DISSOCIATION CONSTANTS OF INORGANIC ACIDS AND BASES IN AQUEOUS SOLUTION

CONSTANTES DE DISSOCIATION DES ACIDES ET DES BASES INORGANIQUES EN SOLUTION AQUEUSE

DIVISION DE CHIMIE ANALYTIQUE COMMISSION DE CHIMIE ELECTROANALYTIQUE*

CONSTANTES DE DISSOCIATION DES ACIDES ET DES BASES INORGANIQUES EN SOLUTION AQUEUSE

D. D. PERRIN Department of Medical Chemistry Institute of Advanced Studies Australian Xational University, Canberra

*1. M. Koithoff, Président (U.S.A.), P. Zuman, Secrétaire (G.B.), 0. Chariot (France), W.

Kemula (Pologne), L. Meites (U.S.A.), D. D. Perrin r(Australie), N. Tanaka (Japon); Membres associés: E. Bishop (G.B.), S. Bruckenstein (U.S.A.),J. Coetzee (U.S.A.), Z. Galus (Pologne), H. Nurnberg (Allemagne), R. Robinson (U.S.A.), B. Tremillon (France).

ANALYTICAL CHEMISTRY DIVISION COMMISSION ON ELECTROANALYTICAL CHEMISTRY*

DISSOCIATION CONSTANTS OF INORGANIC ACIDS AND BASES IN AQUEOUS SOLUTION

D. D. PERRIN Department of Medical Chemistry Institute of Advanced Studies Australian Xational University, Canberra

*1. M. Koithoff, Chairman (U.S.A.), P. Zuman, Secretary (U.K.), G. Chariot (France), W. Kemula (Poland), L. Meites (U.S.A.), D. D. Perrin (Australia), N. Tanaka (Japan); Associate members: E. Bishop (U.K.), S. Bruckenstein (U.S.A.),J. Coetzee (U.S.A.), Z. Galus (Poland), H. Nurnberg (Germany), R. Robinson (U.S.A.), B. Tremillon (France).

CONTENTS Introduction

133

I

How to use the Table

137

II

Methods of measurement and calculation

139

III Table

143

IV References

219

V

INTRODUCTION Most of the existing tables of dissociation constants of inorganic acids and bases in aqueous solution are fragmentary in character, include little or no experimental details, and give few references. Easily the most comprehensive of the previous collections is Stability Constants of Metal-Ion Complexes, compiled

by L. G. Sillén and A. E. Martell, and published as Special Publication No. 17 of the Chemical Society, London, in 1964. However, because of the

nature of this compilation, the pK values in it tend to be overlain by the much greater bulk of the stability constant data. In many cases, also, it is difficult to decide by inspection which of the pK values should be taken from the wide range sometimes given for a particular substance.

The present Table follows the pattern of the similar Tables for organic acids and organic bases, which were also prepared at the request of the International Union of Pure and Applied Chemistry as part of the work of the Commission on Electrochemical Data. The Table of organic acids, compiled by Kortum, Vogel, and Andrussow was published in Pure and Applied Chemistry, 1, 187—536 (1960), and also separately as a book*. The Table of organic bases, by the present author, was published in 1965 as a supplement to Pure and Applied Chemistry4

For convenience, the dissociation constants of inorganic acids and bases have been given, in most cases, in the form of pKa values, and the classes of compounds include not only conventional acids and bases such as boric acid and magnesium hydroxide, but also hydrated metal ions (which behave as acids when they undergo hydrolysis) and free radicals, such as the hydroxyl radical, .OH. All of these reactions have in common the gain or loss of a proton or a hydroxyl ion. On the other hand, the hydrolyses of metal-complex ions such as the cobaltammines have been excluded, as being more appropriate to the stability constant compilation mentioned above. In general, and largely because of the difficulties attending pK measurements on inorganic species, it is not possible to offer a critical assessment of

most of the published values. In particular cases, such as water, highly precise constants are available over a range of temperatures, and the uncertainty is only of the order of 000 1 pH unit. More commonly, only a few, often widely discordant, values have been reported.

This is partly because of the chemical reactivity of the materials themselves. For example, nitrous acid readily decomposes to dinitrogen trioxide. At concentrations above 001 M, boric acid is appreciably polymerised to

polyboric acids; molybdic acid solutions contain Mo70246 and higher species; bisuiphite ion is in equilibrium with pyrosuiphite ion, S2052; and many transition and higher-valent metal ions from polynuclear species on hydrolysis. * G. Kortutu, W. Vogel and K. Andi ussow. Dissociation Constants of Organie Acids in Aqueous

Solution. Butterworth & Co. Ltd., London, i61.

t D. D. Perrin. Dissociation Constants of Organic Bases in Aqueous Solution. Butterworth & Co.

Ltd., London, 1965.

133 PAC-.B

INTRODUCTION

Often, too, unsatisfactory methods of determination have been used. Thus, pH titration measurements are seldom satisfactory if pK values lie below 2 or above 12, and in such circumstances can give quite misleading results. Again, pK values for the hydrolysis of metal ions have often been obtained from measurements of the pH values of solutions of their purified salts in water. As Sillén has pointed out (Quart. Rev., 13. 146(1959), inorganic

salts often adsorb tenaciously onto their surfaces traces of acidic or basic impurities, which persist even on repeated recrystallization, so that the measured pH values of their solutions may be much higher or lower than expected.

