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Vogel's textbook of macro and semimicro qualitative inorganic analysis

発行年: 1979
エディション: 5ed.
出版社: Longman
言語: english
ページ数: 615
ISBN 10: 0582443679
ISBN 13: 9780582443679
File: DJVU, 4.72 MB
ダウンロード (djvu, 4.72 MB)

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Fifth Edition Revised by G. Svehla, Ph.D., D.Se., F.R.I.C. Reader in Analytical Chemistry, Queen's University, Belfast


.... .111.

Longman London and New York

Longman Group Limited London Associated companies, branches and representatives throughout the world Published in the United States of America by Longman Inc., New York @ Longman Group Limited 1979 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the Copyright owner. First Published under the title 'A Text-book of Qualitative Chemical Analysis' 1937 Second Edition 1941 Reissue with Appendix 1943 Third Edition under the title 'A Text-book of Qualitative Chemical Analysis including Semimicro Qualitative Analysis' 1945 Fourth Edition under the title 'A Text-book of Macro and Semimicro Qualitative Inorganic Analysis' 1954 New Impression (with minor corrections) 1955 New Impression 1976 Fifth edition 1979 Library of Congress Cataloging in Publication Data Vogel, Arthur I. Vogel's Macro and semimicro qualitative inorganic analysis. First-3d ed. published under title: A text-book of qualitative chemical analysis; 4th ed. published under title: A text-book of macro and semi micro qualitative inorganic analysis. Includes index. 1. Chemistry, Analytic-Qualitative. 2. Chemistry, Inorganic. I. Svehla, G. II. Title. III. Title: Macro and semimicro qualitative inorganic analysis. QD81.V6 1978 544 77-8290 ISBN 0-582-44367-9

Printed in Great Britain by Richard Clay (The Chaucer Press) Ltd, Bungay, Suffolk



CHAPTER I THE THEORETICAL BASIS OF QUALITATIVE ANALYSIS 1 A. Chemical formulae and equations 1 1.1 Symbols of elements 1 1.2 Empirical formulae 1 1.3 Valency and oxidation number 3 1.4 Structural formulae 4 1.5 Chemical equations 5 B. Aqueous solutions of inorganic substances 6 1.6 Electrolytes and non-electrolytes 6 I. 7 Electrolysis, the nature of electrolytic conductance, ions 7 1.8 Some properties of aqueous solutions 9 1.9 The theory of electrolytic dissociation 9 1.10 Degree of dissociation. Strong and weak electrolytes 11 1.11 The independent migration of ions. Calculation of conductivities from ionic mobilities 15 1.12 Modem theory of strong electrolytes 17 1.13 Chemical equilibrium; the law of mass action 19 1.14 Activity and activity coefficients 22 C. Classical theory of acid-base reactions 25 1.15 Acids, bases, and salts 25 1.16 Acid-base dissociation equilibria. Strength of acids and bases 28 1.17 Experimental determination of the dissociation equilibrium constant. Ostwald's dilution law 33 1.18 The dissociation and ionic product of water 35 1.19 The hydrogen-ion exponent (PH) 36 1.20 Hydrolysis 39 1.21 Buffer solutions 48 1.22 The experimental determination of pH 53 D. The Br.nsted-Lowry theory of acids and bases 61 1.23 Definition of acids and bases 61


1.24 Protolysis of acids. Strength of acids and bases 1.25 Interpretation of other acid-base reactions with the Brensted-Lowry theory E. Precipitation reactions 1.26 Solubility of precipitates 1.27 Solubility product 1.28 Applications of the solubility product relation 1.29 Morphological structure and purity of precipitates 1.30 The colloidal state


66 67 67 68 75 83 85

F. Complexation reactions 89 1.31 The formation of complexes 89 1.32 The stability of complexes 92 1.33 The application of complexes in qualitative inorganic analysis 96 1.34 The most important types of complexes applied in qualitative analysis 97 G. Oxidation-reduction reactions 100 1.35 Oxidation and reduction 100 1.36 Redox systems (half-cells) 101 1.37 Balancing oxidation-reduction equations 104 1.38 Important oxidizing and reducing agents 108 1.39 Redox reactions in galvanic cells 112 1.40 Electrode potentials 115 1.41 Oxidation-reduction potentials 119 1.42 Calculations based on the Nernst equation 124 1.43 Conclusions dra wn from the tables of oxidation-reduction potentials 126 1.44 Equilibrium constant of oxidation-reduction reactions 128

H. Solvent extraction 1.45 The distribution or partition law 1.46 The application of solvent extraction in qualitative analysis

130 130 131


11.1 Introduction 11.2 Dry reactions 11.3 Wet reactions 11.4 Semimicro apparatus and semimicro analytical operations 11.5 Micro apparatus and microanalytical operations 11.6 Spot test analysis

135 135 136 145 153 173 180


111.1 111.2

Classification of cations (metal ions) into analytical groups Notes on the study of the reactions of ions


191 191 192

111.3 First group of cations: lead(II), mercury(I) and silver(I) 193 111.4 Lead, Pb (Ar: 207'2) 194 111.5 Mercury, Hg (Ar: 200'59) - Mercury(I) 199 . 111.6 Silver, Ag (Ar: 107'9) 204 111.7 Second group of cations: mercury(II), lead(II), bismuth(III), copper(II), cadmium(II), arsenic(lII) and (V), antimony(lII) and (V), tin(lI) and (IV) 208 111.8 Mercury, Hg (Ar: 200'59) - Mercury(lI) 209 111.9 Bismuth, Bi (Ar: 208'98) 212 111.10 Copper, Cu (Ar: 63'55) 215 111.11 Cadmium, Cd (Ar: 112'90) 221 111.12 Arsenic, As (Ar: 74'92) - Arsenic(lII) 223 111.13 Arsenic, As (Ar: 74'92) - Arsenic(V) 225 111.14 Special tests for small amounts of arsenic 228 111.15 Antimony, Sb (Ar: 121'75) - Antimony(lII) 231 111.16 Antimony, Sb (Ar: 121'75) - Antimony(V) 234 111.17 Special tests for small amounts of antimony 236 111.18 Tin, Sn (Ar: 118'69) - Tin(lI) 237 111.19 Tin, Sn (Ar: 118'69) - Tin(IV) 240 111.20 Third group of cations: iron(lI) and (III), aluminium, chromium(III), nickel, cobalt, manganese(lI) and zinc 241 111.21 Iron, Fe (Ar: 55'85) - Iron(II) 241 111.22 Iron, Fe (Ar: 55'85) - Iron(lII) 245 111.23 Aluminium, Al (Ar: 26'98) 250 111.24 Chromium, Cr (Ar: 51'996) - Chromium(lII) 254 111.25 Oxianions of group III metals: chromate and permanganate 259 111.26 Cobalt, Co (Ar: 58'93) 259 111.27 Nickel, Ni (Ar: 58.71) 264 111.28 Manganese, Mn (Ar: 54'938) - Manganese(lI) 268 111.29 Zinc, Zn (Ar: 63'58) 272 111.30 Fourth group of cations: barium, strontium, and calcium 277 111.31 Barium, Ba (Ar: 137'34) 278 111.32 Strontium, Sr (Ar: 87'62) 281 111.33 Calcium, Ca (Ar: 40'08) 282 111.34 Fifth group of cations: magnesium, sodium, potassium, and ammOnIum 285 111.35 Magnesium, Mg (Ar: 24. 305) 285 111.36 Potassium, K (Ar: 39'098) 289 111.37 Sodium, Na (Ar: 22'99) 291 111.38 Ammonium, NH 4 (M r : 18'038) 293 CHAPTER IV REACTIONS OF THE ANIONS 297 IV.l Scheme of classification 297 IV.2 Carbonates, CO

- 298 IV.3 Hydrogen carbonates, HC0 3 300 VII

IV.4 IV.5 IV.6 IV.7 IV.8 IV.9 IV. 10 IV. 11 IV.12 IV.l3 IV.14 IV.15 IV.16 IV.17 IV.18 IV.19 IV.20 IV.21 IV.22 IV.23 IV.24 IV.25 IV.26 IV.27 IV.28 IV.29 IV.30 IV.31 IV.32 IV.33 IV.34 IV.35 IV.36 IV.37 IV.38 IV.39 IV.4O IV.41 IV.42 IV.43 IV.44 IV.45

Sulphites, SO

- Thiosulphates, S20

- Sulphides, S2- Nitrites, N0 2 Cyanides, CN- Cyanates, CNO- Thiocyanates, SCN- Hexacyanoferrate(II) ions, [Fe(CN)6]4- Hexacyanoferrate(lII) ions, [Fe(CN)6]3- Hypochlorites, OCl- Chlorides, Cl- Bromides, Br- Iodides, 1- Fluorides, F- Nitrates, NO; Chlorates, CIO; Bromates, BrO; Iodates, 10; Perchlorates, CIO; Borates, BO

-, B40

- , B0 2 Sulphates, SOi- Peroxodisulphates, S20

- Silicates, SiO

- Hexafluorosilicates (silicofluorides), [SiF 6]2- Orthophosphates, PO

- Pyrophosphates, P20

-, and metaphosphates, PO; Phosphites, HPO

- Hypophosphites, H 2 P0 2 Arsenites, AsO

- , and arsenates, AsO

- Chromates, CrOi-, and dichromates, Cr20

- Permanganates, MnO; Acetates, CH 3 COO- Formates, HCOO- Oxalates, (COO)

- Tartrates, C4H40

- Citrates, C6HsO

- Salicylates, C 6 H 4 (OH).200- or C 7 H s O; Benzoates, C 6 H s COO- or C 7 H s 0 2 Succi nates, C 4 H 4 0i- Hydrogen peroxide, H 2 0 2 Dithionites, S20i- Special tests for mixtures of anions

301 305 308 310 313 316 317 319 322 323 325 327 329 332 334 337 339 340 342 343 346 349 350 353 354 358 358 360 361 361 364 366 368 369 371 374 376 377 378 379 382 383



V.l Introduction V.2 Preliminary tests on non-metallic solid samples V.3 Preliminary tests on metal samples VA Preliminary tests on liquid samples (samples in solution) V.5 Preliminary tests on insoluble substances V.6 Dissolution of the sample V.7 Examination of the insoluble residue V.8 Separation of cations into groups V.9 Separation and identification of the Group I cations (silver group) V.IO Separation of Group II cations into Groups IIA and liB V. 11 Separation and identification of Group IIA cations V.l2 Separation and identification of Group liB cations V.13 Removal of interfering ions before the precipitation of the Group III cations V.l4 Separation and identification of Group iliA cations V.15 Separation and identification of Group 11m cations V.16 Separation and identification of Group IV cations V.17 Identification of Group V cations V.18 Preliminary tests for and separation of certain anions V.19 Confirmatory tests for anions

395 395 395 405 406 407 411 411 413

420 421 424 428

431 436 437 441 444 446 458


VI.1 VI.2


VIA VI. 5 VI.6 VI. 7 VI. 8

VI. 9 VI.10



Introduction The study of reactions of cations and anions on the semimicro scale Systematic analysis on the semi micro scale. General considerations Preliminary tests on the semimicro scale Testing for anions in solution on the semimicro scale Confirmatory tests for anions on the semimicro scale Special tests for mixtures of anions on the semi micro scale Preparation of solution for cation testing on the semimicro scale Separation of cations into groups on the semimicro scale Separation and identification of Group I cations on the semimicro scale Separation of Groups IIA and liB and separation and identification of Group IIA cations on the semimicro scale Separation and identification of Group liB cations on the semimicro scale


