded to a highly electronegative element such as nitrogen, oxygen or fluorine This can

be deduced by comparing the boiling point o f water (H 2 O) with that of hydrogen sulphide

forces between H 2 O molecules must be much stronger than that between H2S molecules Water is a highly po lar m olecule and the strong attraction between water m olecules is

bonding because of the strength o f such attractions as compared to other dipole-dipole

attractions {Table 1.1) Hydrogen bond is defined as follows:

In com pounds where a hydrogen atom is covalently bonded to a highly electronegative atom such as nitrogen, oxygen o r flu o rin e the strong attrative fo rce between a hydogen atom o f one molecule fo r the electronegative atom o f another

m olecule is called the hydrogen bond.

The large electronegativity difference between the hydrogen atom and the electronegative atom gives rise to a partial positive charge on the hydrogen atom and a

partial negative charge on the other atom joined by a covalent bond HCl is an example as

shown before

As a result a stabilizing interaction between two or more molecules is developed that

binds the molecules together A common example o f H-bonding is found in water:

State o f aggregation o f m atter : IntermoleuLilar forces 9

It should be understood that hydrogen bond is an interm olecular fo rce a nd not a bond

as is understood in the cases o f ionic o r covalent bond No transfer o r sharing o f electrons occur.

Evidences of hydrogen bonding are found throughout nature Hydrogen bonding explains why the density of ice is less than that of liquid water In the liquid state the water molecules joined by hydrogen bonds constantly change partners When water starts freezing the hydrogen bonds between the molecules get fixed and in the solid state, as the moleculcs can not move, the hydrogen bonds between molecules get fixed in position In the solid state (ice) each oxygen atom is surounded tetrahedrally by four hydrogen atoms: two forming covalent

bonds with the o atom and arc close to it to form HzO molecule and two from other H 2 O

molecules farther away from it forming two hydrogen bonds The result is a three­dimensional structure with empty space This is why ice is less dense than water When ice melts and liquid is formed again hydrogen bonds are constantly breaking and forming so that molecules can get close to each other giving rise to the liquid This is a unique property of water and is very important to life on eaith

Figure 1.6 S tru c tu r e o f ice

Intramolecular hydrogen bonding (i.e hydrogen bonding between the hydrogen atom

in one part of the molecule with an electronegative atom like oxygen or nitrogen in

another part o f the same molecule) can also take place For example, in 0- nitrophenol the hydrogen atom of ihe 0 - H group forms a hydrogen bond with one O- atom o f the

N O group of the same molecule as shown below:

H 'B onding

u

% ỵ ° ~ n " N

Figure 1.7(b)

Intramolecular hydrogen bonding in o-nitrophenol causes this compound to have a lower boiling point than /j-nitrophcnol where intermolccular hydrogen bonding (hydrogen bonding between two or more molecules) is present In p-nitrophenol intramolecular hydrogen bonding is not possible because of the distance between the atoms which form such a bond This is shown in Figure 1.7(b) ơ-nitrophenol is much less soluble in water compared to p-niirophenol This is bccause p-nitrophenol can form hydrogen bonds with water Figure 1.7(c) whereas y-nitrophenol cannot

Intramolecular hydrogen bonding in macromolecules o f biological origin is o f great importance in living beings Examples are the proteins in silk, hair, DNA, RNA etc Many proteins are linear polymers (macromolecules) formed by reactions of a-amino

acid RC H (N H 2)C O O H (Figure 1.8) As a result proteins consist of long chains o f repeating units shown below in which the amide group - NH - CO - is repeated This is

known as the peptide group in proteins, and proteins are sometimes referred to as polypeptides

c - o

IINV

Figure 1.8 A part of protein molecule

showing NH-CO bond formation

State o f aggregation o f m a tte r: Interm olecular forces 11

In some naturally occurring proteins

two or more linear polymer molecules are

joined together by hydrogen bonding

(Figure 1.9) This creates secondary

structures o f proteins In many proteins,

including those in silk, hair, wool and nails

hydrogen bonding causes the polypeptide

chains to become twisted into tightly coiled

helices (a helix is a spiral structure).

Intramolecular hydrogen bonding is

important in the formation o f the double

helix structure o f DNA (deoxyribonucleic

acid) DNA is present in the nuclei o f

living cells and carry genetic information

The DNA molecule consists o f two helical

nucleic acid chains Each nucleic acid is

made up of 3 (three) components : a sugar,

a phosphoric acid unit and a nitrogen-

containing heterocyclic base - adenine (A),

cytosine (C), guanine (G) or thymine (T)

The iwo nucleic acid chains are held

together by hydrogen bonding

These hydrogen bonds are formed between

The two strands coil tightly around each other (1

QUESTIONS AND PROBLEMS

states.

2 in ihe gaseous state what type movements the m olecules can make?

