1261
ASSOCIATION CONSTAXTS IN ~ T O L T E N MIXTURES OF K N 0 3 WITH Ca(N03)2
Association Constants in Molten Mixtures of Univalent and Divalent Nitrates.
I.
Silver Chloride in Mixtures of Potassium Nitrate with
Calcium Nitrate or Strontium Nitrate’
by Jerry Braunstein and Judith D. Brill Department of Chemistry, University of M a i n e , Orono, Maine
(Received hrovember 10, 1965)
Association constants of silver ion with chloride ion were measured potentiometrically in the mixed molten salt solvents, KN03-Ca(NO& and KNOrSr(N03)z. The results are compared with those obtained in pure and mixed alkali metal nitrates and are discussed in terms of the reciprocal coulomb effect and the effective radius of the nitrate ion.
Introduction Association constants of silver ion or cadmium ion with halide ions have been reported in a number of molten alkali nitrates and mixtures of alkali nitrates.2 I n a given solvent a t a single temperature, the association constants of a cation with halide ions increase in the order C1 < Br < I. The effect of the solvent has been shown to depend on the relative sizes of the ions involved in the exchange reaction
RID
+ SX = MX + SD
where l!t refers to the solute cation (Ag+ or Cd2+), S the solvent cation (Lif, Na+, K+, or Cs+), X the solute anion (halide ion), and D the solvent anion (nitrate). I n the solvents NaN03, KN03, CsN03, and their mixtures, the order of the association constants correlates with the calculated reciprocal coulomb effect.2cle The calculated reciprocal coulomb effect takes into account the contribution to the energy of association of the change in coulombic energy on exchange of pairs of nearest-neighbor ions in the above reaction but not the long-range coulombic energy or the dispersion or polarization energy. I n solvent mixtures containing lithium nitrate, the association constants are not consistent with the reciprocal coulomb effect unless a smaller “effective radius” (or distance of closest approach) is assumed for nitrate ions adjacent to lithium ions than for nitrate ions adjacent to the other alkali metal cations. I n this paper we present the results of potentiometric
measurements of the association of silver ions with chloride ions in solvents consisting of 80 mole % potassium nitrate and 20 mole % calcium nitrate or strontium nitrate. We show that the effect of divalent solvent cations on the association constants is in the direction predicted by the reciprocal coulomb effect (destabilization), but a smaller effective radius of nitrate ion is indicated than the value (2.19 A) assumed previously.
Experimental Section The electromotive force was measured of the concentration cell I by methods similar to those described
previ~usly.~The measurements in KN03-Ca(N03)z [and some of the measurements in KK03-Sr(nT03)2], however, were made with a silver electrode coated with silver iodide (by adding a small crystal of potassium (1) This work was supported by the U. S. Atomic Energy Commission under Contract No. AT(30-1)-2873. (2) (a) C. Thomas and J. Braunstein, J . Phys. Chem., 6 8 , 957 (1964) ; (b) J. Braunstein, H. Braunstein, and A. S. Minano, Inorg. Chem., 3 , 1334 (1964); (c) J. Braunstein and A. S. Minano, ibid., 3 , 218 (1964); (d) J. Braunstein and R. E. Hagman, J . P h y s . C h m . , 6 7 , 2881 (1963); (e) D. L. Manning, R. Bansal, J. Braunstein, and M. Blander, J . Am. Chem. SOC.,84, 2028 (1962) ; (f) J. Braunstein and R. M. Lindgren, ibid., 84, 1534 (1962); (9) D. L. Manning, J. Braunstein, and M. Blander, J . P h y s . Chem., 66, 2069 (1962). (3) M. Blander, F. F. Blankenship, and R. F. Newton, ibid., 63, 1259 (1959).