461 461


463 464 470 473 476

479 480




VI.13 Separation and identification of Group ilIA cations on the semimicro scale 488 VI.14 Separation and identification of Group 11m cations on the semimicro scale 489 VI.15 Separation and identification of Group IV cations on the semimicro scale 490 VI.16 Identification of Group V cations on the semimicro scale 492 VI.17 Modifications of separation procedures in the presence of interfering anions 493 VI.18 Separations by paper and thin layer chromatography. General introduction 495 VI.19 Apparatus and technique for chromatographic separations 497 VI.20 Procedures for selected chromatographic separations 500 CHAPTER VII REACTIONS OF SOME LESS COMMON IONS 507 VII.l Introduction 507 VII.2 Thallium, Tl (Ar: 204'34) - Thallium(I) 507 VII.3 Thallium, Tl (Ar: 204'34) - Thallium(lII) 509 VilA Tungsten, W (Ar: 183'85) - Tungstate 509 VII.5 Separation and identification of Group I cations in the presence of thallium and tungsten 511 VII.6 Molybdenum, Mo (Ar: 95'94) - Molybdate 511 VII.7 Gold, Au (Ar: 196'97) - Gold(lII) 514 VII.8 Platinum, Pt (Ar: 195'09) 516 VII.9 Palladium, Pd (Ar: 106'4) 518 VI 1.1 0 Selenium, Se (Ar: 78'96) - Selenites, SeO

- 520 VI 1.1 1 Selenium, Se (Ar: 78'96) - Selenates, SeOi- 521 VII.12 Tellurium, Te (Ar: 127'60) - Tellurites, TeO

- 522 VII.13 Tellurium, Te (Ar: 127'60) - Tellurates, TeOi- 523 VII.14 Separation and identification of Group II cations in the presence of molybdenum, gold, platinum, palladium, selenium, and tellurium 524 VII.15 Vanadium, V (Ar: 50'94) - Vanadate 527 VII. 16 Beryllium, Be (Ar: 9'01) 530 VII.l 7 Titanium, Ti (Ar: 47'90) - Titanium(IV) 532 VII.18 Zirconium, Zr (Ar: 91'22) 535 VII.19 Uranium, U (Ar: 238'03) 538 VII.20 Thorium, Th (Ar: 232'04) 540 VII.21 Cerium, Ce (Ar: 140'12) - Cerium(lII) 541 VII.22 Cerium, Ce (Ar: 140"12) - Cerium(IV) 542 VII.23 Separation of Group III cations in the presence of titanium, zirconium, thorium, uranium, cerium, vanadium, thallium, and molybdenum 544 VII.24 Lithium, Li (Ar: 6'94) 546 VII.25 The borax bead test in the presence of less common cations 548 x



Introduction Reactions of cations and anions Systematic analysis. General considerations Preliminary tests on solutions Testing for anions in solution Confirmatory tests for anions Special tests for mixtures of anions Separation and identification of cations in solution Modifications in the presence of anions of organic acids, fluoride, and phosphate

550 550 550 551 552 553 556 557 560



IX.l IX.2 IX.3 IXA IX.5 IX.6 IX.7 IX.8

Relative atomic masses of the elements Reagent solutions and gases Solid reagents Solubilities of salts and bases in water at 18°C Logarithms An tilo gari thIns Concentrated acids and bases Periodic table of the elements

566 566 568 589 592 593 595 597 598





Experience of teaching qualitative analysis over a number of years to large numbers of students has provided the nucleus around which this book has been written. The ultimate object was to provide a text-book at moderate cost which can be employed by the student continuously throughout his study of the subject. It is the author's opinion that the theoretical basis of qualitative analysis, often neglected or very sparsely dealt with in the smaller texts, merits equally detailed treatment with the purely practical side; only in this way can the true spirit of qualitative analysis be acquired. The book accordingly opens with a long Chapter entitled 'The Theoretical Basis of Qualitative Analysis', in which most of the theoretical principles which find application in the science are discussed. The writer would be glad to hear from teachers and others of any errors which may have escaped his notice: any suggestions whereby the book can be improved will be welcomed.

A. I. Vogel Woolwich Polytechnic London S.E.18




A. CHEMICAL FORMULAE AND EQUATIONS 1.1 SYMBOLS OF THE ELEMENTS To express the composition of substances and to describe the qualitative and quantitative changes, which occur during chemical reactions in a precise, short, and straightforward way we use chemical symbols and formulae. Following the recommendations of Berzelius (1811), the symbols of chemical elements are constructed by the first letter of their international (Latin) names with, in most cases, a second letter which occurs in the same name. The first letter is a capital one. Such symbols are: o (oxygen, oxygenium) H (hydrogen, hydrogenium), C (carbon, carbonium), Ca (calcium), Cd (cadmium), Cl (chlorine, chlorinum), Cr (chromium), Cu (copper, cuprum), N (nitrogen, nitrogenium), Na (sodium, natrium), K (potas- sium, kalium), etc. As well as being a qualitative reference to the element, the symbol is most useful in a quantitative context. It is generally accepted that the symbol of the element represents 1 atom of the element, or, in some more specific cases, 1 grammatom. Thus C represents 1 atom of the element carbon or may represent 1 grammatom (12'011 g) of carbon. In a similar way, 0 represents one atom of oxygen or one grammatom (15'9994 g) of oxygen, H represents one atom of hydrogen or 1 grammatom (1'0080 g) of hydrogen etc. Names, symbols, and relative atomic masses of the elements are given in Section IX.l.

1.2 EMPIRICAL FORMULAE To express the composition of materials whose molecules are made up of more atoms, empirical formulae are used. These are made up of the symbols of the elements of which the substance is formed. The number of atoms of a particular element in the molecule is written as a subscript after the symbol of the element (but 1 is never written as a subscript as the symbol of the element on its own represents one atom). Thus, the molecules of carbon dioxide is formed by one carbon atom and two oxygen atoms, therefore its empirical formula is CO 2 , In the molecule of water two hydrogen atoms and one oxygen atom are present, therefore the empirical formula of water is H 2 0. In the molecule of hydrogen peroxide on the other hand there are two hydrogen and two oxygen atoms present, its empirical formula is therefore H 2 0 2 . Although there are no strict rules as to the order of symbols appearing in a formula, in the case of inorganic substances the symbol of the metal or that of hydrogen is generally written first followed by non-metals and finishing with oxygen. In the formulae of organic substances the generally accepted order is C, H, 0, N, S, P.


The determination of the empirical formula of a compound can be made experimentally, by determining the percentage amounts of elements present in the substance using the methods of quantitative chemical analysis. At the same time the relative molecular mass of the compound has to be measured as well. From these data the empirical formula can be determined by a simple calcu- lation. If, for some reason, it is impossible to determine the relative molecular mass the simplest (assumed) formula only can be calculated from the results of chemical analysis; the true formula might contain multiples of the atoms given in the assumed formula. If the empirical formula of a compound is known, we can draw several con- clusions about the physical and chemical characteristics of the substance. These are as follows: (a) From the empirical formula ofa compound we can see which elements the compound contains, and how many atoms of each element form the molecule of the compound. Thus, hydrochloric acid (HC1) contains hydrogen and chlorine; in its molecule one hydrogen and one chlorine atom are present. Sulphuric acid (H 2 S0 4 ) consists of hydrogen, sulphur, and oxygen; in its molecule two hydrogen, one sulphur, and four oxygen atoms are present etc. (b) From the empirical formula the relative molecular mass (molecular weight) can be determined simply by adding up the relative atomic masses (atomic weights) of the elements which constitute the compound. In this summation care must be taken that the relative atomic mass of a particular element is multiplied by the figure which shows the number of its atoms in the molecule. Thus, the relative molecular mass of hydrochloric acid (HC1) is calculated as follows: M r = 1'0080+35,453 = 36,4610 and that of sulphuric acid (H 2 S0 4 ) is M r = 2 x 1.0080 + 32'06 + 4 x 15.9994 = 98'0736 and so on. (c) Based on the empirical formula one can easily calculate the relative amounts of the elements present in the compound or the percentage composition of the substance. For such calculations the relative atomic masses of the elements in question must be used. Thus, in hydrochloric acid (HC1) the relative amounts of the hydrogen and chlorine are H : Cl = 1'0080: 35,453 = 1'0000: 35.172 and (as the relative molecular mass of hydrochloric acid is 36-461) it contains 1'008 100 x 36'461 = 2.76 per cent H


35'453 100 x _ 3 = 97'24 per cent Cl 6'461 Similarly, the relative amounts of the elements in sulphuric acid (H 2 S0 4 ) are H: S:O = 2 x 1,0080:32'06:4 x 15'9994 = 2'016: 32'06:63'9976 1: 15'903:31'745



and knowing that the relative molecular mass of sulphuric acid is 98'0763, we can calculate its percentage composition which is 2'0160 100 x 98,0736 = 2'06 per cent H 32'06 100 x 98'0736 = 32'69 per cent S

and 63,9976 100 x 98'0736 = 65'25 per cent 0 and so on. (d) Finally, if the formula is known - which of course means that the relative molecular mass is available - we can calculate the volume of a known amount of a gaseous substance at a given temperature and pressure. If p is the pressure in atmospheres, T is the absolute temperature in degrees kelvins, M r is the relative molecular mass of the substance in g mol-I units and m is the weight of the gas in grams, the volume of the gas (v) is v = mRT t pMr where R is the gas constant, 0'0823 t atm K - 1 mol- I. (The gas here is con- sidered to be a perfect gas.)

1.3 VALENCY AND OXIDA nON NUMBER In the understanding of the composition of compounds and the structure of their molecules the concept of valency plays an important role. When looking at the empirical formulae of various substances the question arises: are there any rules as to the number of atoms which can form stable molecules? To understand this let us examine some simple compounds containing hydrogen. Such compounds are, for example, hydrogen chloride (HC1), hydrogen bromide (HBr), hydrogen iodide (HI), water (H 2 0), hydrogen sulphide (H 2 S), ammonia (H 3 N), phosphine (H 3 P), methane (H 4 C), and silane (H 4 Si). By comparing these formulae one can see that one atom of some of the elements (like Cl, Br, and I) will bind one atom of hydrogen to form a stable compound, while others combine with two (0, S), three (N,P) or even four (C, Si). This number, which represents one of the most important chemical characteristics of the element, is called the valency. Thus, we can say that chlorine, bromine, and iodide are monovalent, oxygen and sulphur bivalent, nitrogen and phosphorus tervalent, carbon and silicon tetravalent elements and so on. Hydrogen itself is a monovalent element. From this it seems obvious that the valency of an element can be ascertained from the composition of its compound with hydrogen. Some of the elements, for example some of the metals, do not combine with hydrogen at all. The valency of such elements can therefore be determined only in an indirect way, by examining the composition of their compounds formed with chlorine or oxygen and finding out the number of hydrogen atoms these elements replace. Thus, from the formulae of magnesium oxide (MgO) and magnesium chloride (MgC1 2 ) we can conclude that magnesium is a bivalent metal, similarly from the composition of aluminium chloride (AIC1 3 ) or aluminium oxide (A1 2 0 3 ) it is obvious that aluminium is a tervalent metal etc.



In conclusion we can say that the valency of an element is a number which expresses how many atoms of hydrogen or other atoms equivalent to hydrogen can unite with one atom of the element in question.. If necessary the valency of the element is denoted by a roman numeral following the symbol like Cl(I), Br(I), N(III) or as a superscript, like C1 1 , Brl, N llI , etc. Some elements, like hydrogen, oxygen, or the alkali metals, seem always to have the same valency in all of their compounds. Other elements however show different valencies; thus, for example, chlorine can be mono-, tri-, penta- or heptavalent in its compounds. It is true that compounds of the same element with different valencies show different physical and chemical characteristics. A deeper study of the composition of compounds and of the course of chemical reactions reveals that the classical concept of valency , as defined above, is not quite adequate to explain certain phenomena. Thus, for example, chlorine is monovalent both in hydrochloric acid (HC1) and in hypochlorous acid (HCIO), but the marked differences in the chemical behaviour of these two acids indicate that the status of chlorine in these substances is completely different. From the theory of chemical bondingt we know that when forming hydrochloric acid, a chlorine atom takes up an electron, thus acquiring one negative charge. On the other hand, if hypochlorous acid is formed, the chlorine atom releases an electron, becoming thus a species with one positive charge. As we know, the uptake or release of electrons corresponds to reduction or oxidation (cf. Section 1.35), we can therefore say that though chlorine is monovalent in these acids, its oxidation status is different. It is useful to define the concept of oxidation number and to use it instead of valency. The oxidation number is a number identical with the valency but with a sign, expressing the nature of the charge of the species in question when formed from the neutral atom. Thus, the oxidation number of chlorine in hydrochloric acid is - 1, while it is + 1 in hypochlorous acid. Similarly we can say that the oxidation number of chlorine in chlorous acid (HCI0 2 ) is + 3, in chloric acid (HCI0 3 ) is + 5, and in perchloric acid (HCI0 4 ) + 7. The concept of oxidation number will be used extensively in the present text.

