Volumetric properties of aqueous alkali halides and ionic hydration

Jownal of Mokcdar Liquids, 49 (1991) 209-223 Elmwier Science Publishers B-V., Amsterdam

Volmuetric c7_ Onori,

properties A_ Snntmcci

lXpart.imento

209

of aqueous

alkali

halides

and

ionic

hydration

amI F. Mnrchso~ti

di FisicR,

UCvmsi

t.A fli Perllgia

I-OG100 PmIlgiz3 (It+) (Received

12 February

1991)

Abstract

1. INTRODUCTION The lx-fqxt.im

of d?lect.rolytc?s in aq~~~fms sollltions H owevcr,

H~WW af mricnce [l]_ Llie niolecrdr~r The

imt.lim

of

iiitmermAifm of ions with

Ir~drdiorr

ihdf,

they

niinil~ers

vary

prmessm

since

availaldle

to inclividiml with

of

wntm

th

is not. coiiipl~tdy

in m;n~y fdd-IiCt.11re~

rii~flerstm~fl_

flcscril~cfl iii t.m-mFi01 ion hydralion, ions

in the literat.iire,

as A nicamirc

121. The

at. mm time

as well

are lmsecl on different.

of t.lie ii~iiiil~cr of VEL~IIPSof the

wd.imat.ed

m the definit.ion

pictmrm

and

of the

of liydrzhon

underlying

moleciil,2l-

[2,3] _

The

di.srdution

of an electrolyte

solvent. and a &cream I.IIC water

nmlccdes_

hydrathn

mechnisnl.

h-ml conq~re~ihi1it.y afmune

int.cmct.ions

watt?r is ohm

intzmtct

thy

to the sc~arcc? knowledge

ion-wnt.cr

numnimx m-f+ afGgnec1

waker mdecules l~yclrathn

due

the

arc ol importmlc~

The

magnitude

Many &h.

Their

msnmpthm

is negligild~

[2,4].

has neither

0167-7822/91/$03&9

6

h-id,

apr)roacL

in fact, may vmy

of the ionic: rmlide M m-c rmxmt,ly,

tl~coretid

1991 -

cf~usm R volume

dile tm iiiterat&mr;

of t.hesie changes

m~thors

that0 the coniprehl~i1it.y

nmlecules

in water

of it.s conipremildit.y,

it, hm

nor experimental

contrmticn

lsehveen

CAII be IW& t.0 extrmd

from

to qlmntify

hydrat.ion

OII~ mother,

lmt

mid the mlevmlto llydndefl hen

pinLed

jnr;t.ificathn

of the

the ions mid

out

the

ntuidsem t.lley dl water

tlmt fmdi ali

[5,6].

Elmvier Science Publishers B.V. All rights maewed

210

The

volnme

contmctinn,

too, 11ns hen

of the hydmtioii

inecl~anisni.

largely

the relevant

unknown,

Aotit

the effective

voltmie

eZect~n.~i~icfiorr [2,7].

However,

propphies

Most

of the salvatd

Therefore,

of the me~urements

rc.~tdts ohtainerl law_

I.0 the tcnlperat.ure [S-11] pilldished aqueous mnge.

electrolyte

in the hydratinn idependent..

water

per mole

of salt,

with

is a rlecre~ing

the i&9,

EXPE~NTAL Ultrasonic

contml

Tbe velocity fdutions

developed

velocities

intemctionw,

within

reprodticilde

d.ial~atic

inft~rniation tempcmtiire

intemctinns is ftirly

existing

tenipemhure

to estimate

the values

of water

and sdt. concentmtions.

of

0f

vohne,

in liydmtion In particular,

function

of salt concentration.

by Gurney

This

1121, of 43.11increz4ing

result.

overlap

of

wi t.li the sd t concent.mt.ion.

emphyed

Nnaonic

Corporation

less tlizui O.lOC with ahdate

compre=ihili

~llrl the density

with standard

of papers

the ionic intrinsic

the density

and

conipr~ud~i1it.y

in a suitaIde

we succeeded and

mnge

tlint important

wah=

and the

the Debye-Hiidd

Iii a series

the diahtic

were tiied3sured by means

AvRilalde from

7I, were

from

concentmtions

quanti th4_ shown

conditions

SET-UP

wr3s accnmte

velocity,

for

nunil~er, defined as the niinil~er of iiiole~s of hydmtion

wxt.er layers (or shells)

