Activity Coefficients of Ions in Aqveotts Solutions

8/3/2019 Activity Coefficients of Ions in Aqveotts Solutions

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Sept., 1937 A C T I V I T Y COEFFICIENTS O F I O N S I N AQvEOtTS S O L U T I O N S

Individual Activity Coefficients of Ions in Aqueous Solutions

BY JACOB K I E L L A N D ~

1675

Lewis and Randall2 in 1923 published a table of

26 individual ionic act ivi ty coefficients, which hassubsequently been of frequent use to chemists.The authors emphasized, however, that the pre-sented values should be regarded as preliminaryvalues only. In 1927 Redlich3 reprinted the sametable, and no corrections were made even byJellinek4 in his comprehensive textbook of 1930.

It has been pointed ou t5 th at the concept ofindividual activity coefficients cannot be definedaccurately, and such coefficients may not even bedetermined experimentally without some sup-plementary definition of non-thermodynamic na-ture. But the concept may not the less be, andhas often been, quite u ~ e f u l , ~ ~ ~ hen estimatingmean ionic activity coefficients in cases wheregreat accuracy is not claimed.

I t is th e purpose of the present paper to presenta revised and extended table of ionic activitycoefficients, which has largely been computed byindependent means, taking into consideration thediameter of th e hydrated ions,* as estimated byvarious methods.

For sufficiently dilute solutions one may use thewell-known Debye-Hiickel formula (aqueous so-lution at 25)

wherefi denotes the rat ionalIg nd yi the practicalactivity coefficient of the ith ion with valence q,

and I s the ionic concentration given by

with ci in moles per liter.i = l

It has been shown recently by BriillO that ai(1 ) Research chemist, Norsk Hydro-Elektrisk Kvaelstofaktiesel-

skab.(2) G . N. Lewis and M. Randall, Thermodynamics, McCraw-

Hill Book Co., Inc., New York, 1923.(3) G. N. Lewis and M. Randall, Thermodynamik, translated

and with supplementary notes by 0 . Redlich, Verlag von J. Springer,Wien, 1927.

(4) K . Jellinek, Lehrbuch der physikalischen Chemie, Vol. 111,Ferd. Enke, Stuttgart, 1930.

( 5 ) E. A. Guggenheim, J . Phys . Chem. , 3.3, 842 (1929).(6) E. A. Guggenheim and T. D. Schindler, i b id . , 38, 533 (1934).(7 ) G . Scatchard, Chem. R r o . , 19, 323 (1936).(8) The part of the eEect on ogfi, which is taken into account by

the increase nf ai caused by the hydrated water molectlles, is rathasmall in the case of some anions and a few cattons, but may be ofm o r e mportance in other cases-compare diameters of hydrated andnot hydrated ions in Table I.

(9) E. A. Guggenheim, P k l . Mag., 9, 588 (1935).(10) L. Briill, G a m . ch im. i f a l . ,64, 624 (1931).

may be regarded as the effective diameter of the

hydrated ion. The individual ai-values may nowbe approximately calculated by different methods-for example from the crysta l radius and de-formability, according to the following equationfor cations, given by Bonino

or from the ionic mobilities, using the well-knownequation

or its empirical modification, given by BriilllO

One can also determine the chemical hydrationnumber by th e entropy deficiency method ofUlich,*2 nd calculate ai from this and the effec-tive radius of t he ion.

Results

The diameters of a number of inorganic andorganic ions, hydrated to a quite different extent,have been calculated by these methods, and theresults are shown in Table I. Values of effectiveionic radii (ri) were taken from Grimm and

Wolff,13 deformability ai f ions from Born andHeisenberg* or calculated from th e ionic refrac-tion R by th e equation

lOZ4cr = 3 X loz4 I4irN = 0.395R (5 )

Erreras values for R being introduced.15 Ionicmobilities and entropies have been taken fromLandolt-Bornstein. l 6 Entropy and chemical hy-dration numbers of some gaseous anions were es-timated roughly by the author. The parametersof th e other anions, and of the organic ones, havebeen calculated from ionic mobilities only, and are

therefore not included in the table (they are,however, to be found in Table 11).

