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Association constants of cadmium ion and chloride ion in concentrated aqueous solutions of ammonium nitrate
J. Inorg. Nucl. Chem., 1964,"Vol.26. pp. 811 to 820. PergamonPress Ltd. Printed in Northern Ireland
ASSOCIATION CONSTANTS OF CADMIUM ION AND CHLORIDE ION IN CONCENTRATED AQUEOUS SOLUTIONS OF AMMONIUM NITRATE* J. M. C. HESS, J. BRAUNSTEIN and H. BRAUNSTEIN Department of Chemistry, University of Maine, Orono, Maine
(Received 12 August 1963; in revised.form 28 October 1963) Abstract--Activity coefficients of cadmium nitrate and ammonium chloride were measured potentiometrically in a solvent consisting of 2 moles of water per mole of ammonium nitrate at 39.9 °, Thermodynamic consistency was demonstrated for data obtained with silver-silver chloride electrodes and with cadmium (amalgam) electrodes. Association constants for the formation of CdCI +, CdCI~ and Cd,,C1a+ were, in (moles/mole NH4NOa)-, 340 ~- 20, 75 ± 5 and 5 i 5 respectively. The concentration dependence of the activity coefficients was compared with calculations based on a quasi-lattice model of molten salt solutions.
As the water content of a concentrated aqueous electrolyte solution is reduced, its properties must eventually approach those of a molten salt. The interpretation of the thermodynamic behaviour of concentrated aqueous electrolyte solutions in terms of a quasi-crystalline structure has been suggested as an approach towards the explanation of the observed dependence of the logarithm of the activity coefficients of electrolytes in concentrated solutions on the cube root of the ionic strength.(1, 2) This paper describes measurements of association constants in concentrated aqueous electrolyte solutions, and is the first part of an investigation of the applicability of a quasi-lattice model(3,4,5) of molten salt solutions to concentrated aqueous salt solutions. The system investigated initially consisted of dilute solutions of cadmium ion and chloride ion in concentrated aqueous solutions (1 mole of NH4NO 3 per 2 moles of H~O, or about 11 molar) of ammonium nitrate at 39.9°C. The aqueous ammonium nitrate solution was considered as the solvent. Since relatively few data are available in such concentrated solutions, it was considered worthwhile to determine by independent measurements the activity coefficients of both solute components, cadmium nitrate and ammonium chloride, and to test the thermodynamic consistency of the data. Association constants of cadmium ion with chloride ion were calculated by a method which also has been used for molten salt solutions(6,7) and the concentration dependence of the activity coefficients were compared with calculations based on the quasi-lattice model.~3,4,5) * Based in part of dissertation submitted to the University of Maine by J. M. C. HESS in partial fulfillment of the requirements for the Ph.D. degree. ~1~ R. H. STOKES and R. A. ROBINSON, J. Amer. Chem. Soc. 70, 1870 (1948). ~2~ H. S. FRANK and P. T. THOMPSON, The Structure of Electrolytic Solutions, (Chap. 8. edited by W. J. HAMER), J. Wiley, New York (1959). ta~ M. BLANDER, J. Phys. Chem. 63, 1262 (1959). ~4~ M. BLANDER and J. BRAUNSTEIN, Ann. N. Y. Acad. Sci. 79, 839 (1960). (2) M. BLANDER, J. Chem. Phys. 34, 432 (1961), (6) j. BRAUNSTEIN, M. BLANDER and R. M. LINDGREN, J. Amer. CTtem. Soc, 84, 1529 (1962). (71 j. BRAUNSTFIN and R. M. LINDGRFN, J. Amer. Chem. Soc. 84, 1534 (19t+2). 1~)
811
812
J.M.C.
H r ~ , J. BaAtmSTraN and H. BRAUNSTEIN
EXPERIMENTAL The cell Electromotive force measurements were made of the two concentration ceils: Cd(Hg)
Cd(NOs)= NH~NOs HsO
Cd(NOa)= NH4CI NHaNOs H20
(Hg)Cd
I,
AgCI,Ag
I1.
and
Ag,AgCI
NH4CI NH~NOs
NH4CI Cd(NOs)= NH4NO3
H=O
H20
CONCENTRATION CELL WITH AMALGAM ELECTRODES PYREX ROD ;;7"~RECIPROCATING STIRRERS GROUNDGLASS CAPS
COPPER WIRE POTENTIOMETER
~
GLASS GUARDTUBE FOR LEADS
WIRE
ULTRA FINE FRITTED .PYREX DISK DILUTE CADMIUM
III ~ICURE1
FIo. 1.--Diagram of the Ceil'0) used to measure the activity coefficients of Cd(NOs)2. In the Cell (I1), for measuring the activity coefficients of NH4C1, the cadmium amalgam electrodes were replaced by silver-silver chloride electrodes. A diagram of the cell (1) is shown in Fig. 1. In cell II, silver-silver chloride electrodes were suspended in the arms of the cell in place of the platinum--cadmium amalgam electrodes. The outside of the cell was coated with a silicone varnish to minimize conduction through the glass walls of the cell. The cell was clamped in a water bath thermostatted to -4-0'02 ° at 39.9°C. The temperature was measured with a thermometer which has been calibrated against a thermometer certified to within 0-05 ° by the East German "Deutsches Amt ftir Mass und Gewicht." The solutions in the cell were stirred continuously with motor-driven vertical-reciprocating stirrers with a stroke of about 5 cm. Chemicals Reagent grade ammonium nitrate, ammonium chloride, cadmium nitrate tetrahydrate,and silver nitrate were used without further purification. Ordinary distilled water was used for the solutions
Association constants of cadmium ion and chloride ion
813
after degassing was shown to be unnecessary. Triple distilled mercury and Fisher Certified Cadmium were used to prepared the amalgam electrodes. The ammonium chloride was dried at ll0°C and pelletized to facilitate additions to the cell. Cadmium nitrate was added to the cell as an aqueous solution (filtered to remove traces of cadmium hydroxide) whose concentration was determined by evaporation and ignition of a weighed sample tS~ to cadmium oxide. The effect of the added water (about 0.5 ml) was shown to be negligible by experiments in which up to 1 ml of H20 were added to one arm of the cell with no change of e.m.f. greater than the normal variation of ±0.2 inV.