1.4 STRUCTURAL FORMULAE Using the concept of valency the com- position of compounds can be expressed with structural formulae. Each valency of an element can be regarded as an arm or hook, through which chemical bonds are formed. Each valency can be represented by a single line drawn outwards from the symbol of the element, like H- Cl- 0= N =: C =:

The structural formulae of compounds can be expressed with lines drawn between the atoms t like

· Cf. Mellor's Modern Inorganic Chemistry, newly revised and ediled by G. D. Parkes, Longman 1967, p. 99 el f. t Cf. Mellor op. cil., p. 155 el f. t There are no reslriclions aboul Ihe direclion of Ihese lines (unless dilferenlialion has 10 be made belween slereochemical isomers). Nor is Ihere any reslriclion on Ihe dislances of aloms. Slruclural formulae musl Iherefore be regarded only as a slep in Ihe approximalion of Ihe Irue slruclure. A Ihree dimensional represenlalion wilh Irue direclions and proporlional dislances can mosl adequalely be made wilh molecular model kiIs.



H I N /"- H H

o ,f C '\ o



Structural formulae will be used in this text only when necessary, mainly when dealing with organic reagents. A more detailed discussion of structural formulae will not be given here; beginners should study appropriate textbooks.. Readers should be reminded that the simple hexagon o (Oor@)

represents the benzene ring. Benzene (C 6 H 6 ) can namely be described with the (simplified) ring formula in which double and single bonds are alternating (so-called conjugate bonds): H I H -

;::'<r- H H-(2

-H I H All the aromatic compounds contain the benzene ring.

1.5 CHEMICAL EQUATIONS Qualitative and quantitative relationships involved in a chemical reaction can most precisely be expressed in the form of chemical equations. These equations contain the formulae of the reacting substances on the left-hand side and the formulae of the products on the right- hand side. When writing chemical equations the following considerations must be kept in mind: (a) Because of the fact that the formulae of the reacting species are on the left-hand side and those of the products are on the right, the sides generally cannot be interchanged (in this sense chemical equations are not equivalent to mathematical equations). In the cases of equilibrium reactionst when the reaction may proceed in both directions, the double arrow (+2) sign should be used instead of the equal ( = ) or single arrow ( -+ ) sign. (b) The individual formulae, used in the chemical reactions, must be written correctly. (c) If more molecules (atoms or ions) of the same substance are involved in the reaction, an appropriate stoichiometric number has to be written in front of the formula. This number is a multiplication factor, which applies to all atoms in the formula. (Thus, for example 2Ca3(P04h means that we have 6 calcium, 4 phosphorus, and 16 oxygen atoms in the equation.)

· Cf. Mellor's Modern Inorganic Chemistry, newly revised and edited by G. D. Parkes, Longman 1%7, p. 155. t Theoretically speaking, all reactions lead to an equilibrium. This equilibrium however may be shifted completely towards the formation of the products.



(d) A chemical equation must be written in such a way that it fulfils the law of conservation of mass, which is strictly valid for all chemical reactions. This means, that the equation should be balanced by applying proper stoichio- metric numbers in such a way that the numbers of different individual atoms are the same on both sides. (e) If charged species (ions or electrons) are involved in the reaction, these charges must be clearly indicated (like Fe H or Fe + + +) and properly balanced; the sum of charges on the left-hand side must be equal to the sum of charges on the right-hand side. The electron, as a charged particle, will be denoted by e- in this text. As an example let us express the equation of the reaction between calcium hydroxide and phosphoric acid. Knowing that the products of such a reaction are calcium phosphate and water, we can write the formulae of the substances into the yet incomplete equation: Ca(OHh + H 3 P0 4 -+ CaiP0 4 h + H 2 0 (incomplete) (note that the sides of the equation cannot be interchanged, because the reaction will not proceed in the inverse direction). Now we try to balance the equation by applying suitable stoichiometric numbers: 3Ca(OH)2 + 2H 3 P0 4 = Ca3(P04h + 6H 2 0 It is advisable to check the equation by counting the numbers of individual atoms on both sides. Doing so we can see that there are 3 calcium, 2 phosphorus, 12 hydrogen and 14 oxygen atoms on both sides. It is useful to denote the physical state of the reaction partners. For this purpose the letters s, 1, and g are applied for solid, liquid, and gaseous substances respectively, while the notation aq is used for species dissolved in water. These letters are used in parenthesis after the formula, e.g. AgCl(s), H,-O(l), CO 2 (g), while the aq follows the formula simply, without parenthesis e.g. H 3 P0 4 aq. The systematic use of these notations is important only in thermodynamics, that is when the energetics of the reactions are examined. In the present text we shall use them in some cases. The formation of a precipitate will be denoted by a ! sign (indicating that the precipitate settles to the bottom of the solution) while the liberation of gases will be denoted by a i sign. If not otherwise stated, equations will refer to reactions proceeding in dilute aqueous solutions. Following those considerations discussed in Section 1.2., relative masses, mass balances, and volumes (of gaseous substances only) can be calculated on the basis of chemical equations. Such calculations are involved in all kinds of quantitative analyses based on chemical reactions.


1.6 ELECTROLYTES AND NON-ELECTROLYTES Quantitative in- organic analysis is based mainly on the observation of chemical reactions carried out in aqueous solutions. Other solvents are rarely employed except for special tests or operations. It is therefore important to have a general knowledge of the characteristics of aqueous solutions of inorganic substances.



A solution is the homogeneous product obtained when a substance (the solute) is dissolved in the solvent (water). Substances can be classified into two important groups according to their behaviour when an electric current is passed through their solution. In the first class there are those which conduct electric current; the solutions undergo chemical changes thereby. The second class is composed of materials which, when dissolved in water, do not conduct electricity and which remain unchanged. The former substances are termed electrolytes, and these include, with few exceptions, all inorganic sub- stances (like acids, bases, and salts); the latter are designated non-electrolytes, and are exemplified by such organic materials as cane sugar, mannose, glucose, glycerine, ethanol, and urea. It must be pointed out that a substance which behaves as an electrolyte in water, e.g. sodium chloride, may not yield a con- ducting solution in another solvent such as ether or hexane. In the molten state most electrolytes will conduct electricity.

1.7 ELECTROLYSIS, THE NATURE OF ELECTROLYTIC CONDUC- TANCE, IONS Chemically pure water practically does not conduct electricity, ifhowever, as already stated, acids, bases, or salts are dissolved in it, the result- ant solution not only conducts the electric current, but undergoes chemical changes as well. The whole process is called electrolysis. Phenomena occurring during electrolysis can be studied in the electrolysis cell shown in Fig. 1.1. The electrolyte solution is placed in a vessel, into which Source of current (battery) I1 I 1I1 1 1


+ =-;

-rp-=- - -: - - + _ _ - \:!T_ - -- -- - - --




; - - - - -- - + - - -G)-: - - -8- - - -

Fig I.1 two solid conductors (e.g. metals), the so called electrodes, are immersed. With the aid of a battery (or another d.c. source) a potential difference is applied between the two electrodes. The electrode with the negative charge in the electrolysis cell is called the cathode, while that with the positive charge is termed the anode..

· It must be emphasized that the terms cathode and anode correspond to the negative and positive electrodes respectively only in electrolysis cells. According to Faraday's nomenclature, cathode is the electrode where cations lose their charge, while anions do the same on the anode. Consequently, in a battery (like the Daniell-cell) the anode is the negative and the cathode is the positive electrode.



The chemical change occurring-during the course of electrolysis is observable on or in the vicinity of the electrodes. In many cases such a change is a simple decomposition. If for example a dilute solution of hydrochloric acid is elec- trolysed (between platinum electrodes), hydrogen gas is liberated on the cathode and chlorine on the anode; the concentration of hydrochloric acid in the solution decreases. It is easy to demonstrate that electrolysis is always accompanied by the transport of material in an electrolysis cell. If for example the blue solution of copper sulphate and the orange solution of potassium dichromate are mixed in equimolar concentrations, a brownish solution is obtained. This solution can be placed in a U-shaped electrolysis cell and topped up with a colourless layer of dilute sulphuric acid on each side (Fig. 1.2). If this solution is then electrolysed, the hitherto colourless solution next to the cathode slowly becomes blue, while




H 2 S0 4

H 2 SO 4

Blue (Cu 2")

Orange ( Cr 2 0 ) 2-)

Brown (CUS0 4 + K2Cr20)

Fig. 1.2 the solution next to the anode becomes orange. As the blue colour is associated with copper and the orange with dichromate, it can be said that copper moves towards the cathode and dichromate towards the anode during the electrolysis. As such a movement can be achieved solely by electrolysis, it is obvious that those particles which move towards one of the electrodes must be charged and that this charge must be opposite to that of the electrode towards which they move. The migration of such particles is a result of the electrostatic attraction force, which is created when switching on the current. Thus the particles of hydrogen or copper, which move towards the cathode, must be positively charged, while those of chlorine or dichromate must be negatively charged. Faraday termed the charged particles in the electrolyte ions; the positively and negatively charged ions were called cations and anions respectively. It can be stated generally that solutions of electrolytes do not contain neutral molecules dispersed among the molecules of the solvent, as solutions of non-electrolytes do, but they are composed of ions. Cations and anions are present in equivalent amounts and are dispersed evenly in the solution among the molecules of the solvent; macroscopic portions of the solution therefore appear to be electro- statically neutral in all cases.



1.8 SOME PROPERTIES OF AQUEOUS SOLUTIONS It has been found experimentally that equimolecular quantities of non-electrolytes, dissolved in the same weight of solvent, will acquire identical osmotic pressures, and have the same effect upon the lowering of vapour pressure, the depression of the freezing point, and the elevation of the boiling point. Using water as a solvent, 1 mole of a non-electrolyte when dissolved in 1000 g of water lowers, for example, the freezing point of water by l'86°C and elevates its boiling point by 0'52°C. On such a basis it is possible to determine the relative molecular mass of soluble non-electrolyte substances experimentally. When a non-electrolyte is dissolved in water, its molecules will be present as individual particles in the solution. Consequently, we can say that equal numbers of particles, present in the same amount of solution, will show identical osmotic pressure, lowering of vapour pressure, depression of the freezing point, or elevation of the boiling point. Thus, by measuring the above quantities, the number of particles present in the solution can be determined. When electrolyte solutions are subjected to such measurements, abnormal results are obtained. When substances like sodium chloride or magnesium sulphate are examined, the depression of freezing point or the elevation of boiling point is about twice that calculated from the relative molecular mass, with calcium chloride or sodium sulphate these quantities are three times those expected. Keeping in mind what has been said above, we can say that the number of particles in the solution of sodium chloride or magnesium sulphate is twice the number of molecules present, while in the case of calcium chloride or sodium sulphate there are three particles present for each molecule.

1.9 THE THEORY OF ELECTROLYTIC DISSOCIATION In Sections 1.7 and 1.8 two, seemingly independent, experimental facts were described. These are that electric current is conducted by the migration of charged particles in the solution of electrolytes, and that in solutions of electrolyte substances the number of particles are 2,3 . . . etc. times greater than the number of molecules dissolved. To explain these facts, Arrhenius put forward his theory of electrolytic dissociation (1887). According to 'this theory, the molecules of electrolytes, when dissolved in water, dissociate into charged atoms or groups of atoms, which are in fact the ions which conduct the current in electrolytes by migration. This dissociation is a reversible process; the degree of dissociation varies with the degree of dilution_ At very great dilutions the dissociation is practically complete for all electrolytes. The electrolytic dissociation (ionization) of compounds may therefore be represented by the reaction equations: NaCl +2 Na+ +Cl- MgS0 4 +2 Mg H +SOi- CaC1 2 +2 Ca H +2Cl- Na2S04 +2 2Na+ +soi- Ions carry positive or negative charges. Since the solution is electrically neutral, the total number of positive charges must be equal to the total number of negative charges in a solution. The number of charges carried by an ion is equal to the valency of the atom or radical.