3 W hat types o f forces are responsible fo r keeping the particles together in th e solid state and the liquid

state? D o these forces operate in the gaseous phase?

4 What is the origin o f ihe inter-particle forces?

temperature, while under ll»e same condition B n is a liquid anti /; is u solid.

7 Define hydrogen bonding With an appropriate example show the nature o f hydrogen bonding.

m olecules Hydrogen chloride lias a boiling point o f - 45"C whereas hydrogen iodide boils

at - 3 5 °c In lerrns o f types o f intermolecular forces explain w hy this is so.

e le m e n ts an d the fact sta le d ab o v e.

THE GASEOUS STATE

All substances that we ordinarily call gases (e.g nitrogen, hydrogen etc.) have been liqueiied and solidified by suitable reduction of temperature and application of pressure Many common liquids and solids have been converted into the gaseous state at low temperatures and high pressures Gases, therefore, represent a state of matter Gases are characterised by

(a) high co m p ressib ility and low density

(b) their ability to fill a container irrespective o f the quantity o f gas present in it(c) larg e capacity o f thermal expansion

(cl) m iscibility in all proportions o f a gas with one or more different gases

As pointed out in C hapter 1, from the m olecular point of view these properties can be acc o u n ted for if one rem em bers that in the gaseous state the molecules have sufficient translational energy to overcom e the attractive forces which tend to keep

th em in fixed positions as in a solid or in random m ovem ent as in a liquid

2.1 Ideal G ases: T h e G as L aw s

The great com p ressib ility and large capacity of thermal expansion o f gases v.'ere d escrib e d in the form o f experim entally established laws a long time ago

M athem atical relationship betw een volume, pressure and temperature o f a fixed

mass o f gas are kno w n as ga s law s The relationship between mass and volum e o f a

gas at fixed tem perature was known All gases, irrespective o f their chem ical nature,

o bey these law s provided the pressure is not too high or the temperature is not too low

2.2 B oyle's L aw

The effect o f pressure on the volum e o f a gas was extensively studied by Robert

B oyle in 1662 He enclosed som e gas at the short end o f a J-shaped tube and poured

m ercury at the o th e r end He found that the volum e o f the gas decreased (Figure 2.1) Each addition o f m ercury meant increase o f pressure and this resulted in

d ecrease o f volum e o f the gas The volum e o f a given mass o f gas is 100 mL at atm ospheric pressure The volum e is halved when the pressure is doubled by adding

Hg The v o lu m e is d ecreased to 33 mL by tripling the p ressure to 1520 mm Hg From such ex p erim en ts he form ulated a law o f gases, known as B o y le ’s law

A ccording to this law,

The Gaseous State 13

Figure 2.1 Boyle’s experiment

A t constant temperature a fix e d mass o f gas occupies a volume which is inversely

proportional to the pressure exerted on it.

If the p ressure is doubled the volum e becom es one-half o f the original

E xpressed m athem atically the law states that

y ° c — (ft and T constant) (2.1)

Here n is the number o f moles o f gas and T is the temperature.

it says that if a given mass of gas occupies a volume Vj at a pressure o f p 1 and a

volume Vĩ at a pressure o f P 2 at a constant temperature then

Figure 2.2(a) shows the relation between volume find pressure at constant temperature

A plot o f p against V at constant temperature is shown in Figuic 2.2(a).

Figure 2.2(a) Figure 2.2(b)Pressure-volume re la tio n o f a g a s P V v s p o f a g as

The validity o f B o y le’s law may be ju d g e d from the data given in Table 2.1 Note that the product o f pressure and volum e is very nearly constant as suggested by

equation (2.3) A plol o f p against p would show a graph as in Figure 2.2(b).

Table 2.1 Pressure - Volume relation of helium i)t 0 ° c

Pressure (p )

mm o f Hg

Volume(V)mL

The use o f the equation (2.3) is illustrated in the following example

Example 2.1: 30 L o f a gas exerts a pressure of 7 10 mm Hg at a temperature o f 25°c What will be the volume o f the gas at the same temperature if the pressure is rcduced to

-300

2.3 C h arles’ Law or G ay-L ussac's Law

AM gases increase in volum e when their temperature is raised If numerical data ol

v olum e of a given quantity o f gas held at constant pressure are plotted against temperature in the centigrade scale (as shown in Figure 2.3) it is found that the points fall on a straight line This indicates a linear relationship betw een v olum e and tem perature when the pressure is kept constant