Even with experimentally accurate results, extrapolation to thermodynamic pK values at I = 0 is not always possible. The usual basis of such extrapolation is the Debye-Hiickel equation, —

logf+ = IZ2AI + KaD

—

bI

which is used to calculate the activity coefficient term. For precise work, values of a (the "mean distance of nearest approach" of the ions) and b are chosen to fit the data over a range of ionic strengths, so that the value of the pK, extrapolated to I 0, can be obtained. At low ionic strengths and where

moderate accuracy (say +005 pH unit) is sufficient some simplifying

assumptions can often be made. Thus, Davies' equation (J. Chem. Soc. 1938,

2093) is obtained by taking Ka =

1,

b = 02; Guntelberg's equation (Z.

physik. Chem. Leipzig, 123, 199 (1926)) sets Ka = 1, b

0; and the approxiAl)) is also used. However, with moderately strong acids and bases (pJC values less than 2 or greater than 12), the numerical values of the thermodynamic plC constants depend in part on the assumptions made in deriving them, including the ion-size parameter a used in the extended Debye-Huckel equation (see, for example, R. G. Bates, V. E. Bower, R. G. Canham and J. E. Prue, Trans. Faraday Soc., 55, 2062 (1959); A. K. Covington, J. V. Dobson and W. F. K. Wynne-Jones,

mation Ka =

0,

b = 0 (i.e.—log f =

Zs2

Trans. Faraday Soc., 61, 2057 (1965), E. A. Guggenheim, Trans. Faraday Soc.

62, 2750 (1966). Thus, the pK of bisulphite ion at 25° varies from 1927 to F967 as Ka is varied from FO to 17. In the same way, pKb for Ca(OH)2 varies

from 114 to 127 at 25°, depending on the choice of parameters. A distinction must also be made between true and apparent pK values. The first pK of carbon dioxide in water as measured is about 64 at 20°, whereas the true pK of carbonic acid (H2C03) is 38. The difference between the apparent and the true pK values is due to the slight extent to which carbon dioxide is covalently hydrated in water. Similarly, periodic acid exists as H5106 and H104 (mainly as the latter), so that its measured second pK (8.3) is very much higher than its first one (about 2). In the absence of experimental values, especially for some of the oxyacids, attempts have been made to predict pK values, usually from similarities of

structure. The more commonly used methods are those of J. E. Ricci (J. Am. Chem. Soc., 70, 109 (1948)), L. Pauling (General Chemistry, Freeman,

San Francisco, 1947, p. 394), and A. Kossiakoff and D. Harker (J. Am. Chem. Soc., 60, 2047, (1938)). Even in apparently simple cases, there may be considerable uncertainty. For example different values would be predicted 134

INTRODUCTION

for germanic acid depending on whether it existed mainly as GeO(OH)2 or Ge(OH)4. Because of the many different kinds of uncertainties inherent in the present pK compilation, no attempt has been made to assess the accuracy of each entry. Nevertheless, where possible, I have attempted to select what appear to be the best available values. The results for hydrogen suiphide illustrate this. Thus, several methods have indicated that the second pK of hydrogen suiphide is about 14, which is too high for potentiometric titration methods to be applicable. Hence the pK2 values that have been obtained by potentiometric titration are not set out in the Table. Instead, references to the papers where they are given are included under "other measurements". This heading also covers results where insufficient experimental details are given.

135

I. HOW TO USE THE TABLE GENERAL ARRANGEMENT The Table summarizes data recorded in the literature up to the end of 1967 for the dissociation constants of inorganic acids and bases in aqueous solution. It also includes references to acidity functions for strong acids and bases, and details about the formation of polynuclear species where this is relevant. The substances are listed alphabetically, with chemical formulae, so that the entries are self-indexing. Column 1 gives the name of the substance and the negative logarithm of the dissociation constant (pICa). Wherever possible, these values are thermodynamic ones obtained by extrapolation to ionic strength I = 0, generally by using some form of the Debye-Huckel equation such as that due to Davies. In all cases, pK values are listed in decreasing extent of protonation. Column 2 gives the temperature of measurements in °C. Column 3 lists details such as: = ionic strength I= c = concentration in mole/i, or m = concentration in mole/1000 g. of water. It also records any other details relating to the pK value quoted. Designa-

tion of a constant as "practical" implies that it includes both the activity of the hydrogen ion (usually as measured by pH meter) and the concentrations of the other species. Column 4 summarises the method of measurement, the procedure used in

evaluating the constants, and any corrections that were taken into consideration; the symbols have the meanings set out under "Methods of Measurement", page 7. Because different investigators rarely use identical procedures, these symbols can only serve as guides: for fullest details the original papers should be consulted. Column 5 gives the literature references which are listed alphabetically at the end of the Table.

137

II. METHODS OF MEASUREMENT AND CALCULATION The abbreviations in Column 4 of the Table are, with only minor differences,

the same as those used in "Dissociation Constants of Organic Bases in Aqueous Solution".

CONDUCTOMETRIC METHODS

Cl C2

Measurements in solutions of salt and acid Measurements in solution of base only

ELECTROMETRIC METHODS

[i] Cells without diffusion potentials Ela

Elb

Elcg

Elch

Eld Ele

Method of Harned and Ehlers (J. Am. Chein. Soc. 54, 1350 (1932)) (Cell of type Pt (H2)IB, BC1, NaC1IIB, BC1, NaClAgC1Ag, for which E — E0 + (RT/F) in {BH+] [C1]/[B] = — (RT/F) ln K', and extrapolate to I = 0)

Method of Harned and Owen (J. Am. Chem. Soc. 52, 5079 (1930)) ,Pt(H2)IB, NaCljAgClAg, where molality of B is M, E = E0 (RT/F) in ([mn+] [mcijf±2). Extrapolate to I = 0 at constant M, then to M = 0) Determination of [H+] from cells of the type, GlassJ solution,