Volume 70, Number 4
A p r i l 1966
1262
JERRY BRAUNSTEIN AND JUDITH D. BRILL
iodide to the melt). This lead to Sernst slopes over a larger range of silver concentrations and to more stable readings of the emf than could be obtained with bare electrodes, possibly by restricting access of oxygen to the silver electrode. Measurements in K S 0 3with bare electrodes and with silver electrodes coated with iodide indicated that the activity coefficients (and association constants) with and without iodide were in agreement within the experimental error (about 1 mv) at low enough (below 370") temperatures to keep the solubility of silver iodide small. Reagent grade KN03, Ca(1\;03)2.4H20,Sr(S03)z,KC1, and AgS03 from Mallinckrodt were used without further purification other than drying. Mixtures of K K 0 3 and Ca(N03)2.4Hz0 were dried by bubbling helium through the melted mixture overnight at a temperature of about 250". A series of measurements of the weight loss indicated a stoichiometric weight loss of the water of hydration of the Ca(.Y03)n.4H20after about 4 hr of bubbling helium through the melt.
.IO '
I
5
i
d
KN0,-
Sr(NO3I2
T = 350 'C
I
'0
2
3
4
6
5
7
8
9
IO
Ilklo-3)
REI
Figure 1. Activity coefficients (as -log 7 ~ ~of ~silver 0 ~ ) nitrate us. the concentration of chloride in molten 0.8KN03-0.2Sr(N03)2 at 350" a t several fixed concentrations of silver nitrate. .15,
,
,
,
,
,
,
,
,
,
,
,
,
,
Results In the absence of chloride, the electromotive force of the cell I followed the Nernst equation in the concentration of silver nitrate. When potassium chloride was added to the right-hand half-cell containing a fixed concentration of silver nitrate, the emf decreased. The stoichiometric activity coefficient of silver nitrate ~ FAE/2.3RT is given by the equation log Y A ~ N O = where AE is the change of emf of the cell on addition of KCl. Figures 1 and 2 are plots of -log Y A ~ N Oas ~ a function of the concentration of IiCl at various fixed concentrations of Agx03 in the solvents O.8KNO30.2Sr(N03)2 a t 350" and 0.8KN03-0.2Ca(N03)2 at 320". These data and the data for the activity coefficients in 0.8KN03-0.2Ca(N03)2are available from AD1 (Table III).4 Concentration Units and Association Constants. The concentraticlns are reported as the ion mole ratios RA~NO =, ~ A ~ N O , / [ ~ K X O , ~ C ~ ( N O and ~ ) ~ Rcl ] = ncl/ 2 n ~ a ( ~ 0 ~ )A ~ t] . the low solute concentra[nKN08 tions investigated mole ratio), the ion ratios are numerically nearly equal to the ion fractions N A g + = n A g N o s / n c a t l o n s , N C I = n K c I / n a n i o n s , where n A g N O a , n m , etc., are the numbers of moles of AgS03, (KCa)Cl, etc. (The starred mole ratios Rcl* = n c l / [nKKo3 ~ C ~ ( N O , in ) ~ ]the figures were used for convenience in computations. The association constants were calculated in all cases using the ion mole ratios R c l and R A which ~ are virtually equal to the ion mole fractions.) I n binary mixtures of molten salts of different chcirge types, the use of ion mole fractions (Temkin activities), based on a model of random mixing
+
+
+
The Journal of Physical Chemistry
?
1
KN0,-
1
Ca(NO,),
Figure 2. Activity coefficients of silver nitrate us. the concentration of chloride in molten 0.8KN030.2Ca(?J03)2a t 320" several fixed concentrations of silver nitrate.
of all cations and random mixing of all anions, but no mixing of cations with anions has been shown to give better agreement of experimental results with the laws of dilute solutions than the use of equivalent fractions, e . g . , X ' M += n h l + / ( n h r + 2 n p 2 + ) , which assume the introduction of vacancies with multiply charged ions as in mixed crystalline solids.5-'
+
(4) The data have been deposited as Document No. 8818 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. A copy may be secured by citing the Document number and by remitting $1.25 for photoprints, or $1.25 for 35-mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress. (5) M. C. Bell and 9. N. Flengas, J . Electrochem. SOC.,111, 669 (1964). (6) (a) T. FZrland, Norg. Tek. Vitenskapsakad., Ser. 8, 4 (1957); (b) T.Fpirland, Discussions Faraday SOC.,3 2 , 122 (1962).