When computing the activity coefficients fromth e Debye-Hiickel formula, i t was decided to ar-range the various ions in groups according to th e

108aijzi = 0.9 108ri/1024ai+ 2 (2 )

lo8& = 182~i / l , ( 3 )

108ai = 216~/2/1, ( 4 )

(11) G . B. Bonino and G . Centola, M e m . Accad. Italio. 4, 445

(12) H. Ulich, Z . Elekluochem.. 36, 497 (1930); also J. Sielland,

(13) H. G . Grimm and H. Wolff, Z . phys ik . Chem. ,119, 254 (1926);

(14) M . Born and W . Heisenberg, ib id . , !U, 388 (1924).(15) J. Errera, Polarisation DiClectrique, Presses Univeis itaires,

Paris, 1928, p. 144.(16) From Landolt -Bdrstei n Physikalioch.chemiscba Tabellen ,

5. Aufl. I1 1 Erg. bd., Verlag von Springer, Berlin, 1936, and othersources.

(1933).

J. hem. Ed . , in press.

see also K. Fajans and K. . Herzfeld, Z . P h y s i k , 2, 309 (1920).


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1676 JACOB KIELLAND VOl. 59

TABLEPARAMETER0% AS ESTIMATEDY VARIOUS ETHODS

EBective Hydra-diam. of Bonino Ionic tion no. Rounded

unhy- formula mobilities and ef f. valuesIon dratedion (eq. 2) (eq. 4) radius (Table 11)L i t

N a +K'Rb +CS'

N HT1+

Bel +

Mg2 'Cas +

Sr2 +Bal+Ra2 'c u 2 +

Z n s tCd2

HgzPb2+Mu1

FezNi lCol +SnZ +

Ala

FeatCraLa'CeaPra +

Nda+sea+Sma +

ya+

Inat

Snd +Th4+

Ce4F -

CI -B r-1-clog-clod-NOa -BrOa-1 0 s -HCOa-

Ss -Coal-so,*c ~ 0 4 ~ -

Ag +

zr4 +

0.8

1.01.61.82.1

1.41. 50.6

.91.41.72.12. 3

1 . 1

1.4

1.51

1

1

1

0.8

. . .

. . .

. . .

. . .

. . .

. . .2.0. . ... .. . .1.4

1.61.4

2. 21.62.01.5

1.92.02.2

. . .

. . .

. . *

. . .

. . .

. . .

. I .

. . .2.2. . .. . .. . .

6.2

4.22. 82.452.35

2.152.35

. . .

. . .10

6.255.14.9. . .. . .6.055. 0

4. 94. 55.2

5. 6. . .

. . .

. . .

. . .

. . .

. . .7. 7. . .. . .. . .

10.8.. .8.158.95

12.510.311.51 1

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .. . .

. . .

. . .

(eq. 3)4.7

3.62.52.42.35

2.452.42.958.16.85

6.16.15.75.456. 56.86.75

5. 26.86.86.86.8

8.658.058.157.88.158.358.58.458. 3

. . .

. . .

. . .. . .

. . .

. . .

.. .

. . .3.32.42.32.42.852.72.553.254.454.1

4.253 .84.2

. . .

5.6

4.32.92.82. 82.92.93.456.85.85.155.154. 84.555.455.755.65

4.355.7

5.75. 75.7

6.0

5. 55. 65.45.65.755.85.85.7

. . .

. . .

. . .. . .

. . .

. . .

. . .

. . .3. 92.852.752. 83.353.15

3.03.855.254.85

5.054.555.0

. . .

5.3

4. 73.9. . .

. . .I . .

. . .4. 7

7. 06. 3

5.9

6 .8

6.86. 4

6.35.9

6.8

. . .

. . .

. . .

. . .

. . .

. . .6.2

> 8

> 8. . .. . .. . .. . .. . .. . .. . .I . .