velocimeter

ion-water

wi tli tenipemti~re

that the hydmtioti

have been performed

a5 an effect of strong

ni1nil~en3, the conipreAl~i1it.y

is consistent hydrated

of the involved

ly

the

of devidions

to the intermediate

the l~asis of our analysis czitsed

ty and

regzhding

in isothennnl

the conipressil~~ility of hyt‘lmtion

shells and their vtiat~ion we showed

in tenus

paid

we ;IRsnmed that,

contraction

the liyrlmtion

hypotheses

soli~tiont3 KS a fimct,ion of tempemtiire

shell,

On

t,he volume

za < 0.01)

can he inferred hy nie~tlring

In this contest

is

of the sfllvent

l~ot.11 the compressildi

in the litemtnre

over the pact. few years we hve

t-111the ion liydmtioii

2,

discussed

dependence

water

n~mnptions

sphere_

molar fmctinn

JU-~ often

of the l~ydmtion

the magnitiide

to interpret

investigstion

lmrler various

we need additional

reported

Lit.tle zd.t.ention has hen

the state extracted

ions and

in order

of the Iiyclmtinn

very dilute soliit.ions (sdt

since

data have hen

r1ensit.y data iii terms of ion liydmtion, pliysicd

used in the experin~ental

in the our experiments

accuracy

p, through

ring-arotiiid

The

tempemtnre of the soiind

of fO.17n -9-l_ fmrn

the values

the relation

were prepared

the pre=nt

6080).

the nie~nrements

ty j3 was c.Ictdat,erl

of the solution,

purity_ Thronghold

and

of a coniniercial

(mod.

of the sound

/3 =

by weighting

report water is denoted

l/u’p.

The

compoimrls

as component

211

3. TEMl?EFLA?lXJlXE COMPRESSIBILITY

DEPENDENCE

Here I?1 and i&, c1cnot.e t.h hyd

rrr;pect.ively, wliererrs x1

volume 1%

t.h

molar

tBlieprcfmire

AND

of’ one mole: of free water aml of l~ydrated

On t.aking the derivat.ivr! ol q.(l) enkropy, and neglecting

OF DENSITY

fraction

salt,

of water in the liyclrat,ion region.

wit.11 rcspcct. t-0 th presfmr~ p, at. constmit, , one cd~tains the following clcpenclcnce of x1hard

r&&on

w of dir? climmlved milt. Fhm

6x-p. (1) mC1 (3) it. fdlows

inm~ediakly

6-4

212 am1

(7) where

-

-063 -080

Figure

1. @(cm5

dyne-t moi-t) vs

T (“C) for NaCl

acqueous

different v8h~s

of x2.

Table

SoWions

Figure 2.4pp (cm3 mat-1) vs P,v, 8t

(cm5 dyne-t mol-t) solutions with different %wf

concentrations.

1.

Parameters of the hydration spheres (at 2YC)

as a function of the Pauling ionic

radius.

Salt -~ LiCI

Rclauon

Ranion

A

A

%

lot’P*h

Q

to’?&

Cl

cmaync-’

cm3ffloI-1

cmldyne-*

czr&rt~l-~

0.60

1.81

17.7

3.58

17.83

-3.1

22.24

NaCl

0.95

1.81

21.0

3.49

17.76

-3.3

24.26

KCL

1.33

1.81

18.9

3.52

17.73

-1.4

34.43

CkCl

1.69

1.81

18.0

3-60

17.77

-0.5

45.95

NaBr

0.95

1.95

20.5

3.55

17.75

-1.2

31.08

Lit

0.60

2.16

18.7

3.74

17.94

1.2

Nd

0.9s

2.16

22.3

3.71

17.8 I

0

42.47

KI

x.33

2.16

13.8

3.8t

17.80

0

51,44-

38.46

214 1,) figure 2 shows (5,3O”C)

sotutinns

for N&t

pressildity satiition

This

the quantity

~JB as a function ranging

according

we expect

can

t.emperdure

range con~irtered.

increases

further

a minimum

he neglected

from q.(7)

65°C.

That

alkali hdides

has heen points

for the atkdi

hydrated

by tinesu- fitting Gurney’~

a &creMe

examined

at various 3)

(fig.

proposed

by Gurney

wa t.eX layem increases hydrat,ion nmnber

the data in figure

mdel,

i8 the

the enhanced

of the qilailtit.y I&_

VOtlllllf? OcCIitk't

by

temperature

salt molar with

eq.(ll)

with respect

of S, we ohfain

the equat.ion

[12], according

~Vt~m?

fllj, mwt

ioli volume, flhvh

7~3 s

prodilced

fl2h JUe

respedvety. red.

on

th?