1263
ASSOCIATION CONSTANTS IN MOLTEN MIXTURES OF K N 0 3 WITH Ca(NO&
Table I: Association Constants, K1, and Specific Helmholtz Free Energies of Association,
-K
KI, Kitrate solvent, mole--I% -Ca. Sr
Temp,
Li
OK
100" 80
0 20
0 0
0 0
623 593
80
20
0
0
623
80
0
20
0
623
0
0 0 100
33b 0
664
67 0
100 0
0 a
' Reference 2a.
Reference 2g.
=
RAgNOa
nAg
+
nAgCl
+
nAgNoa
=
=
naolvent cations
553 & 20 518 7 - 16 417 5 - 12 336 & 23 - 32 380 =t25
+ +
=
z = 5
2 = 6
6.12 5.74
5.85 5.48
5.62 5.27
...
...
5.27
5.50
5.23
5.01
...
...
5.9 ( 3 .9IC (2.6)'
Estimated by linear extrapolation of results in KNOa and KN03-Ca(N03)2 or KN03-Sr(N03)2.
2nAgiCIt
*
9
I , , ,
,
I
y
I
I
,
I
I
I
I
I
T = 350 *C
K N O g Sr(N03),
,001 n
T 0
100-
I
f
Ii
0
(1) (2)
2" O/ E , 200 -
KN$-
T = 320 *C
CaNO&,
L
If the association constants are defineds K1
2 = 4
0
+ +. R A ~+ + R A ~ C+I . . .
nAgC1g-
- AA, kcal/mol-
(moles/mole of solvent)
The association constants are evaluated by considering the distribution of silver among the various possible associated species.8 nAgNOs
- AA
RAEI R A g + RCI-
-I
--
I
I
I
(3)
z
f
Ag 0
- AgI ELECTRODE
Ag ELECTRODE
etc., where R A ~and + R c l - are the ion mole ratios of the "free" or unassociated Ag+ and C1-, and R A ~isc ~ mole ratio of the associated species AgC1, eq 2 becomes
R A ~ N= O ,R A g t
+ K ~ R A ~ + R+c (higher ~terms) ... (4)
Writing the activity coefficient of silver nitrate as Y A ~ N O ~ = R A+~/ R A ~ N owhere ~, R A ~ NisO ~the stoichiometric mole ratio of silver nitrate, leads to the result
ordination number 2. The previously reported results in potassium nitrate and 67% potassium nitrate33% lithium nitrate also are shown in Table I. The change of coulombic energy in the exchange of nearest neighbors taking place in the association reactions
+ K+C1- +Ag+Cl- + K+N03-: AUK Ag+NOa- + Sz+C1- + Ag+Cl- + &+NOS: A U , Ag'X03-
RAgNOa'O
The graphical extrapolation of eq 5 is shown in Figure 3 and the results are shown in Table I. Helmholtz Free Energies of Association. The specific Helmholtz free energies of association, AA, were calculated from the equation of the quasi-lattice model
K 1 = Z[exp(-AA/RT) - 13
is AU, - AUK =
Ne2 2Pa[l d
+ ( + P)PI - - 1 ) 4 + a) + 4 ( 1 + P)(l + + P ) Q!
(1
(2
(6)
Q!