Cl-AgClAg Determination of [H+] from the cell, Pt(H2) solution, Cl-AgClAg

Method of Bates (J. Am. Chem. Soc. 70, 1579 (1948)). Determination of K1 and K2 for dibasic acids Method of Bates and Pinching (J. Res. .J'Tatl. Bur. Std. 43, 519

(1949)). A particular case of method Eicg in which the solution is a buffer comprising a weak base and a weak acid

[ii] Approximately symmetrical cells with diffusion potentials E2a E2b

E2c

Method of Owen (J. Am. Chein. Soc. 60, 2229 (1938)) Method of Larsson and Adell (. Physik. Chem. 156, 352, 381 (1931)) (Uses cell Pt(1E12)IB, NaClisat. KC1INaOH, NaC1J (H2)Pt and an approx. K to adjust to equal ionic strengths in

the half-cells. From E obtain {H+] and hence K': extrapolation to I = 0 gives K)

Method of Everett and Landsman (Proc. Roy. Soc. London, A215, 403, (1952)) (This is like E2b but uses a second weak base of known pK

instead of a strong base. The method gives the ratio of the two constants) 139

METHODS OF MEASUREMENT AND CALCULATION

[iii] Unsymmetrical cells with diffusion potentials E3ag

E3ah E3bg E3bh E3b, quin E3c E3d

01

pH measurements in buffer solutions of weak electrolytes using glass electrodes Similar measurements using hydrogen electrodes

Measurements of pH changes during titrations using glass

electrodes Similar measurements using hydrogen electrodes Similar measurements using quinhydrone electrodes Differential potentiometric methods pH measurements at equal concentrations of salt and base

OPTICAL METHODS Direct determination of the degree of dissociation by extinction coefficient measurements in solutions of weak bases and salts

02

Colorimetric determination with an indicator of known pK

03

Colorimetric determination with an indicator calibrated

04

with a buffer solution of known pH Method of von Halban and Brüll (Helv. Chim. Acta 27, 1719 (1944))

(Solutions of the base being studied, plus indicator, are compared with similar solutions containing alkali and 05 •

06

indicator) Light absorption measurements combined with electrometric measurements Light absorption measurements using solutions of mineral

acids of known concentrations and (usually) Hammett's 07

acidity function, H0 Similar to 06 but using solutions of alkalis

OTHER METHODS ANALYT

Constants derived from chemical analysis

CALORIM Calorimetric measurements Constants estimated from catalytic coefficients CAT CRYOSC Cryoscopic measurements Distribution between solvents DISTRIB Constants derived from freezing-point data FP ION Ion-exchange studies

KIN NMR

Constants estimated from kinetic measurements Nuclear magnetic resonance measurements

POLAROG Polarographic measurements Measurements of Raman spectra RAMAN REDOX Oxidation-reduction potentials SOLY Solubility measurements VAP Vapour pressure measurements 140

METHODS OF MEASUREMENT AND CALCULATION

CALCULATIONS

[i] Conductance measurements

Ria

Method of Davies (The Conductivity of Solutions, Chapman

Hall, London 1930) (By successive approximations, fA is calculated from the Debye-Huckel-Onsager equation in the form

Li = 1 Rib

Ric

Rid Rie

—

A(acco)//1o

which assumes that A0 can be obtained from Kohlrausch's law of independent ionic mobilities) Method of Maclnnes (J. Am. Chem. Soc. 48, 2068 (1926)) (The quantity Ae =fAAo is determined directly, where i1 is the conductance of the weak electrolyte if it were completely dissociated at the ionic strength studied: it is necessary to know A for strong electrolytes as a function of I) Method of Fuoss and Krauss (J. Am. Chem. Soc. 55,476 (1933))

(The Debye-Huckel-Onsager equation is used in the form, = c(Ao — A(cco) ) to derive an equation relating A0, c and K, which is solved by successive approximation until A0 is constant at all values) Method of Shedlovsky (J. Franklin Inst. 225, 739 (1938)) (This is like Ric but a different equation is used) Method of Fuoss (J. Am. Chem. Soc. 79, 3301 (1957))

[ii] Differential potentiometric measurements R2a

Method of Kilpi (Z. Physik. Chem. 173, 223, 427 (1935); 175, 239 (1936) (at point of inflection).

141

25 25 25

25 100

496

503

510

4.49

288

10.25

38 292 28 46

82

7.86 8'2 7'7

8'lS 828

33

300

2. Amidophosphoric acid, NH2PO3H2

25

10

20

25

25

25

25

502

1122

25 25

15

20

Al

4•98 4•96

Aluminium ion,

T( °C)

515

1. (Aquo) 5•28

Name, Formula and pK value

l0

A1C13,

+

Other measurements:C19

f±

+H

0'2 (KC1), "practical" constants 1 (NMe4Br), concentration constants, assumed same as for HBr Titration of 01 M solution; pK of NH3PO3H2 given as 2'l

I

I=

+

A14(OH)102+ 2H pK for hydrolysis of A13 pKfor hydrolysis of AL3 pK for hydrolysis of Al3, from dissociation field effect relaxation times pK for hydrolysis of Al3 pKfor A1(OH)3 H20 Al(OH)4 Hydrolysis of A13+ in 2 M NaC1O4 at 40° gives, mainly, one or more polynuclear complexes Other measurements: B94, D23, F5, 120, Li, T7, W25.