. . .

. . .

. . .

. . .

. . .5. 33.93.62.93. 33. 5

3.13. 54. 87

5651/2s1/z

6

4-4.532.52.52.52.52.588

6555665

54.566666999999999

991 1

1 1

1 1

1 1

3.53333. 53.533.54-4.54-4.5

54.544. 5

parameters found above, and use rounded valuesof ai , as clearly stated in Table 11, where the re-sulting ac tivi ty coefficients are given. (Theparameters of hydrogen a nd hydroxyl were no tcalculated independently, but taken as 9 an d

Approximate Formulas

Guggenheim and Schindler6 have proposed th e

following formula for ionic ac tivi ty coefficients upto an ionic concentration of about r = 0.2

3.5 Hi.)

logf, = -0.5 ~ ? p ' / z / ( l + (6 )(7)

which equals -0.354 z y / z / ( i + 3.04 X 0.2325 T v 2 )

This equation is based on a parameter ai = 3 A.for all ionic species. Of t he about 130 ions ex-

amined by th e auth or, 20% have a diamete r of 2.5to 3.5 A., 40% 4 to 5 A., 25% 6 to 8 A., nd 15%9 to 11 A. The inorganic univalent ions are mostfrequently of t he order 3 to 4 A., the divalent ones4 to 6 8., he trivalent about 9 A. and the tetra-valent about 11 A., while the organic ions fallbetween 4.5 to 7 8. Hence, one may suggest thefollowing formulas, which in the case of univalentions give the same results as Guggenheim's, butwhich in the case of organic and polyvalent ionsgive distinctly higher values for th e ac tivi ty coef-

ficients.Inorganic ions" logfi = -0.5 z;pl/z/(l + z , p l / r ) (8)Organic ions logfi = -0.5 z;p%/(l + 2p1/2) (9)Such formulas as the following of Guggenheim6

- l o g f , = 0.5Z7p1/2/(l f p 1 l z ) + Z K B i k C k (10)or th at of Briilll*

-logfi = 0 .358~ ; r~ / z / ( l+ 10*a,0.2325rVz) +

may be more accurate in the more concentratedrange, but they contain additional constants,

which must be determined by the activity coef-ficient measurements themselves.

A ( W + Ph) (11)

Comparison with Experimen tal Values

The individual ionic activity coefficients com-puted in this paper with independently estimatedai-values (except in the case of H+), have beencompared with those obtained experimentally byHass an d Jellinek19 in t he case of C1-, Br-, I- ,S0-i and (COO)-:, and with those found byBjerrum and UnmackZ0 n the case of H f , PO-:and citratea-. In Fig. I we have plotted thesevalues, which agree fairly well with th e calculatedones (drawn lines).

(17) Except such complexes as the ferrocyanides, cobaltamminesand others which are to be treated as organic ions by the formula 9.

(18) L. Briill, Gazz. chim. ital. , 64, 261, 270 (1934).(19) K. ass and K. Jellinek, Z. hys ik . Chem. , A162, 53 (1932).

The activity coefficients of Soi l - were recalculated, using the morerecent value 0.614 for the normal potential of the mercurous sulf ateelectrode [Shrawder, Cowperthwaite and La Mer, THIS OURNAL,66, 2348 (1934)l together with the best value 0.222 for that of th esilver chloride electrode (ref. 16, p. 1855). When computing thesolubility product of silver oxalate, we extrapolated against the func-tion pl / l / ( l + 1.5fi1/2) H. nd J. used p1/2) , and found it to be 1.3.10-11 a t 25'. Hence, all activit y coefficients of oxalate anion (asfound by H. and J . ) , were multiplied by 1.2.

(20) N. Bjerrum and A. Unmack, K g l . Danskc Vidensk. Selskab,MaL-fys. M e d d . , 9, 1 (1929).