Preparation of electrodes Silver-silver chloride electrodes were prepared by a modification of the method of PURLEEand GRUNWALD.~a~ Platinum wires, with foils (about 5 mm squares) welded to the ends were sealed through soft glass tubes and, after cleaning with aqua regia, were silvered by the Rochelle salts silver mirror process ~I°~for about 45 rain in an ice-water bath. (The slower deposition of silver in the ice-bath appeared to give more uniform deposits and more stable electrodes.) The electrodes were stored under distilled water after rinsing with ammonia, and were chloridized anodically at a current density of 1 mA/cm2 in 0"05 M hydrochloric acid shortly before use in a cell. Pairs of electrodes which gave a difference of e.m.f, greater than 0-2 mV. When dipped in an HCI solution were discarded. Most of the pairs gave an e.m.f, less than 0-05 mV. During a run the positions of the electrodes in the cell were reversed occasionally and were discarded if the e.m.f. change was greater than 0'4 inV. With both electrodes in the same arm of the cell the e.m.f.was generally less than 0"15 mV. Thus, in the solutions in which measurements were made, the precision of the e.m.f, measurements was better than -I-0.2 mV.
Cadmium amalgam electrodes Stick cadmium was allowed to dissolve in mercury in a closed test tube at room temperature to form a saturated amalgam (about 7 per cent weight). The liquid phase of saturated amalgam was diluted tenfold with mercury and stored under a 40 per cent solution of ammonium nitrate. Samples of cadmium amalgam from the same container were used to form pools at the bottom of the half cells, as shown in Fig. 1. The amalgam and platinum leads were placed in a previously dried cell before adding the solutions to the cell to prevent contact of the wires with the solutions. RESULTS AND DISCUSSION T h e results of the m e a s u r e m e n t s of the electromotive force of the Cells I a n d I I at 39"93°C with a m m o n i u m nitrate solutions c o n t a i n i n g 2 moles of water per mole of a m m o n i u m nitrate are given in T a b l e 1. Since the c o n c e n t r a t i o n s of chloride ion a n d of c a d m i u m ion were less t h a n 0.01 mole per mole of a m m o n i u m nitrate it is reasonable to assume that the c u r r e n t is carried almost entirely b y the " s o l v e n t " ( a m m o n i u m nitrate i n water). The activity of a m m o n i u m nitrate a n d water is essentially the same in b o t h half cells. F r o m a consideration of the electrode reactions a n d the t r a n s p o r t processes, the free energy change per faraday for a n infinitesimal difference of concent r a t i o n of Cd(NOz)2 in the right a n d left h a n d cells is
--dE -----1(1 - - ted2+) d#cd2÷ - - tr,-H,+ d#~n,+ + ti~%- dl~o3- + tcl- d#cl-. The t are H i t t o r f transference n u m b e r s of the ions, relative to water, a n d the # are " i o n i c chemical p o t e n t i a l s " which, c o m b i n e d , give
- - d F = {(1 - - tca~+) d/*eOtNOa)a - - ( t ~ 4 + + tcl-) d/ZNH4NOa -~- tel- d/zNa,Cl. W. W. EWlNGand W. R. F. GOYER,d. Amer. Chem. Soe. 60, 2707 (1938). t,J E. L. PURLEEand E. GRUNWALD,J. Phys. Chem. 50, 1112 (1955). ~1o~Handbook of Chemistry and Physics, (33rd Ed. p. 2729. Chemical Rubber Publishing Co., Cleveland, Ohio (1951-52). ts~
814
J.M.C.
HESS, J. BRAUNSTEtN and H. BRAUNSTEIN
TABLE I.----CHANGE IN EblF IN THE CELL (I) X 10 3
RCalNoa~3
1.047
R~H4OI X
103
1 "963
--AEMF(mV) RNIt401 X 103
0.466 1-377 1.913 2.806 3.694 4.569 5.369 5"999
1.72 4'77 6"46 9"13 11"84 •4'26 16"45 18.16
0"877 2"010 2.826 3"637 4"391 5"351 6"240
--AEMF(mV)
0.567 1"260 1"816 2"682 3.549 4"290 4.888 5"645 6'220
3.951
2"978
1"45 3"25 4"77 7'03 9"15 11"05 12"57 14"17 15'63
R~ra4cl X 103
--AEMF(mV)
0"497 0"965 1"560 2' 179 3"085 3"954 4"780 4"939
1"13 2"22 3"64 5 "04 7"09 9'03 10"86 13"36 14'97
5'020 1.94 4"40 5"68 7.21 8'63 10"55 12"38
0.825 1.610 2"921 3'993 5"256 6"312 6.834
1'42 2"87 5"22 7"13 9"37 11"27 12"31
CHANGE OF EMIt OF THE CELL (II)
RNa~Cl × 10a 0"503 Rca~r~oal 2 × 103
0"640 1"771 2"865 3"843 6"077 8"418
1"037 AEMF(mV) 5"02 12'09 17 '60 21 "76 29"41 35"70
Rca~o3~ 2 × 103 0-916 1"1811 2"721 3"593 4"736 5-770
4"026 1.096 2.088 3"149 4"584 5"734
2.007 AEMF(mV) Roa~r,%~ 2 × 103 AEMF(mV) 6-56 11"91 16"52 20"34 24"74 28.14
0"793 1'958 2"823 3"706 4"548 5"581
6-028 6'18 11 '30 16"22 21 "97 25" 89
0"765 2"035 2"846 3"879 4"956 5"969
5-00 11.54 15' 83 19'70 22"98 26"50 7.997
3"99 10"33 13-96 18-23 22"26 25"66
0'686 1 "802 2"887 4"015 5' 128' 6"213
3'16 8"04 12'61 17"71 21.65 25"23
Association constants of cadmium ion and chloride ion
815
At the concentrations investigated, the current carried by Cd 2+ or C1- must be negligible compared with the current carried by NH4 + and NO3-, and the chemical poten1 tial of NH4NOz (and water) is virtually constant. Integration of dF = --~d#c,~(No3)2 and introducing activities leads to the equation for the e.m.f., within the approximations noted above, 2-303RT ac,,l~NO~)~ E -~-ff log a,ca(N%h, where aca(NOp 2 is the activity of cadmium nitrate and the prime refers to the reference (left) half cell. (Note that in the absence of NH4NO a and NH~C1 the expression for dF reduces to ½(1 -- tca~+) d/tca(yop~, which is the correct expression for the aqueous concentration cell with cadmium electrodes and different concentrations of Cd(NO3)2 in the two half cells. If the concentrations are expressed as the mole ratios, RCd(NO3)~ , the number of moles of cadmium nitrate per mole of ammonium nitrate, the activity coefficient of the component cadmium nitrate may be defined as 7cdINo~l~ = a~'o(N%),../ Rt, aiNop. ~1a,~2) This definition of the activity coefficient is chosen to simplify the numerical calculations. Its numerical value differs negligibly, in the concentration range investigated, from the value of the activity coefficient defined in terms of the ionic concentrations : t __