If the temperature is sufficiently

lowered, the gas liquefies and no

more experim ental points can be

obtained H owever, it the straight

line jo in in g the experim ental points

is extended as shown by the dotted

line, it cuts the point of zero volum e

at a tem perature of - 2 7 3 1 6 ° c

Experim ents have shown tha.1 this

temperature, i.e - 2 7 3 '1 6 ° c does not

depend on the nature of the gas

provided it is stable, nor docs it

depend on the p ressure at which the

ex p erim en t is perform ed This tem perature is know n as the a b so lu te zero OJ

the sam e as 273.16 °A Similarly 1 0 0 °c would be (100 + 273.16 =) 373.16 °A

T em peratures below absolute zero would correspond lo negative volum e, w hich docs not have any physical meaning, ỉn the absolute scale tem p eratu re IS also recorded as °K (degree Kelvin) or jusL K in honour o f Lord K elvin who first deduced this sculc o f tem perature from theoretical considerations, l h e expression

for the relation betw een the volum e of a gas and tem p eratu re is k now n as Charles

law in honour o f the French physicist w hose experim ents established it (1787) I he

law may now be stated as follows:

Tile volume o f a given quantity o f gas is directly proportional to the absolute

M athem atically it may be expressed as

Figure 2.3 Volume of a given mass of gas VJ

temperature in °c

or

T

( n and p constanl)

(k is a constant at constant pressure)

The value o f the constant k depends on the m'es'-urc

(2.5)

mv! on tly? C[ìiuní.ĩ' y o f gas

Figure 2.4 shows some plots o f V against T (°K) pt different p.

Figure 2.4 Volume of a fixed quantity of gas against temperature ( K) at different pressures.

ỈÍ follows from this expression that if a given quantity o f gas at a particular

p ressu re has v olum e Vi at tem perature T/ and volume Vj at tem perature T: then we

should have

r t T2 (2.6)

T h is law is also som etim es know n as G ay-Lussac's Law (1802) Gay-Lussac

studied the effect o f temperature on the pressure o f gases keeping the volume constant G ay -L u ssac’s law may now be expressed in the following form :

The p re ssu re exe rted by a fix e d m ass o f a g a s is d irectlv p ro p o rtio n a l to absolute

tem perature o r the Kelvin tempers Hire

A ccording to this law by following the same argument as in the case o f C h arles’ law

we can write

p \ _ p2

(2.7)

E x a m p le 2 2: A given mass o f gas at a pressure o f t.o atm pressure occupies a

volum e o f 20.0 L at a tem perature o f 25.0 °c When the tem perature is raised to 50.0 °c keeping the pressure at 1.0 atm what will be the volume o f the gas?

and 50.0°c = 273.16 + 50.0 = 323.16 K

The Gaseous State 17

Using equation (2.6) 20.0 _ V,

298.16 323.16

= 21.7 L

Like Boyle's law, C h arles’ law represents the behaviour o f ideal o r p erfect

gases Ai high pressures and tem peratures near the liquefaction p oin t any real gas

shows deviation From C h a rle s ’ law

2.4 The A bsolute Zero of T em perature

At - 2 7 3 1 6 ° c or 0°K the volum e o f any gas would theoretically be zero In reality most gases becom e liquid long before the absolute zero IS reached A temperature as low as absolute zero has never been reached b u t low tem perature scientists have been able to reach within a tem perature o f about JO K As the te m ­perature of a substance is lowered the energy of its m olecules also decreases

C onsequently the movem ents o f the molecules becom e less v igorous At the absolute zero all m ovem ents o f the molecules will cease or will be minimum It has been shown theoretically by quantum mechanics that the only type o f energy that the

molecules may possess at 0°K is the energy due to vibrational m otion and this energy

at 0°K is know n as the zero-point energy.

Although Figure 2,4 shows that at 0°K the volum e o f a gas is zero, in reality it is not so At this temperature the molecules would be com pressed so close to each otliei that they would not have space to move This volume, however, would be very small com pared to the volume occupied by the substance in the gaseous state under ordinary temperatures

2.5 A vogadro's Law

In describing the behaviour of gases A v o g ad ro(1 8 1 1), an Italian physicist,

proposed that equal volum es o f all gases at the sam e tem perature a n d p ressu re

contain equal num ber o f m olecules This is known as Avogadro s hypothesis or

Experimentally it was found that one gram molecular mass (one mole) o f some gases at 0 ° c and 1 atmosphere pressure occupied a volume o f 22.414 L From Avogadro's law it follows that one gram molecular mass (one mole) of any gas at 0 ° c and 1 atmosphere pressure (STP, i.e., standard temperature and pressure) will occupy

a volume of 2 2 4 )4 L, since one mole o f ail gases contains the same num ber of molecules Mathematically the law may then be stated as

Here n is the num ber o f moles o f the gas present The molecular mass expressed

in grams is known as the gram m olecular mass One eram mole or one mole signifies that quantity o f the substance whose mass is equal to one gram molecular mass

The volum e occupied by one mo!c of gas is its molar volume and the number of

molecules in one mole of a substance is known as the Avogaclro n u m b erịo r A vogadro

Constant),

2.6 The Ideal Gas E quation

Boyle's, C harles’ and Avogadro's laws may be combined to give a general relation

between the V, p, T and n o f a gas Such a general relation is known as an equation o f

state The equation o f state shows how p, V, T and II are interrelated.