I

= 00005 — 001 M in

extrapolated to = 0 pK for hydrolysis of A13+;= also log K = 755 for 2AIOH2 A12(OH)24+, and log K 689 for 2A12(OH)42+ 2H20

c

of A13, I varied from 00025 to 0019, extrapK for hydrolysis polated to 1 = 0 — 10—2 M in Al(Cl04)3, pK for hydrolysis of A13, c

pK for hydrolysis of Al3, extrapolated against 1k

Remarks

III. TABLE

E,h

E3b E,Sb

E3bg E3bg

Ci

KIN KIN

E3ag E3AG

E3,quin

E3ag

E3ag

E3ag

Methods

1—2

H15 RiO

M26

K29

R41

C13 112

B97

K69 M9

K67 119 H64a

K12

F33

H41

S17

Reference

Nos.

Name, Formula and pK value 25

T(°C) pK3; I = 1-0 (NaC1)

Remarks

6.

9.555 9-240 8-946 8-670

8-539

8670

9-400 9-245 9-093 8-947 8-805

9564

8•540 10-081 9-904 9-731

8671

9-401 9-246 9-093 8-947 8-805

9564

9-903 9-730

10-081

25 35 45

15

20 25 30 35 40 45 50

10 15

0 5

40 45 50

25 30 35

20

0 5 10 15

Ammonia, NH3

5. Aminophosphoricacid, see Amidophosphoricacid.

Thermodynamic quantities are derived from these values.

Thermodynamic quantities are derived from these values.

Ivaries from 0-06 to 0-20. Extrapolated to zero concentration of NH4 at each I, then extrapolated against I

concentrations of NH3 and KH phenol suiphonate, c varied from 0-011 to 0-104 M, activity coefficients calculated from Debye-Hückelequation, pK plotted against I

Equal

4. Aminophosphazenes,see Hexaminotriphosphazene,Octaminotetraphosphazene.

3. Aminodisuiphonic acid, NH(HSO3)2 8-50

E2b

Ela

Elch

E3ag

E23

B19

B20

D37a

Methods Reference

Nos. 3—6

100

25 25 25 45 45 45 45

429

200 3272

221 211

2•68 2•42

295

332

3.74

430

4'71

365

3.95

391 361 432

293

758

271

182 227

138

218 306 49 93

156

100

35 45 0 18 25

5

15 25

6•21 6•62

5.76

504 536

4•83

645 560 574 468

7'45

935

9'58

l0•19

8923 8645

9•215

9867 9529

1 = 007 to 02, extrapolated to I = 0, c = 0

11000 12000 Self-ionization of liquid ammonia, from cell potential data

2500 4000 5400 6800 8200 9600

1100

from 0° to 300°. pKb values 1000 atmospherespressure 2000 3000 1000 2000 3000 1 atmosphere pressure pKj, values

taking pKW 1238; inversion of sucrose Ref. H49a gives an equation fitting literature values of pK

=

O•02 to 008;

pKb values

c

BIOS

K69

W29

N24

E25

P30

Cl, Ria H17

Cl, Ria

CAT

Cl

CI

E2b

25 25

T(°C)

25

2-332

2-296

2-265

2-223

2-114 2-138 2-163 2-194

7-032 7-015 6-999 6-990 6-980 6-974 6.973 6-973

20 25 30 35 40

5 10 15

Aquo metal ion, See entry under appropriate metal iron 9. Arsenic acid, H3AsO4 2089 7-054 0

255

Remarks

ofliquid ammonia,from thermodynamicdata

10

H

extrapolated to

I (for0 K2);

and 0-010to 021

I varied from 0007 to 0096 (for K1).

nuclear complexes are also formed.

pK for HSb(OH)6 Sb(OH)tr + H; I = 0-5(NMe4C1); Sb concentration < M; at higher concentrations poly-

H

pK for Sb0H2 SbO + pK for Sb0 + H20 HSbO2 + 1-1+ pK for Sb0 + H20 HSbO2 + H pK for HSbO2 + 2H20 Sb(OH)4- +

ofliquid ammonia, from thermodynamic data Approximate pK ofNH2—, theoretical calculation A value of 4-20 at 25° has been claimed from high field conductance measurements to be the true pKb of NH4+ + + 0H NH4OH A similar value, 4-28 at 200,has been estimated from published data For pK values in methanol-water mixtures, see E26, P1Other measurements: B51, F41, H26, H37, K3, K26, L49, M44, N25, 016, P13, S31, W22. Self-ionization

Self-ionization

8. Antimony pentoxide,Sb205 See also IDodeca-antinionic acid.

0-87 11-0

7. (Aquo) Alimony 111 ion, Sb3 14 25 11-8 25

40

25

27-66 29-8

248

—33-2

3249

Name, Formula and pK value

7—12

Ela,quin

E3b

SOLY SOLY SOLY SOLY

AlO

L17

P29

K5

M43

S29 B35

J13

C32

Methods Reference

Nos.

7•08

6.80

687

694

705

1192

11•50 11.64

1133

6973 6980 pl(r = 2014 + 5 = 6971 + 5

135 138

acid, HSCSN3

060

12. (Aquo) Barium ion, Ba2 062

167

11. Azido-dithiocarbonic

94

926 908

9•294 9•22

881

909 897 8885

9•265 9•18

9295

5 15

25

32

Room

25 18 25

20 25 30 35 40 45 25

15

50 25 25

35

25

10

45 50

x 105 (t — 400)2 x 10 (1 39.4)2, tin °C.