The explanation of the abnormal results obtained when measuring the depression of freezing point or elevation of boiling point is straightforward on the basis of the theory of electrolytic dissociation. In the case of sodium chloride and magnesium sulphate the measured values are twice as great as those calcu- lated from the relative molecular mass, because both substances yield two ions per molecule when dissociated. Similarly, the depression of freezing point or elevation of boiling point of calcium chloride or sodium sulphate solutions are three times as great as of an equimolar solution of a non-electrolyte, because these substances yield three ions from each molecule when dissociating. The phenomenon of electrolysis also receives a simple explanation on the basis of the theory of electrolytic dissociation. The conductance of electrolyte solutions is due to the fact that ions (charged particles) are present in the solution, which, when switching on the current, will start to migrate towards the electrode with opposite charge, owing to electrostatic forces. In the case of hydrochloric acid we have hydrogen and chloride ions in the solution: HCl +2 H+ +Cl-

and it is obvious that hydrogen ions will migrate towards the cathode, while chloride ions will move towards the anode. In the solution, mentioned earlier, containing copper sulphate and potassium dichromate we have the blue copper(II) ions and the orange dichromate ions present, besides the colourless potassium and sulphate ions: CUS04 +2 Cu H +soi- K 2 Cr 2 0 7 +2 2K+ +Cr 2 0i- and this is why copper ions (together with potassium ions) moved towards the negatively charged cathode, while dichromate ions (as well as sulphate ions) moved towards the positively charged anode. Those changes occurring on the electrodes during electrolysis can also be explained easily on the basis of the theory of electrolytic dissociation. Returning to the example of the electrolysis of hydrochloric acid, where, as said before, hydrogen ions migrate towards the cathode and chloride ions towards the anode, the electrode processes are as follows: hydrogen ions, when arriving at the cathode first take up an electron to form a neutral hydrogen atom: H++e--+H Pairs of hydrogen atoms will then form hydrogen molecules, which are dis- charged in the form of hydrogen gas: 2H -+ H 2 (g) On the anode the chloride ions release electrons, forming chlorine atoms: Cl- -+ Cl+e- which again will form chlorine molecules: 2Cl -+ C1 2 (g) and are discharged in the form of chlorine gas. The electrons are taken up by the anode, and travel through the electric circuit to the cathode, where they are then taken up by hydrogen ions.



The phenomena of electrolysis are not always as simple as discussed in connection with hydrochloric acid, but it is always true that electrons are taken up by ions on the cathode and electrons are released by ions on the anode. It is not necessarily the cation or anion of the dissolved substance, which reacts on the electrodes, even though these ions carry the electrical current by migration. In aqueous solutions very small amounts of hydrogen and hydroxyl ions are always present due to the slight dissociation of water (cf. Sections 1.18 and 1.24): H 2 0 p H+ +OH- The ions of the dissolved substance and hydrogen as well as hydroxyl ions compete for discharge on the electrodes, and the successful ion is the one which needs the least energy for discharge. Using electrochemical terms we can say that under given circumstances the ion which requires a lower negative electrode potential will be discharged first on the cathode, while the one that requires a lower positive potential will be discharged on the anode. The discharge of hydroxyl ions on the anode results in the formation of oxygen gas: 40H- -+ 4e- +2H 2 0+0 2 (g) The competition of various ions at the electrodes for discharge may lead to various combinations. If for example sodium sulphate is electrolysed (with platinum electrodes), neither sodium nor sulphate ions (Na2S04 p 2Na+ +SOi-) will be discharged, but hydrogen and hydroxyl ions; the result of the electrolysis therefore is the formation of hydrogen gas on the cathode and oxygen on the anode. As hydrogen ions are removed from the vicinity of the cathode, the hydroxyl-ion concentration will surpass that of the hydrogen ions, making this part of the solution alkaline. The opposite happens around the anode, where hydrogen ions will be in excess and the solution there becomes acidic. When after the electrolysis the solution is mixed, it again becomes neutral. When electro lysing sodium chloride (NaCl p Na + + Cl-) under similar circumstances, hydrogen and chloride ions are discharged in the form of hydrogen and chlorine gas on the cathode and anode respectively. Sodium and hydroxyl ions are left behind, and the whole solution becomes alkaline. Finally, if copper sulphate (CuS0 4 p Cu H + SOi-) is electro lysed under the same circumstances, copper and hydroxyl ions will be discharged, the cathode being coated with a layer of copper metal, while oxygen gas is liberated on the anode. Hydrogen and sulphate ions are left behind in the solution, making the latter acidic. In later parts of the present text we shall see that the uptake of electrons always means reduction, while the release of electrons is associated with oxidation. Briefly therefore we can say that during the course of electrolysis reduction takes place on the cathode, while oxidation occurs on the anode. This rule is true for any kind of electrochemical process, e.g. the same is true for the operation of electromotive cells (batteries).

1.10 DEGREE OF DISSOCIA nON. STRONG AND WEAK ELEC- TROLYTES When discussing the theory of electrolytic dissociation, it was stated that it is a reversible process and its extent varies with concentration (and also with other physical properties, like temperature). The degree of dissociation (IX) is equal to the fraction of the molecules which actually dissociate.




number of dissociated molecules total number of molecules

The value of rx may vary within 0 and 1. If rx = 0, no dissociation takes place, while if rx = 1 dissociation is complete. The degree of dissociation can be determined by various experimental methods. The cryoscopic and ebullioscopic techniques are based on the measurement of the depression of the freezing point and the elevation of the boiling point respectively. As mentioned before, the experimental values of these were found to be higher than the theoretical ones. The ratio of these

(obs) . =1

(theor) is closely associated with the number of particles present in the solution. The value i (called van't Hoff's coefficient) gives the average number of particles formed from one molecule; as this is an average number, i is not an integer. It is always greater than unity. This number can easily be associated with the degree of dissociation. Let us consider an electrolyte which when dissociated gives rise to the formation of n ions per molecule. If 1 mole of this electrolyte is dissolved, and the degree of dissociation is rx, we can calculate the total number of particles (ions plus undissociated molecules) in the following way: the number of ions (per molecule) will be nrx, while the number of undissociated molecules 1 - rx. The sum of these is equal to i, the van't Hoff coefficient: i = nrx + 1 - rx = 1 + (n - l)rx from which the degree of dissociation can be expressed as i-l rx=- n-l Thus, by calculating i from experimental data, rx can be computed easily. An important method of determining the degree of dissociation is based on the measurement of the conductivity of the electrolyte in question (conductivity method). This method is associated with the fact that the electric current is carried by the ions present in the solution; their relative number, which is closely connected to the degree of dissociation, will determine the conductivity of the solution. Conductivity itself is a derived quantity, as it cannot be measured as such. To determine conductivity one has to measure the specific resistance (resistivity) of the solution. This can be done by placing the solution in a cube- like cell of 1 em side, two parallel faces of which are made of a conductor (platinum).. This cell can then be connected as the unknown resistance in a Wheatstone-bridge circuit, which is fed by a perfectly symmetrical (sinusoidal) alternating current at low voltage. Direct current would cause changes in the concentration of the solution owing to electrolysis. The specific resistance, p, is expressed in Q em units. The reciprocal of the specific resistance is termed

· It is not in fact necessary to use such a particular cell for the measurements; any cell of constant dimensions is suitable, provided that its 'cell constant' has been determined by a calibration pro- cedure, using an electrolyte (e.g. potassium chloride solution), with a known specific resistance.



specific conductance or conductivity, K, and is expressed in a-I cm- I units. For electrolytic solutions it is customary to define the quantity called molar conductivity, A. The latter is the conductance of a solution which contains 1 mole of the solute between two electrodes of indefinite size, 1 cm apart. The specific conductance and molar conductivity are connected by the relation: A =KV =

c where V is the volume of the solution in cm 3 (ml), containing 1 mole of the solute, c is the concentration in mol cm - 3. The molar conductivity is expressed in cm 2 a-I mol-I units. Kohlrausch discovered, in the last century, that the molar conductivity of aqueous solutions of electrolytes increases with dilution, and reaches a limiting value at very great dilutions. The increase of molar conductivity, in line with the Arrhenius theory, results from the increasing degree of dissociation; the limiting value corresponds to complete dissociation. This limiting value of the molar conductivity is denoted here by Ao (the notation A<XJ is also used), while its value at a concentration c will be denoted by Ac. The degree of dissociation can be expressed as the ratio of these two molar conductivities Ac r:J.=- Ao for the given concentration (c) of the electrolyte. The variation of molar conductivity with concentration for a number of electrolytes is shown in Table 1.1. Because the conductance of solutions varies with temperature (at higher temperatures the conductance becomes higher), the temperature at which these conductances are measured must be given. Values shown on Table I.l were measured at 25°C. It can be seen from this table that while the variation of molar conductivity of some solutions with Table 1.1 Molar conductivities of electrolytes at 25"C in cm 2 rr J mor J units

CODceDtratioa Electrolyte mol r- I KCI NaCI HCI NaOH KOH CH 3 COONa CH 3 COOH ->0( = Ao) 150'1 126'2 423'7 260'9 283.9 91.3 388,6 00001 149'2 125-3 0-0002 104,0 0'0005 148'3 124'3 422,2 246.5 270'1 89,4 64,5 0001 147'5 123.5 421'1 244'7 268-2 88'7 48,7 0'002 146-5 122.2 419'2 242.5 266'2 87-7 35'2 0'005 144,2 119.8 414'9 238'8 262,1 85'7 22-8 0-01 141'6 117.8 410-5 234'5 258,9 83,7 16'2

concentration is slight for most of the electrolytes listed, there is a strong dependence on concentration in the case of acetic acid. The difference in be- haviour can be seen better from Fig. 1.3, where molar conductivities are plotted as functions of concentration, using a logarithmic scale for the latter to provide a wider range for illustration. The five substances selected for illustration repre- sent five different groups of inorganic compounds, within each of which there is little variation, e.g. the curve for nitric acid would run very close to the curve



500 o e




HCI (strong acids) CH 3 COOH (weak acids)

KOH (strong bases) NH 4 0H (weak bases)

KCI (salts)

100 10- 1 10- 2 10- 3 10- 4 10- 5 10- 6 10- 7 10- 8 c/moJ. I-I

Fig. 1.3

of hydrochloric acid. But if we think in terms of degrees of dissociation, we can see that there are only two groups showing different behaviour. The first group, made up of strong acids, strong bases, and salts (including those of weak acids and weak bases), is termed strong electrolytes. (These dissociate almost com- pletely even at relatively low degrees of dilution 0'01 M solutions), and there is little variation in the degree of dissociation at further dilution. On the other hand, weak electrolytes (weak acids and weak bases) start to dissociate only at very low concentrations, and the variation in the degree of dissociation is considerable at this lower concentration range. The two methods, the cryoscopic and ebullioscopic techniques on one hand and the conductivity method on the other hand, yield strikingly similar values for the degree of dissociation, despite the substantially different principles in- volved in the two types of measurements. Some representative results are shown in Table 1.2. It can be noted that agreement is particularly good for dilute solutions of binary electrolytes (KC1). The more concentrated the solutions, the more considerable the differences. Table 1.3 shows the degree of dissociation of

Table 1.2 Degree of dissociation of electrolytes, calculated from freezing point and conductivity measurements Substance Conceatration (J(from (J(from No. of Ions molC I freezIng conductivl ty for one point molecule, n KCI 0.01 0.946 0,943 2 0.02 0.915 0.924 0,05 0'890 0'891 0.10 0.862 0,864 BaCI 2 0.001 0.949 0,959 3 0.01 0,903 0'886 0'10 0'798 0,754 K 2 S0 4 0'001 0,939 0'957 3 0'01 0'887 0'873 0'10 0'748 0.716 K 3 [Fe(CNM 0,001 0,946 0'930 4 0'01 0,865 0'822 0'10 0'715 14


Table 1.3 Degree of dissociation of electro- lytes in O'lM aqueous solutions


Hydrochloric (H + , CI-) Nitric (H+, NO;) Sulphuric (H+, HSO;) Phosphoric (H+, H 2 PO;) Hydrofluoric (H+, F-) Acetic (H+, CH 3 .COO-) Carbonic (H+, HCO;) Hydrosulphuric (H+, HS-) Hydrocyanic (H+, CN-) Boric (H+, H 2 BO;)

0'92 0.92 0.61 0'28 0'085 0.013 0'0017 0'()()()7 O. ()()() I O.()()() I


Potassium chloride (K +, CI-) Sodium chloride (Na + , CI-) Potassium ni trate (K + , CI:;) Silver nitrate (Ag+, N0 3 ) Sodium acetate (Na+, CH 3 .COO-) Barium chloride (Ba H , 2CI-) Potassium sulphate (2K +, SO

-) Sodium carbonate (2Na + , CO

-) Zinc sulphate (Zn H , SO

-) Copper sulphate (Cu H , SO

-) Mercuric chloride (HgH, 2CI-) Mercuric cyanide (HgH, 2CN-)

0'86 0'86 0'82 0'82 0'80 0'75 0'73 0'70 0'40 0'39 <0.01 very small


Sodium hydroxide (Na+, OH-) 0'91 Potassium hydroxide (K +, OH-) 0.91 Barium hydroxide (Ba H , 20H-) 0'81 Ammonia (NH;, OH-) 0'013

a number of electrolytes in O'lM concentrations. From these values we can easily decide whether a particular substance is a strong or a weak electrolyte.