=

khhh,

straight

tilles (fig.4).

by eq_ (12) with fj2hVzh aid

3. spheres

wouIrl

i~li

-

s

(11)

Of Fiatt in the

fXdllkkIi

exctlldillg

region_

the pressure dependence

w Water

it. wa

mid

fomirl that

experimentd

independent

the

Differ-

,&vl,,

studied The

t.he

for zero salt,

Vlh

IllOte

/&hVlh

The This

to whidl

So ext.rapotabed

of the tlydratiOll

COlq~rCSitdi~

In at1 the cse,r,

~2. X2.

concentration.

overlap of the hydration

-i-

By

have been

fractions

wi t.h the fdt

to the pressure and neglecting

fihv,

range_

increAsing

Iii fact, Vh can l,e exprP*ed

One

exhibits

of @p for some

hydrat.ion shell and VI,, is the molar vohm~e of water in the hydration entiating

of

N 0.11 in the

of S and ljhvh

decrease

-

V2h

comof the

dependence

[Afllvl

investigation

our

the values

v, = V2h + s Where

of &VI

to t.he (5,30°C)

e+(7),

oldained

In tatde 1 we also report t.he limiting

determine

apparent

fact. that. the water compressit~itity

limited

with the model

inmlt~er of overlapping

Fbllowing

molar

t.he tempemture

might he no longer t.he case FLSt-he temperature

with

halides

IjrhVh thus

result is consixt.cnt

concentration

lud

the temperature

to that

Bertring this in mind,

t.he experimentnl of S and

when

with respect

c11le to the welt-known

at. aronnd

determined vatliss

u~t_ The

interval

to the linear law

is the hehaviour

aqueous

from 4 to 18%

in the temperatlrre

‘98 tnrnx ant to ctepslld on t;he concent.ration

S and ljhv,

fitting

of fllvl

vatnes

the

tlyctKih?d

the values are closely

of re-

of die salt, concentration.

216

S

S

22 20 18 16

_

i

Nal

14

NaBr ~. NaCl

0

0.04 X2

0.02

_c;E,-

l

10

.

-

1

.

.

0.06

_

.

_

.

0.08

-

KCI

12

14

16

S

18

20

22

21% Fitting

of oar data for cJn& according

and slopes

coIlectd

in tdde

to eq_(12),

1. Expression

(11)

yidds

the v&us

for the int.ercepts

for vj, cond-hd

with

e+(G)

ImcIs

[7j, in terms

of the

to

Here,

the ionic

apparent

mlhtract.ed

ionic

ion-solvent

interaction

Figure The

eq_(13)

with

temperature. sidts.

The

NaCl tml-es.

I”““““’

20-

16-

vohne

vg,,

points

Fllld

(V,

Andogom valae~

is expressed,

as nmd

dlowmulce for the vdmne

contraction

amset

by

(e~ectmtriclion)_ soInt.iona as a fnnct~ion of S at 10,20,25

are closely

the ruune intercept

the expe_rinienta.l Fignre

molar

to make

5 slmws @v for N&I

experimentd

s1t-q~~ and

volume

-

on the GV

1~eImviom-s have - vlh)

&I ta wit.Ji eq.(13)

soI~d.ions at, different.

axis.

independent0

i&h)

of vzr, and (VI

5. @V (nn3moZ-‘)

fit.terl by straight,

VR S for t.empera-

heen

Such A hehvior of X2, And vph ol~erved

f or smne dkdi

are &o

lines with

reported

and 3OOC.

slight.Iy

different

ifi predict.ecl

i~ldep?lid#?Ii~

Of

by the

for so11h-n~~ of different. Imlide~

in talde

1.

obtained

by fitding

217

On the h&s contraction drati&

af our analysis

nilmher,

their vrrridona all ddoricles

and iodide

and dear&y

investigated

volume,

of w;rtPx in hydrAian

show a consistent

now a few important

l),

It f&odd

pttern

the hy-

shells zxncl

he noticed

thlit

for the above qimnti-

with the only exception

of lithium

remarks:

for So are close to, hot. higher

immlxx-.

iiidic~txs

of the volmne

vdiiefi

to hehave ~~~omdody.