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Sept., 1937 ACTIVITYCOEFFICIENTSF IONS N AQTJEOUSOLUTIONS 1677

TABLE 1INDIVIDUAL CTIVITYCOEFFICIENTS F IONS N WATER

cis,cs= lParameter Total ionic concentration r =1oSai 0,001 0.002 0.005 0.01 0.02 0.05 0.1

Inorganic ions:H + 9 0.975 0.967 0.950 0.933 0.914 0.88 0.86Li + 6 .975 ,965 .948 .929 ,907 .87 ,835Rb+, S+, NH4+, T1+, Ag+ 2 . 5 .975 ,964 ,945 .924 ,898 .8 5 .8 0K+, C1-, Br-, I-, CN-, NOz-, NOS- 3 .975 ,964 .945 ,925 ,899 .85 ,805

0.2

0 .83.80.7 5.755

.76

.775

,355

.37

868 ,805 .744 .67 .555 . 465 .3 8

,905 ,870 ,809 ,749 ,675 .57 ,485aZ+, Cu2+, Zn2+, SnZ+, Mn2+, Fez+, Ni2+,

Mg*+, Be2+ 8 ,906 ,872 ,813 ,755 .69 ,595 .52co2 + ,405

.45

,095

.13

.18

,021,027,065,009

.796

.798

,802

.668

.670

.678

. a 2

,725

,731

.738

.57,575.588.4 3

.612

,620

,632

,425.43,455.28

.505

.52

.54

.31,315.35.18

,395

,415

,445

.2 0

.2 1,255,105

.2 5

.28

,325

.10

.105,155.045

.1 6

,195

,245

,048,055.10,020

,975.975

.975

,964,964

,964

,946,947

.947

,926,927

.928

,900,901

,902

,855,855

.86

.81,815

.82

.7 6

.77

,775

.964 ,947 .928 .904 .865 .83975 .79

.975 .965 ,948 .929 .go7 .8 7 ,835 .80

,965,966,867.868

,870

.975

.975

.903

.903

.905

,948.949.804.805

,809

,930,931,741,744

.749

,909,912,662.67

.675

,875 .845.85.4 5,465

,485

.81

.82

.36

.38

,405

,880.55,555

.5 7

[OOC CHz)sCOO ]'-, [OOC CH2)eCOO 1'- .906 .872 ,812 ,755 ,685 .58 .5 0 .425

5 .796 .728 .616 .5 1 .405 .27 .1 8 .115itratea-Congo red anion2-

As another test we have in Table 111 comparedthe experimentall6 mean act ivit y coefficients forsome strong electrolytes with those calculatedfrom individual coefficients. The last four col-

umns represent: (1) author's Table I1 (formula 1,with calculated ai-values) ; (2) author's approxi-mate formulas ; (3) Guggenheim's formula ; and(4) Lewis and Randall's old tables.


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1678 H. L. HALLER N D F. B. LAFORGE Vol. 59

0.2

k 0 . 4

I 0.6

0. 8

M

0.2 0.4 0.6 0.8

Fig. 1 -Individual act ivi ty coefficients of ions: drawnlines represent calculated values, with rounded ai - fig-ures given in Table I.

Square root of ionic strength, 4 ;.

TABLE 11

Mean ionic activitv coefficientIonicconcn.

Electrolyte rH I 0 . 0 1

. 0 2

.0 4

. I

. 2

HCI .0 1.02

.0 4

. 1

. 2HCI in LaCla .125

.1 5,175

NH4N03 . 0 2.0 4. 1

Gusgen- Lewis--

Exptl. I 1 formula formula table sTable Approx. heim Randal l

0.927 0 . 9 2 8 0,927,902 ,906 .9 0, 8 7 0 ,875 ,865.822 .8 3 .8 1.787 .79 .76

. Q 2 8 .Q28 ,927

.QO5 .QO6 . Q O

. 8 7 8 ,875 ,865

.831 .8 3 .8 1,799 .79 .76

,818 . 8 2 ,795,811 .81 .78.794 .8 0 .7 7

, 8 8 2 ,898 .90,84 0 .86: .87,783 .8 0 .8 1

0.927. Q O.865.8 1.76

,927I 90,865.8 1.7 6

,795.7 8.77

.9 0

.87

.8 1

0.95-9 2,895.86.815

.9 5

.92

.895,813.815

.85

.84, 8 2 5

. . .. . .