1.11 THE INDEPENDENT MIGRATION OF IONS. CALCULATION OF CONDUCTIVITIES FROM IONIC MOBILITIES For strong elec- trolytes the limiting value of the molar conductivity, Ao, may be determined by extending the measurements to low concentrations and then extrapolating the graph of conductivity against concentration to zero concentration. For weak electrolytes, such as acetic acid and ammonia, this method cannot be employed, since the dissociation is far from complete at the lowest concentrations at which measurements can be conveniently made ('" 1O-4 M ). It is however possible to calculate these limiting conductances on the basis of the law of independent migration of ions. As a result of prolonged and careful study of the conductance of salt solutions down to low concentrations, Kohlrausch found that the difference in molar conductivities of pairs of salts, containing similar anions and always the same two cations, is constant and independent of the nature of the anion. He found for example that the following differences of limiting molar conductivities (measured at 18°C in cm 2 0-1 mol- 1 units)



Ao(KC1) - Ao(NaCl) = 130,1-109,0 = 21.1 A o (KN0 3 )-A o (NaN0 3 ) = 126,3-105,3 = 21'0 are very nearly equal. From these and similar results, Kohlrausch drew the conclusion that the molar conductivity of an electrolyte is made up as the sum of the conductivities of the component ions. Mathematically this can be ex pressed as Ao = A

+A(; where A

and A(; are the limiting molar conductivities or mobilities of the cation and anion respectively. The ionic mobilities are computed from values of Ao with the aid of transference numbers. These represent the current carried by the cation and anion respectively, and can be determined experimentally from the difference of concentration of electrolytes between the bulk of the solution and parts of the solution close to the cathode and anode.. Thus, for example, the transference number of chloride ion in a potassium chloride solution was found to be 0'503, while that of potassium is 0,497 (the sum of transference numbers for one particular electrolyte is by definition equal to one). The limiting value of the molar conductivity of potassium chloride solution (at 18°C) is 130'1 cm 2 0-1 mol-I. Thus the mobility of the potassium ion is A

(K +) = 0'497 x 130.1 = 64'6 cm 2 0-1 mol- 1 and that of the chloride ion is A(;(Cl-) = 0'503 x 130.1 = 65'5cm 2 a- 1 mol- 1

Table 1.4 Limiting ionic mobilities at )SOC and 25°C in cm 2 rr J mol- J units 18"C 25°C H+ 317.0 OH- 174.0 H+ 348,0 OH- 210'8 Na+ 43'5 CI- 65'5 Na+ 49,8 CI- 76,4 K+ 64,6 NO:; 61'8 K+ 73-4 10:; 42.0 Ag+ 54'4 Br- 67,7 Ag+ 61.9 CH 3 COO- 40,6 1/2 Ca H 52.2 r 66.1 1/2 Sr H 51.7 F- 46,8 1/2 Ba H 55'0 CIO:; 55,0 1/2 Pb H 61'6 10:; 34,0 1/2 Cd H 46'5 CH 3 COO- 32.5 1/2 Zn H 46,0 1/2 SOl- 68,3 1/2 Cu H 45'9 1/2 (COOW 61.1

A selected number of ionic mobilities at 18°C and 25°C is shown in Table 104. This table may be utilized for the calculation of the limiting molar conductivities of any electrolytes made up of the ions listed. Thus, for acetic acid at 25°C A o (CH 3 COOH) = A

(H+)+A(;(CH3COO-) = 348'0+40'6 = 388'6 cm 2 0-1 mol-I

· For a more delailed discussion oflransference numbers lexlbooks of physical chemislry should be consulled (cf.: Waller J. Moore's Physical Chemistry. 41h edn., Longman 1966, p. 333 el f).



The degree of dissociation can be calculated from the relation Ac a=- Ao where Ac is the molar conductivity at the concentration c; this can be measured experimentally.

1.12 MODERN THEORY OF STRONG ELECTROLYTES The theory of electrolytic dissociation can be used to explain a great number of phenomena which are important in inorganic qualitative analysis. The theory, as put forward by Arrhenius, can be applied without much alteration as far as weak electrolytes are concerned but as further evidence - particularly of the structure of matter in the solid state - emerged, it became less and less adequate for strong electrolytes. It became clear that substances which are classified as strong electrolytes are made up of ions even in the solid (crystalline) form. In a crystal of sodium chloride, for example, there are no sodium chloride molecules present, (such molecules exist only in the sodium chloride vapour). The crystal is built up of sodium and chloride ions, arranged in a cubic lattice, one sodium ion being



/ uO (:)






f)V(!)V(3 nt] . 0o

6_Q0 0 n w A G (d) \.UG)\V


Fig. 1.4



surrounded always by six chloride atoms and vice versa (see Fig. IAa). As the ions are there in the solid state, it is incorrect to suggest that at dissolution 'molecules' di

sociate into ions. The dissolution of an ionic crystal in water is a physical process. It has been proved that in the water molecule the two hydrogen and the oxygen atoms are arranged in a triangle with a distance of 0,0958 nm between the centres of the hydrogen and oxygen atoms, and with an angle of 106 0 between the directions of the two hydrogen atoms (cf. Fig. IAb). Because of this arrange- ment, that side of the water molecule containing the hydrogen atoms, becomes electrostatically positive, while the opposite end, where the oxygen atom is, becomes negative. Thus, the water molecule has a dipole character. If an ionic crystal is placed in water, these dipoles will orientate around the ions present in the outer layer of the lattice. Electrostatic force will tend to pull these ions away from the crystal (see Fig. IAc). When an ion has been removed from the lattice, a symmetrical sphere of water molecules will orientate around it, and the whole hydrated ion with its sphere of water molecules will be taken away from the crystal by thermal motion. A new ion will thus be exposed to the action of water molecules, and slowly the whole crystal will dissolve. It can be stated therefore that in the solution of a strong electrolyte there are only (hydrated) ions present; in other words, 'dissociation' is complete. When accepting this model for the dissolution of strong electrolytes, further problems have to be faced. As was said in the previous section, the theory of electrolytic dissociation was in excellent agreement with the fact that the molar conductivity of strong electrolytes varies considerably with concentration at higher concentrations (cf. Fig. 1.3). This fact does not seem to be in accordance with the theory outlined above. As the number of ions is constant if a certain amount of electrolyte is dissolved, irrespective of its concentration, one would expect that the molar conductivity of such solutions would be constant. It was not until 1923 that Debye and Hiickel, (followed by Onsager in 1925) tried to interpret these phenomena with their famous interionic attraction theory. This theory was elaborated in a quantitative way and led to a number of important discoveries in solution chemistry. For a fuller treatment textbooks of physical chemistry should be consulted.. In the present text the theory is outlined only to the extent necessary for the better understanding of phenomena occurring in qualitative inorganic analysis. The Debye-Hiickel-Onsager theory accepts the fact that in solutions of strong electrolytes ionization is complete. When at rest, i.e. when there is no electrical potential difference applied on the electrodes, each ion is surrounded by a symmetric 'atmosphere' of ions of the opposite charge. When a potential difference is applied, the ions start to migrate towards the electrode with the opposite charge, owing to electrostatic forces. The migration of an individual ion is however far from being free of obstacles. According to the theory there are two discernible causes to which the retardation of ions can be attributed. The first of these is called the electrophoretic effect, and originates from the fact that the ion under consideration has to move against a stream of ions of the opposite charge moving towards the other electrode. As said before, these ions carry a large number of associated water (or solvent) molecules, and the friction be- tween these hydrated (solvated) ions retards their migration. The higher the

· cr. Walter J. Moore's Physical Chemistry. 4th edn., Longman 1966, p. 359 et r.



concentration, the nearer are these ions to each other and the more pronounced is this effect. The second, the asymmetry or (relaxation) effect, is the result of the breakdown of the symmetrical atmosphere of oppositely charged ions around the ion in question. As soon as the ion starts to move towards the particular electrode, it leaves, the centre of the sphere of its ionic atmosphere, leaving behind more ions belonging to the original sphere. For a while at least an unsymmetrical distribution of ions will develop, those ions, which are 'left behind' will electrostatically attract the ion in question. As this force is exerted in just the opposite direction to that of motion, the migration of the ion is slowed down. This effect is the more pronounced the more concentrated the solution. If the electric circuit is broken, it takes some time for the arrange- ment of ions to become symmetrical again (in other words, for relaxation to be complete), and this time, called the time of relaxation, can be expressed mathematically as the function of measurable parameters of the solution. It is inversely proportional to the concentration. The change of conductivity with dilution is therefore not attributed to changes in the degree of dissociation, as suggested by Arrhenius, but to the variation of the inter ionic forces outlined above. The molar conductivity, at a concentration c, can be expressed by the (simplified) equation: Ac = Ao-(A+BAo)jc where Ao is the limiting value of the molar conductivity at zero concentration. A and B are constants (for a particular ion in a particular solvent at constant temperature) and correspond to the asymmetry and electrophoretic effects respectively. The great merits of the Debye-Hiickel-Onsager theory can be judged from the fact that both A and B can be expressed with measurable para- meters of the solution and with some natural constants, and that conductivities calculated with this equation agree well with the experimental values, especially if concentrations are not too high. The ratio Acl Ao in the modem theory of strong electrolytes, based on complete ionization, no longer gives the degree of dissociation r:J. for a strong electrolyte (for which it should be equal to unity); it is more proper therefore to call it the conductivity coefficient or conductance ratio. It does give the approximate degree of dissociation for weak electrolytes, but even here there are interionic forces contributing towards a lessening of the conductivity, and a correction may be applied with the aid of the Debye-Hiickel-Onsager theory.