10. Arsenious acid, H3AsO3 (HAsO2)

2301

195 2.15

2•19

249

2•420

2383

= 0008, I = 01 (KC1)

extrapolation to

I

0; from e.m.f. data

of H.S. Harned and

pK ofBa0H; I == 01 ; f+ calculated by Davies' equation, for

Free acid readily decomposes

Z2

Othermeasurements:B58, Cli, G5, K36, K48, T15, W5, W25,

pK2 obtained from ultraviolet spectra

Taking pK of boric acid as 919 "Practical" constant, titration of 0017 M H2AsO3

c

In KCI solutions, extrapolated to I = 0

Molal scale;

For values of pKi in D20JH20 mixtures, see S3 Other measurements:B58, B86, C23, K48, L50, M8, S54, W4, W5

Taking pK2 of H3P04 as 716

Thermodynamic quantities are derived from the results.

B86 115

A28 H78

A29

H78 S3

F19

Cl

S55

0 G33 CRYOSC S61

E3ag E3bg E3ag

E

E3dg

E3ag E3ag

E,g

25 25

062 072

000

25

>6•1

1046

1082

25

65

5.7

13. (Aquo)

20

25

085

....7

25

064

Beryllium ion, Be2

25 45

0.72

069

25

T(°C)

064

Name, Formula and pK value

I=

I

J. +

+ 2H

pK for Be2

I

BeOH + H; I = 1 (NaCIO4); Be20H3 also formed pK for Be2 Be0H + H; = 3(NaClO4); recalculation of data from refs. C8 and KI using a computer; also — log K = 1087 for Be2 + 2H20 Be(OH)2 + 2H+; constants given for Bea(OH)aS+ and Be2OH3+ pKb for Be(OH)2 Be0H + OH—; c 001; between pH 62 — 54; at lower pH values di- and tn-nuclear complexes are formed; constants are given + H20 Be(OH)a + H; tracer concenpK for Be(OH)s trations; also — log K = 1365 for Be2 + 2H20 Be(OH)2

Bea(OH)33+

I

Beryllium ions readily hydrolyze in solution and form condensed species containing more than one beryllium atom. See, for example,C8 and Ki. Successive pK values for hydrolysis of Be2; 01 (NaClO4); rapid-reaction measurements; BeOH+ quickly forms trimer

1 = 3 (NaC1O4) Other measurements:B32, K64

cator

= I=

I=

Thermodynamic quantities are derived from the results. 004 to 017; using Davies' equation and pKb of BaOH; activity measurements of H. S. Harned and C. M. Mason, Am. Chem. Soc. 54, 1441 (1932) c 002 — 0.05 (Ba(OH)s), 023 to 06 (Ba(OH)s BaCI2), extrapolation to 0, using Davies' equation 01 to 045 Concentration constant; 02 — 1 N BaC12; salt effect on mdi-

C. G. Geary, J.Arn. Chem.Soc. 59 2032 (1937)

Remarks

B30

D7

Reference

13—15

A9

H56

M21

S30

C7

DISTRIB G39

E3b

E3bg

E3ag

E2ah

CAT,KIN B31 03 K39

KIN

Methods

Nos.

9-280

9327

9-440 9-380

9-1013 9•0766 9-0537 9-0310

91282

9-1605

91947

9-3785 9-3255 9-2780 9-2340

94374

9-5078

15. Boric acid, H3B03

14. (Aquo) Bismuth(IIJ)ion, Bi3+ 158

20

10 15

5

15 20 25 30 35 40 45 50 55 60

5 10

0

25

+ 12H, with logK = 0-33

I

I

pK = 2237-94/T + 0016883T— 3305 (Tin °K) Thermodynamic quantities are derived from the results. Molal scale. varied from 002 to 3 by adding NaC1; extrapo-. lated to zero boric acid concentration at constantI, then to = 0

I

Molal scale; equimolal concentrations (0-003 to 003 M) of MaCI, borax and boric acid; extrapolated to = 0 using extended Debye-Huckel equation

I

Hydrolysisof Bi3 gives Bi6066 + 12H, with —log K 0-53 at 25° and == 1(NaCJO4), and at higher pH values Bi6O6(0H)s3, with logK = — 81 Hydrolysis of Bi6066 (= Bi6(OH)i+) gives Bi9(OH)2o7, Bio(OH)216+ and Bi9(0H)225; constants are listed

Bi6(OH)126+

H; I

= 3(NaC1O4); [Bi3] deterBiOH2 + mined by Bi-Hg electrode; main equilibrium is 6Bi3 + H20 pK for Bi3

Other measurements:L40, W26.

species.

— log K = 8-81 for 3Be2 Bea(OH)a3 H- 3H; — log K = 324 for 2Be2 Be2OH3 + H; — log K = 110 for Be2 Be(OH)s + 2H; all for I = 0-5(NaC1O4), c 0-001 to 008 M in Be2 — K = 109 for Be2 ± 2H, at 25° and I =log3(NaC1O4); constants alsoBe(OH)2 given for di- and tn-nuclear

Elch

Elch

E3bg

018

Mu

07

T9

06

K!

B37

n

—

90

10-2

16. (Aquo) Cadmium ion, Cd2 25

25

25

9-00

9-00

9-21

898

30 40 50

25

20

15

10

50

40

30 35

T(°C) 25

20 25 25

9-380 9•327 9-280 9-236 9•197 9•132 9•080

9198 9164 9132 9080

9-237

Name, Formula and pK value

I

ar

I

I

I

hydrolysis of Cd2; = 3(NaC1O4 + Cd(C104)2); c 0-i to 1-45 (Cd(C104)s); CdzOI13 and Cd4(OH)44- are also formed for hydrolysis of Cd2; = 3(NaC1O4 + Cd(C104)2); pK c = 0-01 to 09 (Cd(C104)2)

for pK =

Other measurements:B71, B88, E6, F9, Hl0, H25, 15, 16, K42, K48, L15, L41, M24, 017, P39.