Y in which the N are the ion fractions i(:d~+
nCd2+
aCd(NOa)z
N(,d:+N~.o3_, RCd(NOa)2
nc~12+ + nNH4+ -- 1 + RNHaC 1 - - R(,O(N~)3)z
and NNoa --
nNo a-
1 -~- 2Rcd(NOa)2
~, 1.(lt,12 )
n N o 3- -~- nC1- - - 1 + 2Rcd(Nop 2 + RNtqCl
The R are the mole ratios (mole of solute per mole of NHaNOz). (It should be noted that the activity coefficients used throughout the paper are stoicheiometric activity coefficients and not single ion nor mean ionic activity coefficients.) The standard state is chosen such that the activity coefficient is unity at infinite dilution of cadmium nitrate and ammonium chloride in the solution of fixed concentration of ammonium
nitrate in water. In the absence of chloride ion from the Cell I, the e.m.f, of the Cell I followed the Nernst equation in the mole ratio of cadmium nitrate in the range 2 × 10-a -< Rcd(SO3)2 <~ 6 × 10-a to ±0-2 mV., indicating that the activity coefficient ofCd(NO3)," is constant (unity) in this range and that the liquid junction potential of the cell is negligible. The activity coefficient of cadmium nitrate in the presence of chloride ion, hence, is given by 1 2F log - = - AE (1) ~Ca(NOp~ 2"303RT where AE is the difference between the e.m.f, of the Cell I in the presence and in the absence of ammonium chloride from the right-hand half cell. ~al) M. BLANDER, F. F. BLANKENSHIP and R. F. NEWTON, J. Phys. Chem. 63, 1259 (1959). ~a2~j. BRAUNSTEIN and M. BLANDER, J. Phys. Chem. 64, 10 (1960).
816
J . M . C . HESS, J. BRAtmSTEINand H. BRAtmSXmS
Similarly, the activity coefficient of ammonium chloride may be calculated from the change of e.m.f, of the Cell II when cadmium nitrate is added to the right-hand half cell (originally containing no cadmium ion). 1 log - ?,~r4cI
F --
-
-
2"303RT
AE
(2)
In the absence of cadmium ion, the e.m.f, of (II) followed the Nernst equation in the mole ratio of ammonium chloride, R~u,c 1. The activity coefficient of ammonium 0.5
I
I
I
]
y
~
/1
0.4
0-3
3 --I~.
g
_J 0-2
0
IP"
I
2
I
i
3
4
I
I
5
6
7
Nc~ x l O -a FIG. 2.--Activity cocf~cients of cadmium nitrate in the presence of NH~CI at 39.9°C.
The circles are measured values and the vertical lines are calculated from the activity coefficients of NH4CI. The N are stoichiometric ion fractions, n0o 2+ Nod=+
nod= + n~a4+
/'/01and N c l -
no1- + n~%-"
chloride is defined as a~,cl/Rz~qc z and the standard state is chosen so that the activity coefficient is unity at infinite dilution of ammonium chloride (in the absence of cadmium ion) in the solvent ammonium nitrate-water. The activity coefficients of cadmium nitrate calculated from the data obtained with the Cell I are shown as the circles in Fig. 2. The activity coefficients of cadmium nitrate also could be calculated from the measurements with the Cell II by integration
Association constants of cadmium ion and chloride ion
817
of the thermodynamic relation ( -0 lOg Yca(-------~N °8)z)
OR3IH,Cl
--
" Red(NO.),
(alog
)
(3)
\' ~-~Cd('~Oa)~ / RNtt,Cl
Thus, log
dRNit4Cl
(4)
The differentiation and integration were performed graphically using slopes which were estimated from the tangents to plots of log 7~H4Cl (obtained from the measurements with the Cell II at various fixed concentrations of NH4C1 ) versus Rca(~o.). The activity coefficients obtained from (4) are shown in Fig. 2 as the vertical lines indicating the estimated uncertainty in the values obtained from the graphical differentiation and integration, Except at the lowest cadmium nitrate concentration, where the agreement of the data are within ~0.5 mV, the agreement is within the estimated experimental uncertainty of 4-0.2 mV* This agreement shows that the two independent sets of measurements are consistent. If the deviations from unity of the activity coefficients of cadmium nitrate and ammonium chloride are attributed to the possible formation of associated species CdC1+, CdC12, Cd~C1~+, etc., the activity coefficients may be written(6, 7) 1
l n - -
~"Cd(NOa)~
= K 1 R N a , c l ._}_ K I ( K ~ _ 1~K1)RsII~,C 2 1
(5)
4- Kx(2K12 -- K1)RNI~,ClRCa(~.o3), --}- . . . and
~NH4C1
-
1 + K1Rca(soo, + KtKI~R 2cd¢so.),
(6)
4- KI(2K~ -- K1)Rcat~,o.h Rr, g,Cl -~ . . .
where the K's are the association constants Rcdcl+ K1 --=-- Rcd~+Rc11(2 -=
Klz =
Reach Rcd ct÷R c l -
Rcaacl3+ RCdcI+ Rcd,+
etc. Equations (5) and (6) were used (rather than, for instance, the analogous equations for 1/TCatNO,)~ and In 1]?NH,Cl) because they lead to extrapolations having less curvature than extrapolations based on other forms of the series.(6,7) * Recent checking of the measurements indicates that the measured values of log 1/Tcatsos~ ~ at 10-3 probably were slightlyin error and that the values calculated from the measurements of cell II are correct.