The equation o f state for an ideal gas may be deduced as follows;

Let p = pressure, V = volume, T = absolute temperature and n = number of moles of

any gas We have seen Lhat

r r o nI the laws or variation it follows that

Equation (2.11) is the equation o f stale for an ideal gas It applies to ail gases The

word 'icỉeal' is used because there is no actual gas whose behaviour follows this

equation strictly under all conditions o f temperature and pressure The relationship is, however, useful in most calculations involving gases where high precision is not necessary

2.7 The Significance of R

When one mole o f gas is considered it follows from equation (2.1 Í) that

The Gaseous State 19

R is called the universal gas constant o r m olar gas constant It follows from equation

(2 13) that for one mole of any gas if the pressure is P i,volume is V/ at temperature Tf

then at temperature 72 the pressure P 2 and volumeVS would be such that

This relation is true for a known quantity o f any gas

The numerical value of R may be calculated by determining the volum e occupied by

1 mole o f a ƠQS at a given pressure and a given temperature The dim ensions o f R may

be easily deduced from the equation (2.13)

E xa m p le 2.3: A 1.00 L flask was filled up with a gas at pressure o f 751 m m H g at

temperature 26°c What volume would this gas occupy at STP?

So lu tio n : The information given are as follows:

2.8 The N um erical V alue of R

The numerical value o f R may he calculated by d eterm in in g the v o lu m e o ccu p ied

by 1 m ole of a gas at a given pressure and a given tem perature The d im en sio n oí R

may be easily deduced from the equation (2.13),

Substituting these data in equation (2.14) and solving for V 2 we get,

X -

forcesincc pressure - area

Thus, the p ro d u ct P V has the dim ension o f work, and R may be expressed in any energy u nit p er mole per degree Kelvin The constant R appears in many formulas in chem istry T h e num erical value o f R to he used depends on the system o f units

em plo y ed in the equation u n d er consideration

(a) L itre -a in to sp h e re u nits: In S ectio n 2 ,5 it was pointed out that the m olar volume

at S.T.P., i e, at Í atm o sp h ere pressure and 0 ° c or 273.16°K is 22.414 L If these values are substituted in equation (2.13) one obtains,

l x ' 7 2 4 1 4

273.16

(b) C.Ci.S units: In these units pressure is expressed in dynes per square centimetre

and vo lu m e in cubic centim etres

S o , 1.987 calories K ’1 mor* = 1.987x4.184 = 8.314 J K_1 mol"1

a n d /? = 8.134 J K ' m o r 1

2 3 T he U se o f the G as E quation in C alculations Involving G ases

V ario u s types o f calculation* using the ideal gas equation are possible For this

purpose the equation may be used in different forms as shown below Here g is the mass of a given quantity o f gas, M is the molecular mass and p is the density o f the gas.

(2.16) (2.17) (2.14)

The Gaseous Stale 2 1

2 10 D iffusion and Effusion: G raham ’s Law o f D iffusion

One characteristic of gases is that it mixes readily with other gases until the mixture is uniform This mixing happens as a result o f diffusion of one gas in to

another D iffusion is the process in w hich one gas spreads ou t through an o th er gas to

occupy the space uniform ly One can find diffusion in liquids also If s u g a i- is p la c e d

in a glass of unstirred water it will be found after some time that sugar distributes Itself throughout the liquid and the mixture becom es uniformly sweet As can be seen, sugar molecules have moved from a region of high concentration to a region wherethere was no sugar until the concentration becomes equal _

G raham found by experim ent that gases diffuse through a porous diaphragm and that a light gas diffuses more rapidly than a heavy gas He d escribed the diffusion ol gases quantitatively in the form o f a law which states that

‘The rate o f diffusion o f a gas at constant pressure a n d tem perature is inversely

prop o rtio na l to the square root o f its density.

This is known as 1G r a h a m ' s law o f d iffu s io n ’.

A related phenom enon is the process in which a gas flows out of a con tain er

through a small hole This is called effusion Experim entally it is sim pler to m easure

effusion than diffusion G raham studied the effusion o f differen t gases through small holes and expressed his results in the form:

This is know n as G ra h a m ’s law of effusion M athem atically

Rate o f effusion oc —r= (constant T and P) (2.18)

VP

Or, r effusion = - f = where k is constant

V PBut from equation (2.17) we see

PM

R T k

If we com pare the rates o f effu sio n o f tw o gases through the sam e hole at the sam e tem perature and pressure it follow s that

o f S a s A J P M a i R T _

M