1.13 CHEMICAL EQUILmRIUM; THE LAW OF MASS ACTION One of the most important facts about chemical reactions is that all chemical reactions are reversible. Whenever a chemical reaction is initiated, reaction products are starting to build up, and these in turn will react with each other starting a reverse reaction. After a while a dynamic equilibrium is reached; that is as many mole- cules (or ions) of each substance are decomposed as are formed in unit time. In some cases this equilibrium is almost completely on the side of formation of one or another substance, and the reaction thus seems to proceed until it becomes complete. In other cases it might be the experimenter's task to create the circumstances under which the reaction, which otherwise would reach an equilibrium, will become complete. This is often the case in quantitative analysis. The conditions of chemical equilibrium can most easily be derived from the



law of mass action.. This law was stated originally by Guldberg and Waage in 1867 in the following form: the velocity of a chemical reaction at constant temperature is proportional to the product of the concentrations of the reacting substances. Let us consider first a simple reversible reaction at constant temperature: A+B +2 C+D The velocity with which A and B react is proportional to their concentrations, or VI = k l x [A] x [B] where k I is a constant known as the rate constant and the square brackets indicate the molar concentration of the substance enclosed within the brackets. Similarly, the velocity with which the reverse process occurs is given by V 2 = k 2 X [C] x [0] At equilibrium the velocities of the reverse and forward reactions are equal (the equilibrium is a dynamic and not a static one) and therefore

VI = V 2


k l x[A]x[B] = k2x[C]x[D] By rearranging we can write [C]x[D] k i [A] x [B] = k 2 = K K is the equilibrium constant of the reaction. Its value is independent of the concentrations of the species involved; it varies slightly with temperature and pressure. The expression may be generalized for more complex reactions. For a reversible reaction represented by the equation vAA+vBB+vcC+ ... +2 vLL+vMM+vNN where V A' VB . . . etc. are the stoichiometric numbers of the reaction, the equi- librium constant can be expressed as:

[L]"L x [M]"M x [N]"N . . . K= [A]"A x [B]"B x [C]"c . . . Expressed in words: When equilibrium is reached in a reversible reaction at constant temperature and pressure, the product of the molecular concentrations of the resultants (the substances on the right-hand side of the equation), divided by the product of the molecular concentrations of the reactants (the substances on the left-hand side of the equation), each concentration being raised to the power equal to the number of species of that substance taking part in the reaction, is constant.

· 11 musl be emphasized Ihallhe condiIions of chemical equilibrium can be derived and explained mosl exactly on the basis of thermodynamics, that is wiIhout involving reaction rates at all. Text- books of physical chemistry will of course contain the thermodynamical interpretation (cf. W. J. Moore's Physical Chemistry. 4th edn., Longman 1966, p. 167 et f.)



The expression for the equilibrium constant given above gives us the clue to the problem one often comes across in qualitative analysis: what to do in order to make a reaction complete, in other words, to shift a chemical equilibrium in a desired direction. To examine this problem, let us consider the reaction of arsenate ions with iodide. If solutions of sodium arsenate, potassium iodide, and hydrochloric acid are mixed, the solution turns yellow or brown, owing to the formation of iodine. The reaction proceeds between the various ions present, arsenite ions and water being formed simultaneously, and can be expressed with the equation AsO

-+2I-+2H+ p AsO

-+I2+H20 Sodium, potassium, and chloride ions, added with the reagents, do not take part in the reaction, and are therefore not included in the equation. This reaction is reversible and leads to an equilibrium. Applying the law of mass action, we can express the equilibrium constant of the reaction as [AsO

-] x [1 2 ] x [H 2 0] K = [AsO

-] X [1-]2 x [H+]2 Let us suppose we want to reduce all the arsenate to arsenite, that is we want to shift the equilibrium towards the right-hand side of the equation. We can do this in several ways. If we add for example more hydrochloric acid to the solution, we can observe that the yellowish-brown colour deepens, that is more iodine is formed. The explanation of this is obvious from the expression for the equi- librium constant. When adding hydrochloric acid, we increased the hydrogen- ion concentration of the solution; thus increasing the denominator in the expression for the equilibrium constant. The equilibrium constant must remain constant, and therefore the numerator of the expression must increase as well. This can be achieved only by the increase of the individual concentrations in the numerator, which means that more arsenite, iodine, and water must be formed. In turn this means that the equilibrium has shifted towards the right- hand side. The same will happen if we add more potassium iodide to the solution. There are other ways however to achieve the same object. We can for example remove the iodine formed during the reaction by evaporation or by extraction in water-immiscible solvent. In this case the numerator of the expression decreases, and in order to keep K constant, the denominator must decrease also. This again means that more reactants are used up (and more products are formed). Generally, we can say that a chemical equilibrium at constant temperature and pressure can be shifted towards the formation of the products either by adding more reactants, or by removing one of the products from the (homogeneous) equilibrium system. In terms of reactions used in qualitative analysis this means either the addition of reagents in excess, or the removal of reaction products from the solution phase, by some means such as precipitation, t:vaporation, or extraction. From the argument above it follows that opposite action will shift the equi- librium in the opposite direction. Thus, for example, adding more iodine to the equilibrium system, or removing some of the hydrogen ions with a buffer, or removing iodide ions by precipitating them with lead nitrate in the form of lead iodide will shift the equilibrium towards the formation of arsenate. A different way of shifting equilibria towards one or another direction is based on the fact that the equilibrium constant depends on temperature and,



at least in some cases, on pressure. Heating is often applied when performing qualitative analyses, though mainly in order to speed up the reactions (that is to influence kinetics) rather than to influence the conditions of equilibrium. In some cases cooling to low temperatures may achieve the object. For example, the equilibrium constant of the reaction Pb H +21- +2 PbI 2 (s) varies with temperature in such a way that at lower temperatures the formation of lead iodide is favoured. Thus, if we want to precipitate iodide quantitatively with lead, besides adding the reagent in excess, we should perform the reaction in the cold. The equilibrium of those reactions in solutions in which some of the reactants or products are gases, may be influenced by varying the pressure above the solution. Calcium carbonate precipitate for example can be dissolved by introducing carbon dioxide gas in a closed vessel until the pressure in the vessel increases to a few atmospheres, when the equilibrium CaC0 3 (s)+C0 2 (g)+H 2 0 +2 Ca H +2HCO; shifts towards the formation of calcium hydrogen carbonate. For the same reason, hydrogen sulphide gas is more effective if added at a slightly increased pressure, than when bubbled through a solution in an open vessel. If, on the other hand, the product of the reaction is a gas, the equilibrium can be shifted easily towards the formation of the products by removing the gas at a reduced pressure.

1.14 ACTIVITY AND ACTIVITY COEFFICIENTS In our deduction of the law of mass action we used the concentrations of species as variables, and deduced that the value of the equilibrium constant is independent of the con- centrations themselves. More thorough investigations however showed that this statement is only approximately true for dilute solutions (the approximation being the better, the more dilute are the solutions), and in more concentrated solutions it is not correct at all. Similar discrepancies arise when other thermo- dynamic quantities, notably electrode potentials or chemical free energies are dealt with. To overcome these difficulties, and still to retain the simple expres- sions derived for such quantities, G. N. Lewis introduced a new thermodynamic quantity, termed activity, which when applied instead of concentrations in these thermodynamic functions, provides an exact fit with experimental results. This

uantity has the same dimensions as concentration. The activity, a A , ofa species A is proportional to its actual concentration [A], and can be expressed as a A = fAx [A] Here fA is the activity coefficient, a dimensionless quantity, which varies with concentration. For the simple equilibrium reaction, mentioned in Section 1.13 A+B +2 C+D the equilibrium constant can be expressed more precisely as _ a c x aD _ fc[C] xfD[D] _ fc xfD [C] x [0] K--- --x aAxa U fA[A]xfu[B] fAxfu [A]x[B] Activities, and thus activity coefficients, must be raised to appropriate powers, just like concentrations, if the stoichiometric numbers differ from 1. Thus, for



the general reversible reaction, dealt with in Section 1.13: vAA+voB+vcC+ ... P vLL+vMM+vNN+ ... the equilibrium constant should be expressed more precisely as

a VL x a VM x a VN x '" K= L M N a

A x a

B x a

c x ...

(fL[L ])"L x (fM[M])"M X (fN[N])"N X = (fA[A])"A X (fo[B])"B x (fc[C)"c x = f

L xf

M xf

N X ... x [L]"L x [M]"M x [N]"N X f

A xf

B xf

c x ... [A]"A x [B]"B x [C]"c x The activity coefficient varies with concentration. This variation is rather complex; the activity coefficient of a particular ion being dependent upon the concentration of all ionic species present in the solution. As a measure of the latter, Lewis and Randall (1921) introduced the quantity called ionic strength, I, and defined it as the half sum of the products of the concentration of each ion multiplied by the square of its charge. With mathematical symbols this can be expressed as I = !


where C i is the concentration of the ith component, and Zi is its charge. Thus, if a solution is 0.1 molar for nitric acid and 0'2 molar for barium nitrate, the concentrations of each ion being Cw = O. 1 mol £ - 1 COaH = 0.2 mol £ - 1 C N 0 3 = 0,3 mol £-1 and the charges ZH+ = 1 ZOa2+ = 2 ZN03 = 1 for the same ions respectively, the ionic strength of the solution will be I = t(cwz

+ + C Oa 2 + Z

aH + CN03Z

03) = t(0'1 x 1 +0'2 x 4+0'3 xl) = 0,6 The correlation between activity coefficient and ionic strength can be deduced from the quantitative relationships of the Debye-Huckel-Onsager theory. Without giving details of this deduction* it is interesting to quote the final result:

log}; = -0'43e 3 N 2 100

3T3 x z

jI In this expression e is the charge of the electron, N the Avogadro constant, R the gas constant, Po the density of the solvent, t: the dielectric constant of the solvent,

· For details textbooks of physical chemistry should be consulted. Cf. W. J. Moore's Physical Chemistry. 4th edn., Longman 1966, p. 354 et f.


1.14 QUALITATIVE INORGANIC ANALYSIS and T the absolute temperature. Though the expression is rather complicated, it is worth noting that it contains natural constants and some easily measurable physical quantities. This shows the great merit of the Debye-Hiickel-Onsager theory: it is able to provide a quantitative picture of the characteristics of electrolyte solutions. Inserting the adequate values of constants and physical quantities for dilute aqueous solutions at room temperatures (T = 298K) the expression can be Table 1.5 Mean activity coefficients of various electrolytes Molar 0.001 0'01 0,05 0.1 0.2 0'5 1.0 2'0 coacentration HCI 0,966 0,904 0'830 0'796 0,767 0'758 0'809 1.01 HBr 0,966 0,906 0,838 0,805 0'782 0'790 0'871 1.17 HN0 3 0.965 0'902 0'823 0.785 0'748 0'715 0'720 0,78 HI03 0,96 0'86 0'69 0'58 0'46 0.29 0'19 0'10 H 2 SO 4 0'830 0'544 0,340 0'265 0.209 0'154 0'130 0'12 NaOH 0'82 0,73 0'69 0,68 0'70 KOH 0.90 0.82 0,80 0,73 0,76 0,89 Ba(OHh 0.712 0.526 0'443 0'370 AgN0 3 0,90 0'79 0'72 0,64 0'51 0'40 0.28 AI(N0 3 h 0'20 0'16 0'14 0'19 0.45 BaCI 2 0'88 0,72 0'56 0'49 0.44 0.39 0,39 0.44 Ba(N0 3 h 0'88 0'71 0'52 0'43 0,34 CaCI 2 0,89 0,73 0,57 0'52 0'48 0'52 0'71 Ca(N0 3 h 0,88 0.71 0,54 0'48 0.42 0,38 0'35 0,35 CdCI 2 0,76 0'47 0'28 0'21 0'15 0'09 0,06 CdS0 4 0,73 0'40 0.21 0'17 0'11 0'07 0,05 0.04 CuCI 2 0,89 0'72 0'58 0'52 0'47 0'42 0'43 0'51 CUS04 0'74 0.41 0.21 0.16 0'11 0,07 0.05 FeCI 2 0,89 0'75 0.62 0'58 0,55 0,59 0'67 KF 0'93 0'88 0,85 0.81 0'74 0.71 0'70 KCI 0,965 0'901 0'815 0'769 0.719 0'651 0'606 0'576 KBr 0'%5 0,903 0.822 0'777 0'728 0.665 0.625 0.602 KI 0,965 0'905 0'84 0'80 0,76 0.71 0'68 0'69 KCI0 3 0,967 0'907 0.813 0'755 KCI0 4 0.965 0'895 0,788 K 2 S0 4 0'89 0'71 0.52 0,43 0'36 K 4 Fe(CN)6 0.19 0'14 0'11 0,67 LiBr 0,966 0,909 0'842 0'810 0,784 0,783 0,848 1'06 Mg(N0 3 h 0,88 0.71 0,55 0'51 0'46 0.44 0,50 0,69 MgS04 0'40 0.22 0'18 0'13 0,09 0,06 0,05 NH 4 CI 0.96 0'88 0'79 0,74 0.69 0.62 0'57 NH4Br 0,96 0,87 0.78 0'73 0,68 0.62 0'57 NH41 0.96 0'89 0'80 0,76 0'71 0'65 0,60 NH 4 N0 3 0'96 0,88 0'78 0'73 0'66 0'56 0'47 (NH 4 hS04 0,87 0,67 0'48 0'40 0.32 0.22 0'16 NaF 0.90 0'81 0,75 0.69 0.62 NaCI 0,966 0,904 0'823 0'780 0'730 0,68 0'66 0'67 NaBr 0,966 0.914 0,844 0'800 0,740 0'695 0'686 0'734 NaI 0.97 0.91 0'86 0'83 0.81 0,78 0'80 0.95 NaN0 3 0.966 0'90 0.82 0,77 0,70 0'62 0'55 0,48 Na2S04 0'89 0'71 0,53 0'45 0,36 0'27 0'20 NaCI0 4 0,97 0'90 0'82 0'77 0'72 0'64 0'58 Pb(N0 3 h 0,88 0,69 0'46 0,37 0'27 0'17 0'11 ZnCI 2 0,88 0'71 0'56 0'50 0'45 0'38 0'33 ZnS04 0'70 0,39 0'15 0'11 0.07 0,05 0'04 24


simplified to log}; = -0'509z

jI F or the mean activity coefficient of a salt the ex pression logf = -0'509z+=-jI is valid, where z + and =- are the charges of the cation and anion respectively. The expression is applicable to solutions of low ionic strengths (up to 1 = 0'01) in the strictest sense. A number of mean activity coefficients are collected in Table 1.5. Activity coefficients generally first decrease with increasing concentrations, then, after passing through a minimum, rise again, often exceeding the value 1. This is illustrated well on the diagrams of Fig. 1.5 where activity coefficients of some electrolyte solutions are plotted against the square root of concentration.