Rca{r, os~ 8 = 1 x
818
J.M.C.
HESS, J. BARUNSTEINand H. BRAUNSTEIN
Using graphical methods described previously(6, 7) K1 was calculated from the relation K x ---- lim (0 In 1/TCd(N08h~ /¢Cd(NOs)2 ~ 0 RNH4C1~ 0
=
lim
0RNH, C1
] Red(N08 h
(0_ 1/~'Z~H,C,)
RCd(N0a)2 ~ 0 \0RCd(N0a)~ R~HiC 1~ 0
RNHiCI
K 2 and Klz were obtained graphically from the relations
K~(ZK2 --/(1) = 2KaK2 =
lira
K1(2K12--KI) 72K1KI~ =
0
[
lim
OR-~-cl
RNHaC1~ 0
F
RNHiC1--~
[0
lim
( 0 1/7~H'cl )
tRCd(NOa)2 --, 0 \0RCd(~roah
{(1 + KIRNH.Cl)
oLaR~-~,cl
lim
}] RNHiC1
( 0 1/~NH'CI.~
nCd(N08)~ ~ 0 \
}]
ORcd(NOa)JRSHiC1
lim F 0 [ lim /0 In li?cd'n°'hl }] RCd(~O,)~~ 0LORc~(~-o.), (RN~4C~~ 0\ OR~n~c1 ] RCd(~rO,)'
lim
Red(NOa)2 ~ 0
va~N'~Rc--o~h {(1
+ K1Rcd'~ORni ! t,,cl Ill-]
which follow from Equations (5) and (6). The extrapolations are summarized in Fig. 3. The abscissa referring to the solid lines is R~n4c 1 and the abscissa referring to the dashed lines is Rco(N%h. The upper solid line is a plot of the extrapolation function (1 -p- KIRNH,el )
(0 l/~'..,~l i
lim
RCd(NOa)2~0
\ORcd(NO,)#2/
RNHaCI
versus RN~cl. The lower solid line is a plot of lim (0_ l/eNd,c, 1 RCd(NO3)2~°\ ORedfNO3)~] R~m4Cl versus Rmi,c 1. The upper dashed line is a plot of (1 +KIRoo(No~)~)
lim
/0 In l/?c~(No ) ~ ~. ~ ~.~)
/~NHicI~O
)IHiCI
/~Cd(NOa)2
versus Red(NO.h, and the lower dashed line is
(Oln l/Tca(~°'ht O R ~ c 1 - / RCd(~Oa)~ RI~HiC1--+O\ lim
plotted against Rca(N%h. The value of K~ obtained from the measured activity coefficients of Cd(NO3)~, 315 -t- 20, is felt to be slightly low because subsequent measurements in other systems indicate that, at the lowest concentrations, measurements with silver-silver halide
Association constants of cadmium ion and chloride ion
819
electrodes are more reproducible than measurements with cadmium amalgam electrodes. The values estimated for K~ (based on the activity coefficients of NH~C1), K 2 and KI~ are 340 ~ 20, 75 ~ 5, and 5 =k 5. The units are moles NH4NO3/mole. The value of KI~ turns out to be negligible, and the value of K~ is somewhat smaller, relative to K1, than in analogous molten salt solutions. I
"1
....
~. . . .
I
l
I
I
I
7'
3
4
t
I
I
l
I
I
800
600
400
:~------~
~--- - - - - -
~-
Ld 200
0
I
5 Mole rofio, xlO~ 3
I
I
I
6
7
8
FIG. 3.--Graphical extrapolations for evaluating K,, K2 and Krz. Upper solid line: (1 + K1R~I~4Cl)
lira
1 ~
/
.
VS.
R~'H4Cl ;
RCd(N03 ) 2~ ° ~ ~Cd(N()3)2~ RNH4CI~
lower solid line: lim
1/alI~.~H4G ~ -.~
V s. RSHaCl;
RC'd(N%) ~] .~Naac 1
Red(N%) z ~ 0 \
upper dashed line: {(1-t-KxRca,.~oa,2) lim
(Sin I/7Ca(NOa,z~
RIgH4CI---v0\
~
I VS.
]//Cd(NO,),t
R~dIN03)2
lower dashed line: lim
(a lnlR/'Ctt(~%'21
BNH4CI~0 \
NH4CI
vs. Rca,~os, 2 .
/ BCd(N03)2
As a preliminary test of the applicability of a quasi-lattice model, activity coefficients of Cd(NO~)2 were calculated from the asymmetricapproximation of the quasilattice model of molten salt solutionsTMusing a value of the quasi-latticeparameter/~ obtained from the association constant calculated from the activity coefficients of Cd(NO3)2 by means of the relation g 1=
Z(fl
--
l)
with the quasi-lattice coordination number Z = 6. The comparison of the experimental and calculated concentration dependence (using one adjustable parameter) in Fig. 4 indicates that although the model may be unrealistic for these solutions, it may provide a useful extrapolation function for obtaining association constants.
820
J . M . C . HEss, J. BRAUN'STEINand H. BRAUNSTEIN 0"5
0*4
0'3 z
o _1 0.2
OI
~" 0
i I
,I
I
I
I
I
2
3
4
5
6
NCl f xlO -3
FIa. 4.--Activity coefficients of Cd(NOa)~ in the presence of NH4C1 at 39-9°C. The solid lines arc calculated from the quasi-lattice model with fl = 53 obtained from the experimental association constant with z = 6. Vertical lines are experimental activity coefficients from measurements of cells I and II. We have presented the results of measurements of association constants in concentrated aqueous electrolyte solutions, and demonstrated the thermodynamic consistency of data obtained from two different sets of measurements. We have shown also that the quasi-lattice model of molten salt solutions may provide a useful extrapolation function in concentrated aqueous electrolyte solutions. Further work is in progress to evaluate the association constants over a range of water contents between molten salts and aqueous electrolyte solutions and over a range of temperatures to determine the applicability of a quasi-lattice model.
