39 1
Application of Pitzer's Equations (12) (13) (14) (15) (16)
J. 8. Oallivan and W. H. Hamill, J. Chem. Phys., 44, 1279 (1966). B. H. J. Bielski and A. 0. Allen, J. Chem. Phys., 71, 4544 (1967). S. L. Hager and J. E. Willard, J. Chem. Phys., 83, 942 (1975). H. J. Haink and J. R. Huber, Chem. Ber., 108, 1118 (1975). R. F. Nelson, D. W. Leedy, E. T. Seo, and R. N. Adams, L Anal. Chem., 224, 184 (1967). (17) A. Bemas, M. Gauthier,and D. Grand, UI Phys Ckm, 76,2236 (1972). (18) W. M. McClain and A. C. Albrecht, J. Chem. Phys., 43, 465 (1965). (19) B. Brocklehurst, Nature(London),221, 921 (1969); B. Brocklehurst, G. Porter, and J. M. Yates, J. Phys. Chem., 68, 203 (1964).
3. The System HBr 4- (Pr),NBr 4- H20 at 25
(20) J. Bullot and A. C. Albrecht, J. Chem. Phys., 51, 2220 (1969). (21) J. E. Adams, W. W. Mantulin, and J. R. Huber, J. Am. Chem. Soc., 95, 5477 (1973). (22) M. Shirom and J. E. Willard, J. Am. Chem. Soc., 90, 2184 (1968); A. Ekstrom, R. Suenram, and J. E. Willard, J. Phys Chem, 74, 1888 (1970). (23) F. S.Dainton, M. J. Pilling, and S. A. Rice, J. Chem. Soc., Faraday Trans. 2, 71, 1311 (1975). (24) T. Ichikawa, H. Yoshkla, and K. Hayashi, 6~11.Chem. Soc. Jpn., 48, 2685 (1975).
OC.
Application of Pitzerz's Equations
Rabindra N. Roy," James J. Glbbons, Ronald Snelling, James Moeller, and Terry Whlte Department Of Chemistry, Drury College, Springfield, Missouri 65802 (Received April 2, 1976; Revised Manuscript Received November IO, 1976)
The species tetrapropylammonium bromide has been used to study the effect of large-sized cations on the quilibrium properties of aqueous electrolyte solutions. Activity coefficients of HBr, in HBr + (Pr)4NBr+ H2O at 25 "C, have been measured at total molality m (where m = ml + mz)ranging from 0.05 to 2.0 mol kg-', using cells containing hydrogen and silver-silver bromide electrodes. It was found that Harned's rule is valid for m = 0.05,0.1, and 0.25 mol kg-'. The results were interpreted in terms of Pitzer's equations for cation-cation doublet (OMN), cation-anion-cation triplet (Qmx),and other interaction parameters. At a dilute concentration (Le,, m = O,l), the results have been discussed in light of the specific interaction coefficient, &pr),N+,Br-, a BrBnsted-Guggenheim parameter. Also, the results are discussed in terms of the water structural changes caused by the presence of the large-sized hydrophobic cation.
Introduction The importance of understanding the effects of cation size on the thermodynamic behavior of aqueous electrolytes, as well as the nature of cation-cation and cationanion-cation interactions, and the behavior of tetraalkylammonium salt-water mixtures, are well recognized.1-5 In a continuation of several previous invesigations resulting in the final calculation of the binary cation-cation interactions, dMN, for the three systems HBr + NH4Br + Hz0,6HC1 + NH4C1 + HzO,' and HBr + ( B u ) ~ N B ~ HzO,*we have undertaken a course of electromotive force studies on the HBr (Pr)4NBr + HzO system at 25 "C. Osmotic and activity coefficient data for pure (Pr)4NBr solutions have been previously reported, from the results of gravimetric isopiestic vapor pressure techniquesFl" but no thermodynamic data based on either isopiestic or emf techniques for aqueous mixtures of HBr + (Pr)4NBrare available in the literature. Emf measurements were made at 25 "C using a cell of the type
+
+
Pt, H,(g,l atm)lHBr(rn,), (Pr),NBr(rn,)IAgBr, Ag
(1)
over the range of total molality m from 0.05 to 2.0 mol kg-l. Experimental Section The tetrapropylammonium bromide was obtained from the Eastman Kodak Co., and was recrystallized twice from suitable solvents (such as benzene-ligroin mixtures).ll The gravimetric analyses of the anion as the silver salt indicated that the molality of the solution was accurate to well within f0.02%. Quadruplicate gravimetric determinations of the stock solution of aqueous HBr (about 4 M) agreed to within f0.01% . The doubly distilled and deionized water used in this study had a specific conductivity of less than 1 X lo4 mho cm-l.