f ),7 ),6 ),5 )-4 ).3 ).2 ).) ),0 0,9 0.8 0.7 0.6 0.5 o



e 1/2

f ),5 ),4 )'3 ),2 ).) ).0 0.9 0,8 0,7 0,6 0,5 0,4 0.3 0,2 0,) 0 0

CaC) 2



e l/ 2

Fig. 1.5 Activity coefficients of non-ionized molecules do not differ appreciably from unity. In dilute solutions of weak electrolytes the differences between activities and concentrations (calculated from the degree of dissociation) is negligible. From all that has been said about activity and activity coefficients, it is apparent that whenever precise results are to be expected, activities should be used when expressing equilibrium constants or other thermodynamic functions. In the present text however we shall be using simply concentrations. For the dilute solutions of strong and weak electrolytes that are mainly used in quali- tative analysis, errors introduced into calculations are not considerable.


1.15 ACIDS, BASES, AND SALTS Inorganic substances can be classified into three important groups: acids, bases, and salts.



An acid is most simply defined as a substance which, when dissolved in water, undergoes dissociation with the formation of hydrogen ions as the only positive ions. Some acids and their dissociation products are as follows: HCl +2 H+ +Cl- hydrochloric acid chloride ion HN0 3 +2 H+ + NO; nitric acid nitrate ion CH 3 COOH +2 H+ +CH 3 COO- acetic acid acetate ion Actually, hydrogen ions (protons) do not exist in aqueous solutions. Each proton combines with one water molecule by coordination with a free pair of electrons on the oxygen of water, and hydronium ions are formed: H+ +H 2 0 -+ H 3 0+ The existence of hydronium ions, both in solutions and in the solid state has been proved by modem experimental methods. The above dissociation reactions should therefore be expressed as the reaction of the acids with water: HC1+H 2 0 +2 H 3 0+ +Cl- HN0 3 +H 2 0 +2 H 3 0+ + NO; CH 3 COOH+H 2 0 +2 H 3 0+ +CH 3 COO- For the sake of simplicity however we shall denote the hydronium ion by H+ and call it hydrogen ion in the present text. All the acids mentioned so far produce one hydrogen ion per molecule when dissociating; these are termed monobasic acids. Other monobasic acids are: perchloric acid (HCl0 4 ), hydrobromic acid (HBr), hydriodic acid (HI) etc. Polybasic acids dissociate in more steps, yielding more than one hydrogen ion per molecule, Sulphuric acid is a dibasic acid and dissociates in two steps: H 2 S0 4 +2 H+ + HS0 4 HSO; +2 H+ +soi- yielding hydrogen sulphate ions and sulphate ions after the first and second step respectively. Phosphoric acid is tribasic: H 3 P0 4 p H+ + H 2 PO; H 2 PO; +2 H+ + HPOi- HPOi- +2 H+ +PO

- The ions formed after the first, second, and third dissociation step, are termed dihydrogen phosphate, (mono)hydrogen phosphate, and phosphate ions respectively. The degree of dissociation differs from acid to acid. Strong acids dissociate almost completely at medium dilutions (cf. Section 1.10), these are therefore strong electrolytes. Strong acids are: hydrochloric, nitric, perchloric acid, etc. Sulphuric acid is a strong acid as far as the first dissociation step is concerned, but the degree of dissociation in the second step is smaller. Weak acids dissociate only slightly at medium or even low concentrations (at which, for example, they are applied as analytical reagents). Weak acids are therefore weak electrolytes.



Acetic acid is a typical weak acid; other weak acids are boric acid (H 3 B0 3 ), even as regards the first dissociation step, carbonic acid (H 2 C0 3 ) etc. Phosphoric acid can be termed as a medium strong acid on the basis of the degree of the first dissociation; the degree of the second dissociation is smaller, and smallest is that of the third dissociation. There is however, no sharp division between these classes. As we will see later (cf. Section 1.16) it is possible to express the strength of acids and bases quantitatively. A base can be most simply defined as a substance which, when dissolved in water, undergoes dissociation with the formation of hydroxyl ions as the only negative ions. Soluble metal hydroxides, like sodium hydroxide or potassium hydroxide are almost completely dissociated in dilute aqueous solutions: NaOH p Na+ +OH- KOH p K+ +OH- These are therefore strong bases. Aqueous ammonia solution, on the other hand, is a weak base. When dissolved in water, ammonia forms ammonium hydroxide, which dissociates to ammonium and hydroxide ions: NH 3 +H 2 0 p NH 4 0H p NH1+0H- It is however more correct to write the reaction as NH 3 +H 2 0 p NH1+0H- Strong bases are therefore strong electrolytes, while weak bases are weak electrolytes. There is however no sharp division between these classes, and, as in the case of acids, it is possible to express the strength of bases quantitatively. According to the historic definition, salts are the products of reactions between acids and bases. Such processes are called neutralization reactions. This definition is correct in the sense that if equivalent amounts of pure acids and bases are mixed, and the solution is evaporated, a crystalline substance remains, which has the characteristics neither of an acid nor of a base. These substances were termed salts by the early chemists. If reaction equations are expressed as the interaction of molecules, HC1+NaOH -+ NaCl+H 2 0 acid base salt the formation of the salt seems to be the result of a genuine chemical process. In fact however this explanation is incorrect. We know that both the (strong) acid and the (strong) base as well as the salt (cf. Section 1.10) are almost com- pletely dissociated in the solution, viz. HCl p H+ +Cl- NaOH p Na+ +OH- NaCl p Na+ +Cl- while the water, also formed in the process, is almost completely undissociated. It is more correct therefore to express the neutralization reaction as the chemical combination of ions: H+ +Cl- +Na+ +OH- -+ Na+ +Cl- +H 2 0 In this equation, Na+ and Cl- ions appear on both sides. As nothing has there-



fore happened to these ions, the equation can be simplified to H+ +OH- -+ H 2 0 showing that the essence of any acid-base reaction (in aqueous solution) is the formation of water. This is indicated by the fact, among others, that the heat of neutralization is approximately the same (56'9 kJ) for the reaction of one mole of any monovalent strong acid and base. The salt in the solid state is built up of ions, arranged in a regular pattern in the crystal lattice. Sodium chloride, for instance, is built up of sodium ions and chloride ions so arranged that each ion is surrounded symmetrically by six ions of the opposite sign; the crystal lattice is held together by electrostatic forces due to the charges of the ions (cf. Fig. 104). Amphoteric substances, or ampholytes, are able to engage in neutralization reactions both with acids and bases (more precisely, both with hydrogen and hydroxyl ions). Aluminium hydroxide, for example, reacts with strong acids, when it dissolves and aluminium ions are formed:

Al(OHh(s)+3H+ -+ A1 3 + +3H 2 0 In this reaction aluminium hydroxide acts as a base. On the other hand, aluminium hydroxide can also be dissolved in sodium hydroxide:

Al(OHh(s)+OH- -+ [Al(OH)4]-

when tetrahydroxoaluminate ions are formed. In this reaction aluminium hydroxide behaves as an acid. The amphoteric behaviour of certain metal hydroxides is often utilized in qualitative inorganic analysis, notably in the separation of the cations of the third group.

1.16 ACID-BASE DISSOCIA nON EQUILIBRIA. STRENGTH OF ACIDS AND BASES The dissociation of an acid (or a base) is a reversible process to which the law of mass action can be applied. The dissociation of acetic acid, for example, yields hydrogen and acetate ions: CH 3 COOH p CH 3 COO- + H+ Applying the law of mass action to this reversible process, we can express the equilibrium constant as

[H+] [CH 3 COO-] K = [CH 3 COOH] The constant K is termed the dissociation equilibrium constant or simply the dissociation constant. Its value for acetic acid is 1.76 x 10-5 at 25°C. In general, if the dissociation of a monobasic acid HA takes place according to the equilibrium HA p H++A-

the dissociation equilibrium constant can be expressed as

[H+] x [A-] K = [HA]



The stronger the acid, the more it dissociates, hence the greater is the value of K, the dissociation equilibrium constant. Dibasic acids dissociate in two steps, and both dissociation equilibria can be characterized by separate dissociation equilibrium constants. The dissociation of the dibasic acid H 2 A can be represented by the following two equilibria: H 2 A p H++HA- HA- p H+ +A 2 -

Applying the law of mass action to these processes we can express the two dissociation equilibrium constants as


[H+] x [HA -] [H 2 A]


[H+] X [A 2 -] K 2 = [HA-]

KJ and K 2 are termed first and second dissociation equilibrium constants respectively. It must be noted that Kl > K 2 , that is the first dissociation step is always more complete than the second. A tribasic acid H3A dissociates in three steps: H3A p H+ +H 2 A- H 2 A- p H++HA 2 - HA 2 - P H+ +A 3 -

and the three dissociation equilibrium constants are

[H+] [H 2 A] KJ = [H3 A ] , [H+] [HA 2 -] K 2 = [H2A -] [H+][A 3 -] K3 = [HA 2 -]

for the first, second, and third steps respectively. It must again be noted that KJ > K 2 > K 3 , that is the first dissociation step is the most complete, while the third is the least complete. Similar considerations can be applied to bases. Ammonium hydroxide (i.e. the aqueous solution of ammonia) dissociates according to the equation: NH 4 0H p NH1 +OH-

The dissociation equilibrium constant can be expressed as

K = [NH1] x [OH-] [NH 4 0H]



The actual value of this dissociation constant is 1'79 x 10-5 (at 25°C). Generally, if a monovalent base BOH* dissociates as

BOH +2 [B+] + [OH-] the dissociation equilibrium constant can be expressed as [B+] x [OH-] K = [BOH] It can be said again that the stronger the base the better it dissociates, and there- fore the larger the value of the dissociation equilibrium constant. The exponent of the dissociation equilibrium constant, called pK, is defined by the equations I pK = -log K = log- K Its value is often quoted instead of that of K. The usefulness of pK will become apparent when dealing with the hydrogen-ion exponent or pH. We saw already that the value of the dissociation constant is correlated with the degree of dissociation, and so with the strength of the acid or base. The degree of dissociation depends on the concentration, and therefore it cannot be used to characterize the strength of the acid or base without stating the circumstances under which it is measured. The value of the dissociation equilibrium constant, on the other hand, is independent of the concentration (more precisely of the activity) of the acid, and therefore provides the most adequate quantitative measure of the strength of the acid or base. A selected list of K and pK values is given in Table 1.6. Accurate values for strong acids do not appear in the table, because their dissociation constants are so large that they cannot be measured reliably. The values of dissociation constants can be used with advantage when calculating the concentrations of various species (notably the hydrogen-ion concentration) in the solution. A few examples of such calculations are given below: Example 1 Calculate the hydrogen-ion concentration in a O'OlM solution of acetic acid. The dissociation of acetic acid takes place according to the equilibrium: CH 3 COOH +2 H+ +CH 3 COO- the dissociation equilibrium constant being K [H+] x [CH 3 COO-] = 1'75 X 10-s = [CH 3 COOH]

· Organic amines behave like monovalent weak bases. Their behaviour can be explained along similar lines as the basic character of ammonia. The general formula of a monoamine is R-NH 2 (where R is a monovalent organic radical), showing that one hydrogen of the ammonia is replaced by the radical R. When dissolved in water, amines hydrolyse and dissociate as RNH 2 +H 2 0 <:! RNH 3 0H;:t RNHj +OH- and the law of mass action can be applied to this dissociation just like for that of ammonia. For more detailed account see I. L. Finar's Organic Chemistry, Vol. J. The Fundamental Principles. 5th edn., Longman 1967, p. 343 et f.