,4cknowledgements--Wcwould like to acknowledgesupport of part of this work by the Coe Research Fund and by the Department of Industrial Cooperation of the University of Maine. Part of this work was supported by the U.S. Atomic Energy Commission, under Contract No. AT(30-1)-2873, for which we also express our gratitude.
ASSOCIATION CONSTANTS OF CADMIUM ION AND CHLORIDE ION IN CONCENTRATED AQUEOUS SOLUTIONS OF AMMONIUM NITRATE* J. M. C. HESS, J. BRAUNSTEIN and H. BRAUNSTEIN Department of Chemistry, University of Maine, Orono, Maine
(Received 12 August 1963; in revised.form 28 October 1963) Abstract--Activity coefficients of cadmium nitrate and ammonium chloride were measured potentiometrically in a solvent consisting of 2 moles of water per mole of ammonium nitrate at 39.9 °, Thermodynamic consistency was demonstrated for data obtained with silver-silver chloride electrodes and with cadmium (amalgam) electrodes. Association constants for the formation of CdCI +, CdCI~ and Cd,,C1a+ were, in (moles/mole NH4NOa)-, 340 ~- 20, 75 ± 5 and 5 i 5 respectively. The concentration dependence of the activity coefficients was compared with calculations based on a quasi-lattice model of molten salt solutions.
As the water content of a concentrated aqueous electrolyte solution is reduced, its properties must eventually approach those of a molten salt. The interpretation of the thermodynamic behaviour of concentrated aqueous electrolyte solutions in terms of a quasi-crystalline structure has been suggested as an approach towards the explanation of the observed dependence of the logarithm of the activity coefficients of electrolytes in concentrated solutions on the cube root of the ionic strength.(1, 2) This paper describes measurements of association constants in concentrated aqueous electrolyte solutions, and is the first part of an investigation of the applicability of a quasi-lattice model(3,4,5) of molten salt solutions to concentrated aqueous salt solutions. The system investigated initially consisted of dilute solutions of cadmium ion and chloride ion in concentrated aqueous solutions (1 mole of NH4NO 3 per 2 moles of H~O, or about 11 molar) of ammonium nitrate at 39.9°C. The aqueous ammonium nitrate solution was considered as the solvent. Since relatively few data are available in such concentrated solutions, it was considered worthwhile to determine by independent measurements the activity coefficients of both solute components, cadmium nitrate and ammonium chloride, and to test the thermodynamic consistency of the data. Association constants of cadmium ion with chloride ion were calculated by a method which also has been used for molten salt solutions(6,7) and the concentration dependence of the activity coefficients were compared with calculations based on the quasi-lattice model.~3,4,5) * Based in part of dissertation submitted to the University of Maine by J. M. C. HESS in partial fulfillment of the requirements for the Ph.D. degree. ~1~ R. H. STOKES and R. A. ROBINSON, J. Amer. Chem. Soc. 70, 1870 (1948). ~2~ H. S. FRANK and P. T. THOMPSON, The Structure of Electrolytic Solutions, (Chap. 8. edited by W. J. HAMER), J. Wiley, New York (1959). ta~ M. BLANDER, J. Phys. Chem. 63, 1262 (1959). ~4~ M. BLANDER and J. BRAUNSTEIN, Ann. N. Y. Acad. Sci. 79, 839 (1960). (2) M. BLANDER, J. Chem. Phys. 34, 432 (1961), (6) j. BRAUNSTEIN, M. BLANDER and R. M. LINDGREN, J. Amer. CTtem. Soc, 84, 1529 (1962). (71 j. BRAUNSTFIN and R. M. LINDGRFN, J. Amer. Chem. Soc. 84, 1534 (19t+2). 1~)
811
812
J.M.C.
H r ~ , J. BaAtmSTraN and H. BRAUNSTEIN
EXPERIMENTAL The cell Electromotive force measurements were made of the two concentration ceils: Cd(Hg)
Cd(NOs)= NH~NOs HsO
Cd(NOa)= NH4CI NHaNOs H20
(Hg)Cd
I,
AgCI,Ag
I1.
and
Ag,AgCI
NH4CI NH~NOs
NH4CI Cd(NOs)= NH4NO3
H=O
H20
CONCENTRATION CELL WITH AMALGAM ELECTRODES PYREX ROD ;;7"~RECIPROCATING STIRRERS GROUNDGLASS CAPS
COPPER WIRE POTENTIOMETER
~
GLASS GUARDTUBE FOR LEADS
WIRE
ULTRA FINE FRITTED .PYREX DISK DILUTE CADMIUM
III ~ICURE1
FIo. 1.--Diagram of the Ceil'0) used to measure the activity coefficients of Cd(NOs)2. In the Cell (I1), for measuring the activity coefficients of NH4C1, the cadmium amalgam electrodes were replaced by silver-silver chloride electrodes. A diagram of the cell (1) is shown in Fig. 1. In cell II, silver-silver chloride electrodes were suspended in the arms of the cell in place of the platinum--cadmium amalgam electrodes. The outside of the cell was coated with a silicone varnish to minimize conduction through the glass walls of the cell. The cell was clamped in a water bath thermostatted to -4-0'02 ° at 39.9°C. The temperature was measured with a thermometer which has been calibrated against a thermometer certified to within 0-05 ° by the East German "Deutsches Amt ftir Mass und Gewicht." The solutions in the cell were stirred continuously with motor-driven vertical-reciprocating stirrers with a stroke of about 5 cm. Chemicals Reagent grade ammonium nitrate, ammonium chloride, cadmium nitrate tetrahydrate,and silver nitrate were used without further purification. Ordinary distilled water was used for the solutions
Association constants of cadmium ion and chloride ion
813
after degassing was shown to be unnecessary. Triple distilled mercury and Fisher Certified Cadmium were used to prepared the amalgam electrodes. The ammonium chloride was dried at ll0°C and pelletized to facilitate additions to the cell. Cadmium nitrate was added to the cell as an aqueous solution (filtered to remove traces of cadmium hydroxide) whose concentration was determined by evaporation and ignition of a weighed sample tS~ to cadmium oxide. The effect of the added water (about 0.5 ml) was shown to be negligible by experiments in which up to 1 ml of H20 were added to one arm of the cell with no change of e.m.f. greater than the normal variation of ±0.2 inV.