Emf measurements were made with a Leeds and Northrup K-3 potentiometer in conjunction with a Leeds and Northrup d.c. null detector (Model 9829). The cells were thermostated at 25.00 f 0.01 OC by means of a constant temperature bath. Preparation of the electrodes (the thermal electrolytic type)," purification of the hydrogen gas, preparation of the solutions, and oxygen exclusion from the cells by means of hydrogen input have all been previously de~cribed.~~' Preliminary emf measurements for 0.1 mol kg-l showed that the standard emf Eo of the AgJAgBrelectrode was equal to 0.071 06 V, in identical agreement with the literature value13 of 0.07106 V, assuming that the activity coefficient of HBr was 0.80514 at 0.1 mol kg-l. In order to help avoid the significant solubility of AgBr at the highest constant total molality tested (m = 2.0 mol kg-l), the cell with the hydrogen electrode was allowed to equilibrate for about 1h before the AglAgBr electrode (kept in a separate standard-joint test tube containing a solution of the same composition) was transferred to the electrode compartment, thus avoiding a drift in the emf values. The equilibrium emf value was noted and recorded every 5 min until no deviation was observed. Results a n d Discussion The results of our various emf measurements, corrected to a partial hydrogen pressure of 1 atm, are summarized in Table I (supplementary material, see paragraph at end of text) as a function of the molality fraction y2 (which is equal to m 2 / m ) . According to Harned's rule,14the logarithm of the activity coefficient of each electrolyte in a mixture of a constant total ionic strength can be expressed by means of two Harned expressions: log X B r = log roHBr - 0 1 1 2 ~ 2- PlZm;
(1)
The Journal of Physical Chemistw, VoL 81, No. 5, 1977
392
and log
Y(Pr)4NBr
= log Y0(Pr)4NBr -
a2lml
- flZlm?
(2) 0.p
where 7mr is the activity coefficient of HBr in the mixture, y o ~ B is r the activity coefficient of pure HBr at the same ionic strength as the total ionic strength of the mixture, and a12,P12, etc., are the Harned interaction coefficients (which are independent of the composition but functions of the total ionic strength). From this, it is seen that the linear forms of eq 1 and 2 are known as Harned's equations. The values of the parameter a12,and the standard deviations a(a12)and a(E) are given in Table I and were obtained from a combination of the Nernst equation
E = E"
-
k log m l ( m l
+ m2)y:
0.3 ocl2
0.2
(3)
with the linear form of eq 1, which resulted in
E
+ k log m l = E" - k log m - 2k log y t
+ 2k a12mZ
0.1
(4)
One can then express eq 4,after proper rearrangement, in a linear and a nonlinear form:
E
+ k log m l = a + bm,
(5)
e
E
+ k l o g m l = a + bm, + cm;
(6) where a12= b/2k, P12 = c/2k, and k = (RT In lO)/F. The values of a12presented in Tables I and I1 (supplementary material) are in excellent agreement among themselves, confirming thereby the constancy of Eo = 0.071 06 V for the AglAgBr electrode. The values of a12at 0.05,0.1, and 0.25 were taken from the linear form (since Harned's rule is valid within this concentration range), while for those of the other four molalities (0.5,1.0,1.5, and 2.0 mol kg-l), the values of the nonlinear form (given in Table I) were used. Bronsted-Guggenheim Equation. If the BronstedGuggenheim equation is assumed to be valid at total molality m = 0.1 mol kg-l for mixtures of HBr (MX) and (Pr)4NBr(NX), then we can write the expression for log YHB, at 25 "C as'' log Y H B ~= -0.5108I" /( 1 f 1" ) + ' / d H @ r m B r + Y a H B r m H + yd(Pr)4N,Brm(Pr)4N