1) the vahies obtained coordination

the

the ionic intrinsic

And Ralt concentrations_

of the crrtionic racliils (tdde

halides which app,ex We m&e

interactian,

the comprtibili~y with temperature

t.ief-i as a fimction

imml~er

we lxsve tlmfz efdimated

CXLWXXIhy the ion-water

Iii this reqlect.,

it dioitld

the mimnl,er of wat.er molecdes

than the corresponding

he noted &redly

that

t.0t.d

the coordination

hoiincl to a.n electxolyte

ion, while, in oiu case, So accxnint.fi for all of the water moleciilcsR whose &xsity compressihi1it.y 2) otu values water

sue dfect.ed

advocded

by the presence of the ion ill];

for (31h are not. negligilde

at 25°C

is 4.477

and

10-11c7r~2

by several aiithors

wit.11 refqect,

dune-’

)_

This

to fl1 (the

result

that the compressibility

compresil~ility

disproves

of

the xxnmption

of water in primary

hydrat.ion

is zero; 3) mruly investigrrtorsi tried t.0 e5timd.e water elect.rostriction l?l - Vlh do indirsta, I.llti

any Itwddde

4) our vdnes with

volume s&on,

[7]_

in whidl

with

In fact,

Va, smrl the cxtioii,

(L=

t.lie difference for anions

fimdler

and

1.46 f

0.02 This

inchiding

space

is related

in agreement,

aroiinrl

not. only

the. crptd

the ion.

t.0 tlie cry&d

ionic

ionic

Such 8 vollune vohime

of the

V, by the linear fitdrip: Izxw (fig_ G)

am-l

c =

yidcls the anionic and cationic

1.8 f

11.2, sepratdy.

lset,ween ion cavit.y and crystal

[19,20]_

ionic voliinies

V2h c~ii he clefincd as t.lir: vczliime of the

for the dcd

the ionic radiiis

The her=&fit. of our data with cq_(l4) fraction

clrtt.zbfor

hiit, nre significxmtly

cnntrxtion,

the ion is coiit.ained,

hiit x&o A correction

increxscs

R vdnmr:

diie to

ef3timnt.e;

predictions

czviby

contrxtion

of hypot.hefzes [73_ 0 ur experimental

II ninnlxr

TtRexptxted,

the volimle

for Vzh xue gresder than the relevant, cry&d

previons

qdierirxd

mxler

t.lie0retidly

intrinsic volnme

It. liafa been pointed

oiit. that

ionic rxGliiis is greater for czt.ioilF; tllAl1

rctnark is conrristent. with onr redts,

being

c larger t.han CL

4.

CONCENTRA’I’ION

DEPENDENCE

OF

DENSITY

AND

coMPFuzssII3ILrrY The

knowledge

pressi1dit.y information that

of the ternperat.111~ dependence

of dectrdyte makes br

acmunt.

Lhe solut.ion.

sohttions

a conpirison

the effect

Fbcently

z&t+

possible

with die predictions

of concent.rat.ion

on the

[13] we t.ried to cletemline

throngh a ainqde model

based on Gurney’s

their increasing

wit.11 salt, cmicentration.

overlap

It was assiimd conlpasses

wit.11 density

11yclration shell of a cat.ion ant1 an anion, belong

toyof cn-sphere

ta different. c~spheres

the con1-

of molecular

cpant~it.atively

at. the center

inorlels

respe1:tiveIy,

at. the sanle tbne.

of

silch a dependence

of a co-sphere

and coniprf?siI~ility

to overlap,

New

clmisity and comprezd~ility

shells and

which en-

essent.idly

dilFere11t

and SC clcnote the mnnl~er of water ~nolecd~s

lronl those of the h11lk_ Let. S$ nccount.ed for the posrddi

and

~nechanism_

idea 1121 of wat.er coor&nat.ion

t.hat esrch ion is plural

all water molecules

of the density

light on the hydration

with So =

So+ + S;.

in the It, was

too, since a water niolec11le inny As a

co~~scc~~le~~cc,

hyclrat.inn

the

1111nll~erS is hllidler

than So ancl te1irli=it.0 So for vanifihi11gly x1nall vall1es of t.he .sdt.

concent.r&on.

clependence

The

of the overlap

Llle fdt, concent~r~t.ion is expct.cclly fdidi a dependence On adding

111echanisn1 and,

very coinplic~tcfl.