. . .

. 2

. 41 . 0

LiCiHiSOa 0.04.25

1. 0

HCOONa 0.004

. O l

.02

.04

.0 3

.0 6

. 3

ZnClr .0 1.0 3.1.17.5

.034

.066,118

,221KaFe(CN)s ,012

,024.0 6.12

LinSO4 .012

La(N0a)a .0145

,726.658.59

.877.782.703

,954

.Q31

.908.879

. 8 6 2

.SO8

.754,801

,857.778.660.609.51

.796

.720

.645

.570

,505,785.717.618.547

.7 5

.69,605

.88.785.7 1

,955

.927,901.87

.8 5

.7 8,725.57

.861

.7 8

.68

.6 3

.5 3

.785

.7 1

.645

.5Q

.525

.79

.72

.61

.52

.76

.70

.6 2

.875

.77,675

.953

,927.9 0,865

.855

.79

.7 3

.58

,865.7 Q.685. 6 3* 53

,785.7 1.645.5 9

.525.7 9.7 3.6 3.5 5

.76

.70- 6 2

.87

.74

. 6 2

.953

.927

. QO

.86,5

.85

.7 8

.7 1,525

.8 6

.7 8

.6 6.5 Q.465

,765.675.59.5 1

.4 2

.7 8

.7 1

. 60.5 1

. . .I. .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. 8 2

.7 5

.70

. . .

,845.7 7. 6 7.62

.79

. 7 2

.64

.57

.so

. 82

.7 6

.69

.62

. . .

Summary

Individual activity coefficients of 130 inorganicand organic ions in water a t concentrations up toI = 0.2 have been computed and tabulated;parameters ai were calculated by various methods.For approximative work, these individual figureshave been shown to give mean coefficients in suf-

ficient accordance with experimental values.PORSGRUNN, ORWAY RECEIVED OVEMBER 3, 1936

[CONTRIBUTION ROM TH E BUREAU F ENTOMOLOGY N D PLANT UARANTINE,NITEDSTATES EPARTMENTF AGRI-CULTURE ]

Constituents of Pyrethrum Flowers. IX. The Optical Rotation of Pyrethrolone andthe Partial Synthesis of Pyrethrins'

BY H. L. HALLER ND F. B. LAFORGE

Among the observations on the chemical andphysical properties of tet rahydropyrethrolone,we have previously reported its specific rotationas +11.9.2 This value agrees in magnitude butdiffers in sign from the one ( - 11.3') reported byStaudinger and Ruzicka3 for th e same compound.

The material on which their rotation is reportedwas prepared by hydrogenation of a pyrethro-lone preparation obtained from a mixture of th esemicarbazones of pyrethr ins I and I1 in whichthe relative proportions of each were unknown.

(1) For Article V I 11 of this series, see J. O rg . Chew , 2, 56 (1937).

(2 ) LaForge and Haller, T H I S JOURNAL, 68 , 1777 (1936).( 3 ) Stnud inge r a n d R u z i c k a , Rdo. C h i m . Ac ln , 7, 2 12 (1024) .

Since the rotation reported by us was also ob-served on material originating from a mixtureof bo th pyrethrins, th e discrepancy between ourvalue and that reported by Staudinger andRuzicka might be explained with the assump-tion that the pyrethrolone present in pyrethrinI differed optically from the one in pyrethrin 11.

We have previously described a method4 bywhich pyrethrin concentrates may be separatedinto fractions in each of which one of th e pyre-thrins predominates. From a fraction in whichpyrethrin I predominates its semicarbazone may

(4 ) 1,aForRe and Haller, THIS OURNAL, 7, 1893 (1936).

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Activity Coefficients of Ions in Aqveotts Solutions