THEORETICAL BASIS 1.16 Table 1.6 Dissociation constants of acids and bases Acid °C Dissociation K pK step Monobasic acids HCI 25 _107 --7 HBr 25 _109 --9 HI 25 - 3 x 10 9 - - 9.48 HF 25 6,7 x 10- 4 3'17 HCN 18 4,79 x 10- 10 3-32 HCNO 25 2.2 x 10- 4 3-66 HCNS 25 1.42 x 10- 1 0,85 HCIO 15 3'2 x IO- s 7.49 HCI0 2 25 4,9 x 10- 3 2.31 HIO 25 2xlO- 10 9,70 HN0 2 20 7 X 10- 4 3'15 HN0 3 30 22 -1,34 CH 3 COOH 20 1'75xlO- 5 4,76 HCOOH 20 1'77xlO- 4 3,75 CH 2 CI-COOH 20 1'39xlO- 3 2-86 CHCI 2 -COOH 25 5.1 x 10- 2 1.29 C 6 H 5 OH 20 1'05 x 10- 10 9'98 C 6 H 5 COOH 20 6'24 x 10- 5 4.20 C 2 H 5 COOH 20 1.34x 10- 5 4,87 Dibasic acids H 2 C0 3 25 I 4.31 x 10- 7 6'37 25 2 5'6IxlO- 11 10.25 H 2 S 20 I 9.1 X IO- s 7'04 20 2 1'2x 10- 15 14.92 H 2 S0 3 18 I 1.66 x 10- 2 1.78 18 2 1'02x 10- 2 1.99 H 2 SO 4 20 I -4xlO- 1 0,4 2 1'27xlO- 2 1'9 (COOHh 20 I 2'4xlO- 2 1.62 20 2 5,4 x 10- 5 4.27 C 4 H 6 0 6 20 I 9'04 x 10- 4 3,04 (tartaric acid) 2 4.25 x 10- 5 4,37 Tribasic acids H 3 As0 4 18 I 5.62 x 10- 3 2.25 18 2 1'70xlO- 7 6,77 18 3 2.95 x 10- 12 11'53 H 3 B0 3 20 I 5.27 X 10- 10 9.28 20 2 1.8 X 10- 13 12.74 20 3 1.6 x 10- 14 13-80 H 3 P0 4 20 I 7'46 x 10- 3 2'13 20 2 6'12xlO-s 7.21 20 3 4.8xlO- 13 12.32 C 6 H s 0 7 20 I 7.21 X 10- 4 3'14 (citric acid) 20 2 1.70 x 10- 5 4,77 20 3 4,09 x 10- 5 4.39


1.16 QUALITATIVE INORGANIC ANALYSIS Table 1.6 Dissociation constants of acids and bases AcId °C DIssocIatIon K pK step Bases NaOH 25 I -4 -0.60 LiOH 25 I 6.65 x 10- 1 0'18 NH 4 0H 20 I 1'7IxlO- s 4,77 Ca(OHh 25 I 4 x 10- 2 1'40 25 2 3'74 x 10- 3 2.43 Mg(OHh 25 2 2.6 x 10- 3 2.58 CH 3 -NH 2 20 I 4, 17 x 10- 4 3,38 (CH 3 h N H 20 I 5,69 x 10- 4 3.24 (CH 3 h N 20 I 5,75 x 10- s 4.24 C 2 H s -NH 2 20 I 3.02 X 10- 4 3.52 (C 2 H s h N H 25 I 8,57 x 10- 4 3'07 (C 2 H s h ==N 25 I 5,6 x 10- 4 3.25 C 6 H S-NH2 20 I 4x 10- 10 9-40 (aniline) CsHsN 20 I . 15 x 10- 9 8,94 (pyridine) C 9 H 7 N 20 5.9 x 10- 10 9.23 ( quinoline)

Neglecting the small amounts of hydrogen ions originating from the dissociation of water (cf. Section 1.18), we can say that all hydrogen ions originate from the dissociation of acetic acid. Hence the hydrogen-ion concentration is equal to the concentration of acetate ions:

[H+] = [CH 3 COO-] Some of the acetic acid in the solution will remain undissociated, while some molecules dissociate. The total concentration c (O'OlM) of the acid is therefore the sum of the concentration of undissociated acetic acid and that of acetate ions:

c = [CH 3 COOH] + [CH 3 COO-] = 0'01 These equations can be combined into [H+]2 K = c - [H +] Rearranging and expr essing [H +] we obtain [H+] = -K+JK2+4cK 2 Inserting K = 1'75 x 10- 5 and c = 0'01 we have [H+] = -1'75 x 1O- 5 +J3'06 x 10- 1 °+ 7 x 10- 7 = 4'10 X 10- 4 molt-I 2


(The second root of equation (i) with a minus sign in front of the square root leads to a negative concentration value, which has no physical meaning.)



From this example we can see that in a O'OlM solution of acetic acid only about 4 % of the molecules are dissociated. Example 2 Calculate the concentrations of the ions HS- and S2- in a saturated solution of hydrogen sulphide. A saturated aqueous solution of hydrogen sulphide (at 20°C and 1 atm pressure) is about O'lM, (the precise figure is 0'1075 mol r 1). The dissociation constants of hydrogen sulphide are KI = [H+] x [HS-] = 8,73 x 10-7 [H 2 S]



K = [H+] x [S2-] = 3'63 X 10-12 2 [HS-] (for 20°C). As the second dissociation constant is very small, the value of [S2-] is exceedingly small. Thus only the first ionization step may be taken into consideration, when the correlation


[H+] = [HS-]


holds. Because of the small degree of even the first ionization, the total con- centration (0'1 mol t - I) can be regarded as equal to the concentration of undissociated hydrogen sulphide: [H 2 S] = 0.1 (iv) Combining equations (i), (iii), and (iv) we have

[HS-] = .) K 1 [H 2 S] = .) 8'73 X 10- 7 x 0.1 = 2.95 x 10- 4 and the combination of (ii) and (iii) yields the value of [S2-]: [ HS- ] [ S2- ] = K - = K = 3'63 X 10- 12 2 [H + ] 2 If one multiplies equations (i) and (ii) together and transposes [ S2- ] = 3'17x1O- 18 [H+]2 one finds that the concentration of sulphide ions is inversely proportional to the square of hydrogen-ion concentration. Thus, by adjusting the hydrogen-ion concentration by adding an acid or a base to a solution, the concentration of sulphide ions can be adjusted to a predetermined, preferential value. This principle is used in the separation of metal ions of the 2nd and 3rd groups.

1.17 EXPERIMENTAL DETERMINATION OF THE DISSOCIATION EQUILmRIUM CONSTANT. OSTWALD'S DILUTION LAW The dis- sociation equilibrium constant and the degree of dissociation at a given con-. centration are interlinked. To find this correlation let us consider the dissociation of a weak monobasic acid. The dissociation reaction can be written as HA p H++A-



with the dissociation equilibrium constant



The total concentration of the (undissociated plus dissociated) acid is c, thus the correlation

c = [HA] + [A -]


holds. The degree of dissociation is rx. The concentration of hydrogen ions and that of the dissociated anion will be equal, and can be expressed as

[H +] = [A -] = crx Combining equations (i), (ii), and (iii) we can write K = crx x c

= crx 2 c - crx 1 - rx or, using the notation V for the dilution of the solution


1 V=- c

(in t mol- 1 units)

the equilibrium constant can be written as rx 2 K= V(l- rx) If c or V is known and rx is determined by one of the experimental methods mentioned in Section 1.10, K can be calculated by these equations. These equations are often referred to as Ostwald's dilution law, as they express the correlation between dilution and the degree of dissociation. As the latter is proportional to the molar conductivity of the solution, the above correlation describes the particular shapes of the conductivity curves shown in Fig. 1.3. The way in which dissociation constants are obtained from experimental data is illustrated in Table 1.7, in which the dissociation equilibrium constant of acetic acid is computed from molar conductivities. The average value

Table 1.7 Calculation of the dissociation equilibrium constant of acetic acid from measured values of molar conductivity

Concentratioa A (J( K X 10 5 X 10 5 1'873 102.5 0.264 1.78 5'160 65'95 0'170 1.76 9-400 50,60 0.130 1.83 24.78 31.94 0,080 1'82 38'86 25'78 0,066 1.83 56,74 21.48 0.055 1,84 68.71 19'58 0,050 1'84 92'16 16'99 0,044 1.84 112'2 15'41 0,040 1'84 0 388'6 34


(1'82 x 10- 5) of the equilibrium constant agrees well with the true value (1'78 x 10- 5 at 25°C).

1.18 THE DISSOCIATION AND IONIC PRODUCT OF WATER Kohlrausch and Heidweiller (1894) found, after careful experimental studies, that the purest water possesses a small, but definite conductance. Water must therefore be slightly ionized in accordance with the dissociation equilibrium: H 2 0 +2 H+ + OH- Applying the law of mass action to this dissociation, we can express the equilibrium constant as [H+] x [OH-] K = [H 2 0] From the experimental values obtained for the conductance of water the value of K can be determined; this was found to be 1'82 x 10- 16 at 25°C. This low value indicates that the degree of dissociation is negligible; all the water can therefore in practice be regarded as undissociated. Thus the concentration of water (relative molecular mass = 18) is constant, and can be expressed as [H 2 0] = 1000 = 55'6 mol r l 18 We can therefore collect the constants to one side of the equation and can write Kw = [H+] x [OH-] = 1'82 x 10- 16 x 55'6 = 1'01 x 10- 14 (at 25°C) the new constant, Kw is called the ionic product of water. Its value is dependent Table 1.8 The Ionic product of water at various temperatures

Temperature Kw x 10 14 Temperature Kw x 10 14 (0C) (0C) 0 0.12 35 2.09 5 0'19 40 2.92 10 0.29 45 4.02 15 0'45 50 5'48 20 0'68 55 7,30 25 1.01 60 9.62 30 1.47

on temperature (cf. Table 1.8); for room temperature the value Kw = 10- 14 is generally accepted and used. The importance of the ionic product of water lies in the fact that its value can be regarded as constant not only in pure water, but also in diluted aqueous solutions, such as occur in the course of qualitative inorganic analysis. This means that if, for example, an acid is dissolved in water, (which, when dis- sociating, produces hydrogen ions), the concentration of hydrogen ions can increase only at the expense of hydroxyl-ion concentration. If, on the other hand, a base is dissolved, the hydroxyl-ion concentration increases and hydrogen-ion concentration decreases.



We can define the term neutral solution more precisely along these lines. A solution is neutral if it contains equal concentrations of hydrogen and hydroxyl ions; that is if [H+] = [OH-] In a neutral solution therefore

[H+] = [OH-] = .JK:, = 10- 7 mol r J In an acid solution the hydrogen-ion concentration exceeds this value, while in an alkaline solution the reverse is true. Thus in an acid solution [H+] > [OH-] and [H+] > 10- 7 in an alkaline solutio