001

3H3B03 H4B307- + 11+ + 2H20, log K = — 684, 3H3B03 H5B3092 + 2H + H20, log K = — 1544 Polymericspecies are important at concentrations above about

19

F31 14

015

E3bg

M12

E3bg, quin B44

E3bh

At boric acid concentrations above 0-4 M, higher than trimeric complexes are also formed I = 3(NaClQ4); boric acid concentrations varied from 0-01 to

Ela

E3ah E3bh

0-60 M. Other equilibria were:

16—18

Methods Reference

= 9-023 8 x 10 — t)2 (tin °C) pK I == 004. The+secondpK (76-7 ofboric acid is greater than 14 1 01 (NaC1O4)

f= 3(NaClO4)

derived from the results Thermodynamicquantities varied from 0-01 to 0-12; constants corrected using DebyeHuckel equation and extrapolated to = 0

Remarks

Nos.

C,'

1-31

25

0 25

124—136

151

0

25

130

125—1-34

40

25

Q

Recalculation of data of F. M. Lea and G. E. Bessey, Soc. 1937 1612

113 (1934)

I I

J. Chem.

extrapolated to 1 0 assumingDavies' equation; Ca(103)2in KOH solutions. pKb for CaOH; Ca(IOs)2 in Ca(OH)2 solutions; extrapolated using Davies' equation. pK3 for CaOH+; I = 018 to 030; value sensitive to choice of activity coefficient = 0025 to 008 re= 003 to 0-15; extrapolatedZ.using Davies' equation; calculation of data of G. Kilde, Anorg. Aligem. Chem., 218

0007 to 008 pK for CaOH; II = = 002 to 008 I=0-04to010

+ CaCI2);f± cal—

pKb for CaOH; 1 = 002 to 0•1 (Ca(OH)z culated assuming Davies' equation

15

25 35

25 40

m = 0002 — 002 Ca(OH)2 in 0003 — 001 pKb for CaOH+;— or 0006 002 M KC1; values ofpKb depend on choice M CaCI2 of yci/You used to evaluate molality of hydroxyl ion.

For alkalinity function for CsOH solutions,see L12a, M40.

Other meazurements:C12, G38, L39

Cd

pK for hydrolysis of Cd; c 002 (CdCI2) pK for hydrolysis of pKb for HCdO2 + H20 Cd(OH)2 + 0HOH CdOH Cd2 + I = 3(NaCJO4),pKb for CdOH+ + 0H pKb for Cd(OH)2 pKb for Cd(OH)3- Cd(OH)2 + 0H pKb for Cd(OH)42- Cd(OH)3 + 0H on assumptionthat log K = log K1 '(3 K3 K4 ± ((5 — 2n)/2) log (K/K1) Cd(OH)42- is about 97 at 25° log K for Cd2 + 40H

0 10

25 25 25

100

148

1-40

140 137

1-34 1•37

1•12—1•24 1-14—1-27 1-36—1.45

102—114

18. (Aquo) Calcium ion, Ca2

17. Caesium hydioxide, CsOH

F72

2-58

430 344

07

9•3

9.49

K69 G14

C2

B30

D6

1332

KIN SOLY

D9

1329

G26

1317

SOLY

SOLY

Elch

Elb

POLAROG L3

DISTRIB D46

SOLY

KIN

03

pK value

6•290

6352 6327 6309 6298

6381

6579 6517 6464 6419

6296 6289 6287

3.3Ø9

6327

6351

6382

6•420

6577 6517 6465

19. Carbonic acid, H2C03

064

1

129

146

Name, Formula and

25 30 35 40 45

20

15

10

5

0

20 25 30 35 40 45 50

10 15

0 5

25

25

25

T(°C)

02 — 1 N CaC12; from salt effect on

I

pK1 340471/T — 148435 + 0032786T(Tin °K) Thermodynamicquantities are derived from the results. ApparentpK values; 0004 — 02, extrapolated to 1

0

Apparent pK values; double extrapolation procedure to eliminate effect of added NaCi and to obtain values at zero bicarbonate concentration

1 3(NaClO4) For the acidity function of Ca(OH)2 solutionsfrom 0—95° and 1=001 to 020, see B18 Othermeasurements:G42

Concentration constant; indicator

f (Phil. Mag., 19, 588 (1935))

Remarks

1 = 013 to 024 (Ca(OFI)z + CaC12); c 002 — OO3 Ca(OH)2; extrapolated using Davies' equation 1 = 002 to 005; calculated from Guggenheim's equation

B30

Reference

Elch

Elch

E2ah

03

H31

H29

C7

K39

CAT, KIN B31

KIN

Methods

No. 19

526

551

631 588

5•17

630 586 549

5•50 5•16

512 632 589

5•45

638 590 548 515 632 585

6•35

635

6•317

6583 6429 6366

6•294

631O

6.349

6514 6421

6•285

20 25

10•377

10329

lO430

10 15

0 5

10•490

10625 10557

65

55

45

35

25 38 25 25 25

15

0

45

35

25

15

5

50

I

I

HC1,

I

and

0

Apparent pK value ApparentpK values, molal scale, 1035I atmosphere, I varied from 00001 to 01, atmosphere 2050 atmosphere 2930 atmosphere 1 atmosphere 1030 atmosphere 2035 atmopshere 2930 atmosphere 1 atmosphere 1015 atmopsherc 2010 atmosphere 3000 atmosphere 1 atmosphere 1020 atmosphere 2010 atmosphere 2950 atmosphere 1 atmosphere 1050 atmosphere 2060 atmosphere 2800 atmosphere varied from 002 to 016; extrapolated to = 0 using extended Debye-Huckelequation