iincler sonif? sinqdifying

of S on

We cM.in1nterl q11ant.it31tsively

11ypothes~_

fZ7rz nlolcs of FULLY. t.cra I;olut.ion containing

al which sit in Lhe frm wder

therefore,

7~1 molts

free of water (7~~

region) and 712 moles of salt., 1,ot.h water 1iiolt3-3~1~ aid

ions (niost.ly wit.h 0pposit.e i+p)

tna_v happen

to lie in t.hc co-siph&-e of the .aclclerlions_

On neglect.ing the lat.t.er effect in view cJf the i1iccpdit.y 712 < 7~1, a fraczt.ion of the SIJrlr2.2mole5 of water nlol~~hs fcJnni11g 1.1~ co-sphcrcs of Lllc ~1712 n&let1 sdt. n1olcs (*onle from t.he free water region, 011 assi1niiii~

that

free mid

while t.hr?rciiininrler conlcs Cm111t.lic hydrat.ion

hatit1cl wat.er nic~lm:~~lr,s

moles of nrldecl salt. wit.11 equal pr~JlJaldit._v, if. follows

eiiI.cr t.11e co-fqdicres t.lJ;rt,

fret = -11.1 /rcc --d7r. so cl7r:! 711

one_

of die rl71.2

Table 2,

for the calculation solutions from eq_(18).

Parameters

of the compressibility

of aqueous NaCl

1ol’P,ylh

101lpai?m

cm5 dyne-1 ~1-1

cx-& dyne-’

%l

10

17.ofo.6

56Itl

-65zt8

15

17.3fo.9

57It2

-70&l 0

20

16.5fo.7

56&l

-633

25

15.8~.6

55fl

-55f8

30

16.1zI10.7

56kl

-59&S

mol-1

Table 3_ Parameters for the calculation of the mean molar volume of some aqueous alkali halide solutions from eq_(17)_

L

Salt

cm3

SO mol-*

SD”

Ref.

wm --

Licl

25

17_909ztO_OO8

21.68zto.08

24.8ko.9

7

23

l-cl

20

17_892-+0.002

21.6ofo.01

26.2M.4

20

22

NaCl

20

17.69ztO.01

24.07M.09

19.2*0_5

25

22

Nail

5

17.68M.0

22.9&o. 1

24.7zt0.6

10

23

NaCl

25

17.8ktO.02

23.41tO.2

23fl

10

23

NaCl

15

17.64fo.01

24.lfo.l

19.3ztO.4

15

24

NaCl

30

17.84ztO.01

23.5A0.1

22.8f0.9

10

24

KC1

25

17.87&0.01

33_3fo.

28fl

7

23

KCl

20

17_82+0_01

33.3&O. 1

27&l

25

22

CsCl

20

17.73fo.02

46Sfo.

2x1

250

22

NaBr

20

17_767fo.O07

19.52kO.06

20.4fo.4

25

22

KBr

23

17.77fo.02

4o.tktO. 1

21fl

60

22

a fit standard

deviation

1

1 1

-71’ 0

’ ’ ’ ’ 1 ’ 1 ’ 1 0.02 o.cN3 0.08 0.04 0.1 %

Figure 7. Maxn nm1a.r volura~~ v and resihals Av (cnr%u~Z-~) 7~13 N&l molar fraction ~:a_ Experimenhl data from ref. 24 (dolx) are fitted (solid line) by memls of eq.(1‘7). Av is the difference hetweem experimedxd data am1 theoretical prediction.

loo

’

I

=

I

m

,

’

,

loo-

-

I

,

,

-

--

*

1

m

*0

1

0.02

.

”

0.04

11 0.06

1

0.08

n

/W and resichmh A@

Expes-imental data from ref.

(cn~~rl?/r~e-~

-mO

7nfLl)

21 (clots) are fittd

is the clifferenm between experinmhd

1

.

0.02

I

I

0.04

x2

Figure 8.

,

-

f - I

0.1

I

.

+o- - . .

55’

,

o_-

:

z=

A/3v

I

.

50: I)

I

71s

N&l

I

*

. I,

0.06 x2

I

0.08

m-

0.1

molar fraction 3;~.

(solid line) lsy meam of eq.(lS).

data and theoretical prediiction.