Preparation of electrodes Silver-silver chloride electrodes were prepared by a modification of the method of PURLEEand GRUNWALD.~a~ Platinum wires, with foils (about 5 mm squares) welded to the ends were sealed through soft glass tubes and, after cleaning with aqua regia, were silvered by the Rochelle salts silver mirror process ~I°~for about 45 rain in an ice-water bath. (The slower deposition of silver in the ice-bath appeared to give more uniform deposits and more stable electrodes.) The electrodes were stored under distilled water after rinsing with ammonia, and were chloridized anodically at a current density of 1 mA/cm2 in 0"05 M hydrochloric acid shortly before use in a cell. Pairs of electrodes which gave a difference of e.m.f, greater than 0-2 mV. When dipped in an HCI solution were discarded. Most of the pairs gave an e.m.f, less than 0-05 mV. During a run the positions of the electrodes in the cell were reversed occasionally and were discarded if the e.m.f. change was greater than 0'4 inV. With both electrodes in the same arm of the cell the e.m.f.was generally less than 0"15 mV. Thus, in the solutions in which measurements were made, the precision of the e.m.f, measurements was better than -I-0.2 mV.
Cadmium amalgam electrodes Stick cadmium was allowed to dissolve in mercury in a closed test tube at room temperature to form a saturated amalgam (about 7 per cent weight). The liquid phase of saturated amalgam was diluted tenfold with mercury and stored under a 40 per cent solution of ammonium nitrate. Samples of cadmium amalgam from the same container were used to form pools at the bottom of the half cells, as shown in Fig. 1. The amalgam and platinum leads were placed in a previously dried cell before adding the solutions to the cell to prevent contact of the wires with the solutions. RESULTS AND DISCUSSION T h e results of the m e a s u r e m e n t s of the electromotive force of the Cells I a n d I I at 39"93°C with a m m o n i u m nitrate solutions c o n t a i n i n g 2 moles of water per mole of a m m o n i u m nitrate are given in T a b l e 1. Since the c o n c e n t r a t i o n s of chloride ion a n d of c a d m i u m ion were less t h a n 0.01 mole per mole of a m m o n i u m nitrate it is reasonable to assume that the c u r r e n t is carried almost entirely b y the " s o l v e n t " ( a m m o n i u m nitrate i n water). The activity of a m m o n i u m nitrate a n d water is essentially the same in b o t h half cells. F r o m a consideration of the electrode reactions a n d the t r a n s p o r t processes, the free energy change per faraday for a n infinitesimal difference of concent r a t i o n of Cd(NOz)2 in the right a n d left h a n d cells is
--dE -----1(1 - - ted2+) d#cd2÷ - - tr,-H,+ d#~n,+ + ti~%- dl~o3- + tcl- d#cl-. The t are H i t t o r f transference n u m b e r s of the ions, relative to water, a n d the # are " i o n i c chemical p o t e n t i a l s " which, c o m b i n e d , give
- - d F = {(1 - - tca~+) d/*eOtNOa)a - - ( t ~ 4 + + tcl-) d/ZNH4NOa -~- tel- d/zNa,Cl. W. W. EWlNGand W. R. F. GOYER,d. Amer. Chem. Soe. 60, 2707 (1938). t,J E. L. PURLEEand E. GRUNWALD,J. Phys. Chem. 50, 1112 (1955). ~1o~Handbook of Chemistry and Physics, (33rd Ed. p. 2729. Chemical Rubber Publishing Co., Cleveland, Ohio (1951-52). ts~
814
J.M.C.
HESS, J. BRAUNSTEtN and H. BRAUNSTEIN
TABLE I.----CHANGE IN EblF IN THE CELL (I) X 10 3
RCalNoa~3
1.047
R~H4OI X
103
1 "963
--AEMF(mV) RNIt401 X 103
0.466 1-377 1.913 2.806 3.694 4.569 5.369 5"999
1.72 4'77 6"46 9"13 11"84 •4'26 16"45 18.16
0"877 2"010 2.826 3"637 4"391 5"351 6"240
--AEMF(mV)
0.567 1"260 1"816 2"682 3.549 4"290 4.888 5"645 6'220
3.951
2"978
1"45 3"25 4"77 7'03 9"15 11"05 12"57 14"17 15'63
R~ra4cl X 103
--AEMF(mV)
0"497 0"965 1"560 2' 179 3"085 3"954 4"780 4"939
1"13 2"22 3"64 5 "04 7"09 9'03 10"86 13"36 14'97
5'020 1.94 4"40 5"68 7.21 8'63 10"55 12"38
0.825 1.610 2"921 3'993 5"256 6"312 6.834
1'42 2"87 5"22 7"13 9"37 11"27 12"31
CHANGE OF EMIt OF THE CELL (II)
RNa~Cl × 10a 0"503 Rca~r~oal 2 × 103
0"640 1"771 2"865 3"843 6"077 8"418
1"037 AEMF(mV) 5"02 12'09 17 '60 21 "76 29"41 35"70
Rca~o3~ 2 × 103 0-916 1"1811 2"721 3"593 4"736 5-770
4"026 1.096 2.088 3"149 4"584 5"734
2.007 AEMF(mV) Roa~r,%~ 2 × 103 AEMF(mV) 6-56 11"91 16"52 20"34 24"74 28.14
0"793 1'958 2"823 3"706 4"548 5"581
6-028 6'18 11 '30 16"22 21 "97 25" 89
0"765 2"035 2"846 3"879 4"956 5"969
5-00 11.54 15' 83 19'70 22"98 26"50 7.997
3"99 10"33 13-96 18-23 22"26 25"66
0'686 1 "802 2"887 4"015 5' 128' 6"213
3'16 8"04 12'61 17"71 21.65 25"23
Association constants of cadmium ion and chloride ion
815
At the concentrations investigated, the current carried by Cd 2+ or C1- must be negligible compared with the current carried by NH4 + and NO3-, and the chemical poten1 tial of NH4NOz (and water) is virtually constant. Integration of dF = --~d#c,~(No3)2 and introducing activities leads to the equation for the e.m.f., within the approximations noted above, 2-303RT ac,,l~NO~)~ E -~-ff log a,ca(N%h, where aca(NOp 2 is the activity of cadmium nitrate and the prime refers to the reference (left) half cell. (Note that in the absence of NH4NO a and NH~C1 the expression for dF reduces to ½(1 -- tca~+) d/tca(yop~, which is the correct expression for the aqueous concentration cell with cadmium electrodes and different concentrations of Cd(NO3)2 in the two half cells. If the concentrations are expressed as the mole ratios, RCd(NO3)~ , the number of moles of cadmium nitrate per mole of ammonium nitrate, the activity coefficient of the component cadmium nitrate may be defined as 7cdINo~l~ = a~'o(N%),../ Rt, aiNop. ~1a,~2) This definition of the activity coefficient is chosen to simplify the numerical calculations. Its numerical value differs negligibly, in the concentration range investigated, from the value of the activity coefficient defined in terms of the ionic concentrations : t __