(7) K. J. MaoLeod and F. E. W. Wetmore, Ann. N . Y. Acad. Sci.,
where 2 is the quasi-lattice coordination n ~ m b e r . ~ 79, 873 (1960). (8) J. Braunstein, M. Blander, and R. LM.Lindgren, J. A m . Chem. Table I summarizes the association constants and the SOC.,84, 1529 (1962). specific Helmholtz free energies of association cal(9) D. G. Hill, J. Braunstein, and M. Blander, J. Phys. Chem., 64, culated for the values 4, 5 , and 6 of the lattice co1038 (1960). Volume 70, Number 4 April 1966
1264
JERRY BRAUNSTEIN AND JUDITH D. BRILL
This equation is an extension of one derived previously for univalent ions ( x = 1).2C d is the sum of the radii of the ions +(I and Nos-; CY and /3 are the relative increments of the radii of the halide ion and of the solvent cation a=
If
01
rc1- d
rNOa-
J/3=-
rS
- rK d
0.8KN03-0.2Ca(N03)zand 0.8KNOr0.2Sr(N03)2, using eq 6 and the assumed linearity of the solvent effect in solvent mixtures, are listed in Table I1 for several values of the effective radius of nitrate ion. Also listed are values of the solvent effect calculated with a smaller effective radius, r ’ N O s - , for a nitrate ion adjacent to a divalent ion than for a nitrate ion adjacent only to univalent cations
and /3 are small, eq 6 may be approximated by
+
(7) Values of AtJca - AUKwere calculated from the Pauling radii of K+, Ca2+,Sr2+,and C1- (1.33, 0.99, 1.13, and 1.81 A) together with the value r N O a - = 2.19 A.2c,10 With the further assumption (which has been shown to be valid in several other molten salt systemsza+) that the specific Helmholtz free energy of association in the mixed molten salt solvent varies linearly with the composition (mole fraction) of the solvent mixture (AAlz(mix) = XIAA1 X2AA2),AgCl was estimated with (6) to be less stable in 0.8KN03-0.2Ca(N03)2than in K N 0 3 by 3.4 kcal/mole. The destabilization of AgCl in 0.8KN03-0.2Sr(N03)2, relative to KN03, was estimaied to be 2.9 kcal/mole. From Table I, the experimental destabilization in 0.8KN03-0.2Sr(NO& is 0.6 kcal/mole and in 0.8KN03-0.2Ca(N03)2 is 0.4 kcal/mole. A smaller radius of nitrate ion, e.g., 1.85-1.90 A, would lead to much better agreement between the experimental solvent effect and the calculated reciprocal coulomb effect, and also would lead to more consistent results for the solvent effect in the univalent ntrates.2a-c However, 1 he greater destabilization observed for strontium than for calcium cannot be explained with a single value of the radius of nitrate ion. We have reported previously that the solvent effect on the association of cadmium ion in mixtures of lithium nitrate and potassium nitrate indicated a smaller effective radius of nitrate ion in lithium nitrate than in potassium nitrate. The results reported in the present paper also would be consistent with a smaller effective radius of nitrate ion in calcium nitrate than in strontium nitrate. Kitpustinskiill has suggested the value 1.89 A for the thermochemical radius of nitrate ion. Meschel and Kleppa,12 from their data on enthalpies of solution of alkali halides in alkali nitrates, suggested the value 1.93 A (1.85 A in lithium nitrate). Calculations of the reciprocal coulomb effect for the solvents
+
The Journal of Physical Chemistry
0.2(AUcu - AUK) = 0.2Ne2 [rK rC1 2 2 rc0 r’NOa rCu rcl
+
+
rK
+l
l
The observed solvent effect would be consistent with the reciprocal coulomb effect with an effective radius of nitrate ion of 1.88 A (1.86 A in calcium nitrate).
Table 11: Experimental Solvent Effect and Calculated Reciprocal Coulomb Effect for Several Values of the Radius of Nitrate Ion
A
A
kcal/mole
0.2 ( 4 Usr - AUK), kcal/mole
2.19 1.90 1.90 1.90 1.88 1.88 1.86
2.19 1.90 1.88 1.86 1.88 1.86 1.86
3.4
2.9
0.89 0.57 0.24
0.75
0 70
0.59 0.30 0.42
0.2(A Uca
moa-,
a
r’NOa-7
-
AUK),
0.37 0.50 0.4“
0.46 0.24
0.6”
Experimental value.
A value of the radius of nitrate ion smaller than the radius of bromide ion would be inconsistent with the direction of the solvent effect on the association of Ag+ with Br- for which the greater stability in Kr\‘Os (than in NaN03) indicates a smaller radius for the bromide ion than for the nitrate ionS2e Although consideration of the long-range coulombic effects, polarization, and dispersion are required for a complete treatment of the solvent effect, the present results appear to indicate a radius of nitrate ion less than 2.00 A. (10) “Handbook of Chemistry,” 9th ed, Handbook Publishers, Inc., Sandusky, Ohio, 1950, p 108. (11) A. F. Kapustinskii, Quart. Rev. (London), 10, 283 (1956). (12) S. V. Meschel and 0. J. Kleppa, J . Phys. Chem., 6 8 , 3840 (1964).