ApparentpK value

+ 000013329i2 (tin °C) pKi = 6572 — 0012173t Apparent pK values; 0001 N in KHCO3, KC1, saturatedCO2 solutions

I

— Apparent pK values; = 0003 3; extrapolated to extended to an Debye-Huckel equation by fitting

S40

N7

E3ah

1139

E2b, quin A45 Elc, quin A44 Cl RIO

Cl,Rld

E3bh

100 156

200 218 25 38

1096 1025 1020 25 35

3.78

376

15

5

200 250 300

100 150

200

100 150

1032 1033 1017 1014 1025 1042 1013 1037 1080 1130 120 1014 1041

631 381 3.75

634

714

681

646

8•70

727 789

6•77

633 655 642

6•29 6•24

635

0 18

10641 10•397

25 25 50

90

10142 10140

70 80

60

10179

10•153

50

35 40 45

T(°C) 30

10•172

10195

10•220

10290 10250

Name, Formula and pK value

I

measurements

1(NaCl)

H

II

1 varied from 001 to 02; extrapolated against Ivaried from 001 to 02; extrapolated against True pK for H2C03 + HC03; high field conductivity

1

1=0 =

I I

= 290910/T— 6119 + 002272T(Tin°K) Double extrapolation, first to values in pure aqueous NaC1 solutions, then against to = 0

pK2

pKs = 2902•39/T — 64980 + 002379T(Tin °K) Thermodynamicquantities are derived from the results. varied from 0005 to 01; extrapolated against I

Remarks

C

E3ag E3ag

Cl

Cl

VAP

E3ah

E,g

W23

MG

M5

R48

R49

N6 E9

W9

C45

Methods Reference

Nos. 21—23

cn

25

235 302 356 4

388

375 382 389 380

9

0'OG

5

25 25

—022

l6

25

25 35

15

082

11

Ce4

23. Chloraniine, see Monochioramine

—l15

—09

070

—1•l8

—0•72

—0'32

22. (Aquo) Cerium(IV) ion,

21. (Aquo) Cerium(III) ion, Ce3 25

05

20. Caro's acid, see Peroxymonosuiphuricacid

45

3•68

38

380 380

S72 — 14

l0

= I

x

I0

M;

di-

pH-dependence of redox potential pK for Ce0H3 Ce(0H)22 + H; HC104 concentration from 02 — 0.4 from pH-dependence of redox potential Other measurements:D2a

c

1= 09 to l7(HClO4) I x 10 M Ce(IV);polymerisatioriwas negligible. pK=valuesfor hydrolysis to CeOH3 and Ce(OH)s2; I 2(HC1O4, NaClO4); c = 35 x M Ce(IV); from

11 — 4(HCIO4, NaCIO4); merization was important

I

in 3 M LiCIO4 Other measurements:R8,

pK for hydrolysis of Ce3; from hydrolysis of "pure" salts; c 0001 — 05 ss Ces(S04)s Ce3(OH)54 was formed at 25° by hydrolysis of 005 M Ce2

REDOX

REDOX

06

06

E3ag

Cl

True pKfor H2COS; 150 atmospheres; pressure method. Other measurements: B79, BlOl, Bill, C40, jump C41, F6, F34, H42, K6, K7, KS, K9, Kl0, K28, K43, M22, M28, M45, Ni2, R37, SI, S69.

KIN

C2

True pKfor HaCO, calculated from apparent pK, using rates of hydration and dehydration TruepKforH2CO3;from highfieldconductivitymeasurements, taking pK0ba 6352 True pK for H2COa; from rapid-reaction measurements

S42

138

Ola

R20a

B49

M38

L38

S13

B34

D31

— 2-7

Chioric acid, HC1O3

T(°C)

6-444 6-478 6-488 6-524 6-569 6-642

074

660

647 652 652 650

6-40

6593

6-500 6-533

6472

27. Chromic acid, H2CrO4

1-97 1-96 1-99

1-94

26. Chiorous acid, HCIO2

25 20

25 25

25 35 45 18 18 25

15

25 35 45 60

5 15

20 23

2

19—20

25

Remarks

Theoreticalprediction, based on structure

I

centrations

I = 01; corrected to I = 0 by Davies' equation, tracer con-

I=

0002 to 0-004 001 to 016; extrapolated to 0; 0023 for CrO72 H20 2HCrO4

I = K + I about016; HCl/KC1 solutions

1

Titrationof 0025 M H2CrO4 Titration of 0-04 M K2CrO4 I = 00018 to 0-0028;f + calculated from Davies' equation =

Spectral differences extrapolated to zero time; c = 0001 to 0-003M NaC1O2, acidified with HC1O4; activity coefficients from Debye-Huckel equation c = 0001 — 01 M NaC1O2; extrapolation against "Practical" constant; concentration of HCIO2 025 M Other measurements:L20, Ti

25. Chiorosuiphuric acid, HC1SO3 For pK in sulphuric acid, see Bi 1

24.