Y in which the N are the ion fractions i(:d~+
nCd2+
aCd(NOa)z
N(,d:+N~.o3_, RCd(NOa)2
nc~12+ + nNH4+ -- 1 + RNHaC 1 - - R(,O(N~)3)z
and NNoa --
nNo a-
1 -~- 2Rcd(NOa)2
~, 1.(lt,12 )
n N o 3- -~- nC1- - - 1 + 2Rcd(Nop 2 + RNtqCl
The R are the mole ratios (mole of solute per mole of NHaNOz). (It should be noted that the activity coefficients used throughout the paper are stoicheiometric activity coefficients and not single ion nor mean ionic activity coefficients.) The standard state is chosen such that the activity coefficient is unity at infinite dilution of cadmium nitrate and ammonium chloride in the solution of fixed concentration of ammonium
nitrate in water. In the absence of chloride ion from the Cell I, the e.m.f, of the Cell I followed the Nernst equation in the mole ratio of cadmium nitrate in the range 2 × 10-a -< Rcd(SO3)2 <~ 6 × 10-a to ±0-2 mV., indicating that the activity coefficient ofCd(NO3)," is constant (unity) in this range and that the liquid junction potential of the cell is negligible. The activity coefficient of cadmium nitrate in the presence of chloride ion, hence, is given by 1 2F log - = - AE (1) ~Ca(NOp~ 2"303RT where AE is the difference between the e.m.f, of the Cell I in the presence and in the absence of ammonium chloride from the right-hand half cell. ~al) M. BLANDER, F. F. BLANKENSHIP and R. F. NEWTON, J. Phys. Chem. 63, 1259 (1959). ~a2~j. BRAUNSTEIN and M. BLANDER, J. Phys. Chem. 64, 10 (1960).
816
J . M . C . HESS, J. BRAtmSTEINand H. BRAtmSXmS
Similarly, the activity coefficient of ammonium chloride may be calculated from the change of e.m.f, of the Cell II when cadmium nitrate is added to the right-hand half cell (originally containing no cadmium ion). 1 log - ?,~r4cI
F --
-
-
2"303RT
AE
(2)
In the absence of cadmium ion, the e.m.f, of (II) followed the Nernst equation in the mole ratio of ammonium chloride, R~u,c 1. The activity coefficient of ammonium 0.5
I
I
I
]
y
~
/1
0.4
0-3
3 --I~.
g
_J 0-2
0
IP"
I
2
I
i
3
4
I
I
5
6
7
Nc~ x l O -a FIG. 2.--Activity cocf~cients of cadmium nitrate in the presence of NH~CI at 39.9°C.
The circles are measured values and the vertical lines are calculated from the activity coefficients of NH4CI. The N are stoichiometric ion fractions, n0o 2+ Nod=+
nod= + n~a4+
/'/01and N c l -
no1- + n~%-"
chloride is defined as a~,cl/Rz~qc z and the standard state is chosen so that the activity coefficient is unity at infinite dilution of ammonium chloride (in the absence of cadmium ion) in the solvent ammonium nitrate-water. The activity coefficients of cadmium nitrate calculated from the data obtained with the Cell I are shown as the circles in Fig. 2. The activity coefficients of cadmium nitrate also could be calculated from the measurements with the Cell II by integration
Association constants of cadmium ion and chloride ion
817
of the thermodynamic relation ( -0 lOg Yca(-------~N °8)z)
OR3IH,Cl
--
" Red(NO.),
(alog
)
(3)
\' ~-~Cd('~Oa)~ / RNtt,Cl
Thus, log
dRNit4Cl
(4)
The differentiation and integration were performed graphically using slopes which were estimated from the tangents to plots of log 7~H4Cl (obtained from the measurements with the Cell II at various fixed concentrations of NH4C1 ) versus Rca(~o.). The activity coefficients obtained from (4) are shown in Fig. 2 as the vertical lines indicating the estimated uncertainty in the values obtained from the graphical differentiation and integration, Except at the lowest cadmium nitrate concentration, where the agreement of the data are within ~0.5 mV, the agreement is within the estimated experimental uncertainty of 4-0.2 mV* This agreement shows that the two independent sets of measurements are consistent. If the deviations from unity of the activity coefficients of cadmium nitrate and ammonium chloride are attributed to the possible formation of associated species CdC1+, CdC12, Cd~C1~+, etc., the activity coefficients may be written(6, 7) 1
l n - -
~"Cd(NOa)~
= K 1 R N a , c l ._}_ K I ( K ~ _ 1~K1)RsII~,C 2 1
(5)
4- Kx(2K12 -- K1)RNI~,ClRCa(~.o3), --}- . . . and
~NH4C1
-
1 + K1Rca(soo, + KtKI~R 2cd¢so.),
(6)
4- KI(2K~ -- K1)Rcat~,o.h Rr, g,Cl -~ . . .
where the K's are the association constants Rcdcl+ K1 --=-- Rcd~+Rc11(2 -=
Klz =
Reach Rcd ct÷R c l -
Rcaacl3+ RCdcI+ Rcd,+
etc. Equations (5) and (6) were used (rather than, for instance, the analogous equations for 1/TCatNO,)~ and In 1]?NH,Cl) because they lead to extrapolations having less curvature than extrapolations based on other forms of the series.(6,7) * Recent checking of the measurements indicates that the measured values of log 1/Tcatsos~ ~ at 10-3 probably were slightlyin error and that the values calculated from the measurements of cell II are correct.