Beiug

x1

fret

*yd, on tmhstitnting

=21-x:1

IIRe of eqrx(ll)

and (12),

/w=xl

we 0lkGn

eq_(lG)

e

Eqna tions (17)

into eqs_(l),

the following

fllh&h

+x1

and (l&) give the concentration respectively,

of a fdt

can he ;serl

to evalurrte

These SO, Vlh, &,,&,V&,

equations

We have verified

that eqQl7)

ad

volved parametelw 3 within

&h&h

sodium

the experimental

chloride

The

dependence

with

Of *Pg (tde

crystd

and c the

1.36 f

5.

fit

of the parameters

of the experimenti

with those ohtinecl

or difference

so, &h,

mle

i&,

&la

of section

dts

up to the

the remilk of mud1

[21] properties

between

The

&h,&$h

VFdli~

of the anion,

for v&

0.01

data.

with redifd.ic values of the in-

and compre.ssil~ility

clistrilmted.

thoRe ol>t.Gned

ionic volmne tile data

wd

of the meml molar

of qiieous

the exp~ximental

stxu-darcl deviation

and

is dwrrys

of the measuremenk

1).

e!cl_(14)_ Fitting wlhe

sqima

(18)

at fixed temperrrtm-e and

for a nnml~er of uni-univdent

randomly

of the pRlXmetelX

agreement

fi2h%h

the values

implemented

The residual,

appear

Vdllt?fi

solution

[13-151 and conipressil~ili~.y

wi & the accm-aq

good

Pading

solntinns.

vdnes,

conqxxrahle

fairly

xcnracy

+ t2h

In talde 2 and figures 7 and 8 we display

of the vohimetric

calculated

a kad

113,211, rep ro d iice the density

sat.m-at.ion concentration. an andysis

~hmllgh

end (18),

for P, Illlcl jY3

dependence

\*olunie and comprefiddity, p-f2SSlWC?.

(2) ELU~(8) and making

expressions

in section

the andysis

2) me ill

(t.ddft

of the temperdure

foiind here are liliW%rly rdatd Va, and of the czdkm,

reported

and 2.2 f

Itlld /&f,v'h

from

in tdde

v=, according

2 with thrrt equation

O-2, respectively,

w1lid1

to the

yields

c0111pare

to

for n

I-f!i%SOllddJ'

3.

CONCLUSIONS The

present

compresfddity

repor?

and density

dboiil. the struct~ixd The

ansdysk

118 to neglect flail

of electrolyte

interactions

the temperature temperzdme

soliitions

occurring

of the compresddity

in it sntitable

adequate

showR thrrt FTsimnkzmeons

data

depend6mce

xniong

provirks

of S and /?hv,

dependence

of both

interesting

the Rolnte and solvent

;t~ a function

range (5,30°C).

to rn~s=sure the temperdnre

investigation

of the with

aclial~atic

inform&on moleciiles.

temperature respect

AR FLconsequence,

to that

we think

of fl Itt 22 fixed rather

lesds of

more

than the

222 isothermal

dependence

the a..umpt.ion

j~~stdicxl than not.dJly,

the

corresponcling

fur the alkali

ldicles

llydrat.ion

mnnlm-,

The

hyyrhtion

ccntration. lmsed

af fl on XZ_ Tn our

This

intq~rr?tation

scht.ionx

yields

nmnlmr

salt. concentration.

Siidi

a niorlel

is meant

t.mly te solutiom

on the concentration. of

s&d

due tm th

approximath~ the main The

the cation

ion-ion

tliiis

long-range

Codo11~1~ forces,

impact. on the

volinnetric:

their

and

function

here,

of the salt conovdap

ilttenipt

nwdwmism

at t.he basis

niodel

of alkali

Moreover,

lea&

of the D&ye-Hiickel

pmpe!rt.ies of eltlectrolyte

acqueous

between pssilde

sat.isfacztorily

aqueous

IIR to co1~11de

of dec-

of the criide

rq~rodnces

halides

the

at singling

have heen negl:lectecl, t,oo. In spite that. om

nu~dc?l

with

that. no rlist~inction made.

the

nmmiing

and conil~resd~ility

IUW heen

data

like

of a simple

increasing rough

h4nst

density

pmuneters,

by mans

to 1~ a f&t

properties

arc lxttcr

intni tive pliysid

of the density

WC hiincl

hydration

and

the anion

intcracrtionfi vchmetric

~UCC~B of Gurney’s

Leir

We remark

mid

intrducccl,

experimental

with

sphermi

the &pndcnce

hydralion

watm

for the rdevant

ha. lmen intcrpreterl

of liyclr~ticm

amunlptions

in the literature.

hums out. to he FLdlecrewing resltlt

governing

hove

of tlille comlwmsil~ilit.y

mtimate~

which arc nmre consistent

on dir: existmim

th

/&, = 0 conn1~1n1y advocated

remarkalh

orit, the fmtom

opinion,

solutions_

that the ion-ion

theory,

have a minor

solritinns_

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