Name, Formula and pK value

L18

N16

H72

B81 B88

L35a

L35a

DISTRIB H13

E3ch

E3ag

05

E3bg E3bg E3bg

05

E3bg

D5 H66 E3bg, R2a L36 E3bg

06

K52

Methods Reference

Nos. 24—28

649

Ca

4•26 3•90

2•58

299

401 3.47

334 301 283 265 249 405 382 466

3•95

366

. . ..j 28. (Aquo) Chronnum(III) ion, Cr3+

—08l

1'74 —101

0•76 —1•91

051

—098

—083 —061 —042

of

SO4ion-pair

20 15

100

25 50 75

0

25

1 = 0068 (LiCIO4); extrapolationfrom results at 46—95°

—

84•8 94•6 15

of Cr3; corrected for Cr3

(LiC!O4); from variation pK for hydrolysis of Cr3; I =of0068 of apparent stability constant CrNCS2 with pH of CrNCS2 with pH

pK for hydrolysis of Cr3; I = 05 (NaNO3) pK for hydrolysis of Cr3; I 0

pK for hydrolysis of Cr3

I=0

00014 — 004; extrapolatedto

462 636 737

formation;

hydrolysis

I

pK

6_o for

pK for hydrolysis of Cr3;

S43a, S66, Tila, T12

The equilibrium constant for Cr2072 + H20 2HCrOr is 00265 at 200 and 0O303 at 25° Othermeasurements:B24, B100, H78,Jia, JO, MiS, S7, S41,

=

pitT1

varies with the proton source because of the formation species such as HCrO3C1and HCrO3(OSO3H) I 10; in MC! solutions, correcting for the formation of CrO3C!

In HC1 solutions, using H_ scale In HNO3solutions, using H0 scale In H3P04 solutions, using H0 scale In HCIO4 solutions,using H_ scale

In H2S04 solutions, using H_ scale

In HCJO4 solutions

KIN

E3bg

Cl

Cl 05

E3ag

06

B94

JiS

B53

P36

P36

Tl9

H4l

D13

H12

L14

B5

05 06 06 06 06 06

c= 25 x lO5M

Ti lb

06

I

Concentration constants corrected for formation of CrO3CI; = 1(LiCIO4, LiCI, HC1O4, HG!)

25

25

25

25 25 25

25

15 25 35 25 25 25

cc

Cul

555

410 396

.

25 18

797

Cu2

282

236

18•5

125

25 35 45 30 100

15

25

25

20

T(°C)

80

31. (Aquo) Copper(II) ion,

1•71

178

210 198

30. (Aquo) Cobalt(III) ion, Co3'

89 87

9•50

985 962

9•96

29. (Aquo) Cobalt(II) ion, Co2

—'56

41

Name, Formula and pK value

to 04

I=

I=

I

The pK for Cu2 is not known; hydrolysis of Cu2 gives almost entirely polynuclear complexes of the type, Cufl(OH)2fl_22+; formation constants for Cuz(0H)s2 from 15—42° are given. pK for Cu2 CuOH + H; = 3(NaClO4): the major species formed is Cus(OH)22+, with — log K = 106 pK for Cu24 Cu0H + H+; the major species formed is Cu2 (011)22+,with — log K 10•89 Hydrolysis of Cu2 gives Cu2(OH)s2, with — log K at 25° ranging from 105 to 109

trations and low aciditiesfavour formation of polynuclear species

I = 1(NaCIO4)

The above values are uncertain because high cobaltic concen-

pK for hydrolysis of Co3;

Other measurements:A7, D23, G12, P31

pK for hydrolysis of Co2; I = 0l(KC1) pK for hydrolysis of Co2

pK for hydrolysis of Co2 at I = 025 and 075 (NaC1O4)

Other measurements:B54, C15, D23, L4

Successive pK values for hydrolysis of Cr3; 01 (NaC1O4); rapid-flow measurements Successive "practical" pK valuesfor hydrolysisofCr3; 004

Remarks

29—36

E3bg

E3bg

06

KIN

E3bg

E3bg

05

E3ag

E3ag

114

P15

B33

P19

S80

S79

K68

C12

B64

E18

S30

Methods Reference

Nos.

25

3.47

612 752

58 25

25

20

+H

+ 50H

I

1

I

+

14H-1H2V1002843(NaCIO4) 1 (NaCIO4); 0025 — 01 M in vatiadate

8H20

I

I

-

S32

C17

R32

S5

M60

J4

CS

Jil

M3

Elch

C32a, C34a

CRYOSC N13

05

05 E E

E3ag

HV190255—

concentrations pKs, pl(6;— I = l(NaCIO4); total vanadium 2 >< 10 2 >< 10 t; also log K — 675 for l0VO +

+ 3H20

E3ag

I = 02;

also log K = — 750 for 10VO2 + 8H20 14H; and log K = 235 for 25 V4O12

pK5;

-

E3ag

1=0 Othermeasurements:A19, B67a, T4

E3ag

E3ag

SOLY SOLY

I varied from 006 to 0.2; ionic strength correction doubtful; extrapolated to zero time

Corrected to I = 0 by extended Debye-Huckel equation; extrapolated to zero time to allow for decomposition

l(NaCIO4); rapid titration = 01(NMe4CI); 445 20 rapid-reaction studies; complex formation occurs with alkali cations 219 33 Saturated Na2SO4 solution; up to 01 M Na3VO4 solutions; also log K 24 for H2V100284 + 14111- l0VO2 + 8H20 Other measurements:C16 35. Deuterium chloride, DC1 For Hammett acidity function in D20, see H63 36. Deuterium oxide, D20 15526 10 Molal scale; extrapolated to = 0 l5l36 20 14955 25

370

35

3'O

34. Decavanadic acid, H6V19028 365

HCuO2

pKfor Cu(OH)2 sHCuOs + H-1Other measurements: A5, C12, C36, D8, F35, K5, K39, Q3

H

Prediction of pK for Cu(OFT)2 + Cu022 pK for HCuO2

33. Decabydrodecaboricacid, H2B10H1, For acidity function, see M50

18

45

10 18 25 35

0

25 25

354

348

3.37

376 364 357 346

32. Cyanic acid, HCNO

153