Rca{r, os~ 8 = 1 x
818
J.M.C.
HESS, J. BARUNSTEINand H. BRAUNSTEIN
Using graphical methods described previously(6, 7) K1 was calculated from the relation K x ---- lim (0 In 1/TCd(N08h~ /¢Cd(NOs)2 ~ 0 RNH4C1~ 0
=
lim
0RNH, C1
] Red(N08 h
(0_ 1/~'Z~H,C,)
RCd(N0a)2 ~ 0 \0RCd(N0a)~ R~HiC 1~ 0
RNHiCI
K 2 and Klz were obtained graphically from the relations
K~(ZK2 --/(1) = 2KaK2 =
lira
K1(2K12--KI) 72K1KI~ =
0
[
lim
OR-~-cl
RNHaC1~ 0
F
RNHiC1--~
[0
lim
( 0 1/7~H'cl )
tRCd(NOa)2 --, 0 \0RCd(~roah
{(1 + KIRNH.Cl)
oLaR~-~,cl
lim
}] RNHiC1
( 0 1/~NH'CI.~
nCd(N08)~ ~ 0 \
}]
ORcd(NOa)JRSHiC1
lim F 0 [ lim /0 In li?cd'n°'hl }] RCd(~O,)~~ 0LORc~(~-o.), (RN~4C~~ 0\ OR~n~c1 ] RCd(~rO,)'
lim
Red(NOa)2 ~ 0
va~N'~Rc--o~h {(1
+ K1Rcd
which follow from Equations (5) and (6). The extrapolations are summarized in Fig. 3. The abscissa referring to the solid lines is R~n4c 1 and the abscissa referring to the dashed lines is Rco(N%h. The upper solid line is a plot of the extrapolation function (1 -p- KIRNH,el )
(0 l/~'..,~l i
lim
RCd(NOa)2~0
\ORcd(NO,)#2/
RNHaCI
versus RN~cl. The lower solid line is a plot of lim (0_ l/eNd,c, 1 RCd(NO3)2~°\ ORedfNO3)~] R~m4Cl versus Rmi,c 1. The upper dashed line is a plot of (1 +KIRoo(No~)~)
lim
/0 In l/?c~(No ) ~ ~. ~ ~.~)
/~NHicI~O
)IHiCI
/~Cd(NOa)2
versus Red(NO.h, and the lower dashed line is
(Oln l/Tca(~°'ht O R ~ c 1 - / RCd(~Oa)~ RI~HiC1--+O\ lim
plotted against Rca(N%h. The value of K~ obtained from the measured activity coefficients of Cd(NO3)~, 315 -t- 20, is felt to be slightly low because subsequent measurements in other systems indicate that, at the lowest concentrations, measurements with silver-silver halide
Association constants of cadmium ion and chloride ion
819
electrodes are more reproducible than measurements with cadmium amalgam electrodes. The values estimated for K~ (based on the activity coefficients of NH~C1), K 2 and KI~ are 340 ~ 20, 75 ~ 5, and 5 =k 5. The units are moles NH4NO3/mole. The value of KI~ turns out to be negligible, and the value of K~ is somewhat smaller, relative to K1, than in analogous molten salt solutions. I
"1
....
~. . . .
I
l
I
I
I
7'
3
4
t
I
I
l
I
I
800
600
400
:~------~
~--- - - - - -
~-
Ld 200
0
I
5 Mole rofio, xlO~ 3
I
I
I
6
7
8
FIG. 3.--Graphical extrapolations for evaluating K,, K2 and Krz. Upper solid line: (1 + K1R~I~4Cl)
lira
1 ~
/
.
VS.
R~'H4Cl ;
RCd(N03 ) 2~ ° ~ ~Cd(N()3)2~ RNH4CI~
lower solid line: lim
1/alI~.~H4G ~ -.~
V s. RSHaCl;
RC'd(N%) ~] .~Naac 1
Red(N%) z ~ 0 \
upper dashed line: {(1-t-KxRca,.~oa,2) lim
(Sin I/7Ca(NOa,z~
RIgH4CI---v0\
~
I VS.
]//Cd(NO,),t
R~dIN03)2
lower dashed line: lim
(a lnlR/'Ctt(~%'21
BNH4CI~0 \
NH4CI
vs. Rca,~os, 2 .
/ BCd(N03)2
As a preliminary test of the applicability of a quasi-lattice model, activity coefficients of Cd(NO~)2 were calculated from the asymmetricapproximation of the quasilattice model of molten salt solutionsTMusing a value of the quasi-latticeparameter/~ obtained from the association constant calculated from the activity coefficients of Cd(NO3)2 by means of the relation g 1=
Z(fl
--
l)
with the quasi-lattice coordination number Z = 6. The comparison of the experimental and calculated concentration dependence (using one adjustable parameter) in Fig. 4 indicates that although the model may be unrealistic for these solutions, it may provide a useful extrapolation function for obtaining association constants.
820
J . M . C . HEss, J. BRAUN'STEINand H. BRAUNSTEIN 0"5
0*4
0'3 z
o _1 0.2
OI
~" 0
i I
,I
I
I
I
I
2
3
4
5
6
NCl f xlO -3
FIa. 4.--Activity coefficients of Cd(NOa)~ in the presence of NH4C1 at 39-9°C. The solid lines arc calculated from the quasi-lattice model with fl = 53 obtained from the experimental association constant with z = 6. Vertical lines are experimental activity coefficients from measurements of cells I and II. We have presented the results of measurements of association constants in concentrated aqueous electrolyte solutions, and demonstrated the thermodynamic consistency of data obtained from two different sets of measurements. We have shown also that the quasi-lattice model of molten salt solutions may provide a useful extrapolation function in concentrated aqueous electrolyte solutions. Further work is in progress to evaluate the association constants over a range of water contents between molten salts and aqueous electrolyte solutions and over a range of temperatures to determine the applicability of a quasi-lattice model.
,4cknowledgements--Wcwould like to acknowledgesupport of part of this work by the Coe Research Fund and by the Department of Industrial Cooperation of the University of Maine. Part of this work was supported by the U.S. Atomic Energy Commission, under Contract No. AT(30-1)-2873, for which we also express our gratitude.