(7)
where I = ml + mz = m, and B(P:)~N,B, = 20/2.3026, which represents the specific interaction coefficient stemming from the interaction between the cation (Pr)4N+and the anion Br-. Similar explanations may be applied to the concept of BH,,. Comparison of eq 6 with the linear form of eq 1 leads to a description of the Harned coefficient, a12, as a12
= %(B€I,Br
1.0
0.0
and
- B(Pr)4N,Br)
(8)
from which the value of B(pr)*~,Br at m = 0.1 mol kg-l can easily be determined. The value of B H , B ~(equal to 0.287 kg mol-l) was supplied by Guggenheim and Turgeonl' and that for a12= 0.3570 is given in Table I. After computation, B(prpF at m = 0.1 mol kg-l is found to be -0.427, as compare wth B m , , = +0.0122,6 or Bp,],, = -0.374; and can be used to calculate the activity coefficient of (Pr)4NBr. Formalism According to Pitzer. The most common method for the evaluation of the interaction parameters such as aZ1and Pzl of eq 2 for the activity and osmotic coefficients of mixtures of strong electrolytes are due to The Journal of Physical Chemistv, Vo/. 81. No. 5, 1977
3.0
2.0 molality
Figure 1. Harned interaction coefficient vs. total molality of Br- for the HBr i-(Pr),NBr H20 system at 25 OC. A In ylm, vs. the parameter 1/2(mHt + mBrr).
+
Scatchard18and McKay.lg In the present study, the more simplified expression of Pitzer14 for aZ1and the activity coefficient of HBr in mixtures of MX (HBr) and NX [(Pr),NBr] has been adopted, as has been previously done in prior work from this laboratory.'v8 This is due to the simplicity of the equations and the fact that each Pitzer parameter has some reasonable physical significance. The finalized version becomes In 71
fY
+ m [ B r M X + YZ(B'NX
- B'MX
+ 6MN)
+ Y l Y 2 me)MNI + m 2 [ C Y M X + Y2(c'iVX + 'WMNX) + '/~Y~Y~$MNX
- C'MX
(9)
where 8MN indicates the interactions between H+ and (Pr)4N+,and @MNX is a measure of the degree of interaction between H+, (Pr)4N+,and Br-. Equation 9 reduces to the more simplified version (eq 10) after imposing the conditions that 8'MN = 0, @MNX = 0, and yz (at the limit) = 0: In
(Tl/$l)
= my2 (B'NX - @MX - C'MX)
+ m2 YZ (C'NX
+ e)
(10) Combination of the linear form of eq 1 with eq 10 and subsequent reduction leads to
e
+
= -2.302601~~f ( @ O )
(11)
where
and
B%x = p o M x
+ b1MX exp(-2m1/*)
(13)
In eq 11, the Pitzer parameter 8 (which, in Scatchard's notation is bA,B(oJ), equal to 28; gM,N according to Fried-
3Q3
Application of Pltzer’s Equations
TABLE 111: Values of the Parameter e , f(@’),a l 2 ,a,,, and a G E for the HBr + (Pr),NBr + H,O System at 25 “C m ,mol
cal kg-’
AGE,
2 . 3 0 2 6 ~ ~- e~a ~ 0.05 0.7683 0.9775 0.2092 0.1 0.6791 0.8220 0.1429 0.25 0.5414 0.7090 0.1677 0.50 0.4310 0.6703 0.2393 1.0 0.3247 0.6473 0.3226 1.5 0.2658 0.6397 0.3739 2.0 0.2244 0.6392 0.4118 From eq 11. From eq 15. kg-’
- 0.4
f(@’)
-a21
0.2598 -0.13 0.2211 -0.50 0.1613 -3.1 0.1134 -13 0.0672 -50 0.0416 -113 0.0236 -201
man,2061,2 from the theory of Guggenheirn;’l or gxMNin the Reilly, Wood, and Robinson23convention) is a constant that is characteristic of the mixtures but independent of the total molality (as opposed to a12,which is a function of the total molality). The values of the parameters of eq 12 have been furnished by Pitzer and Mayorga2 for (MX), and those of (NX) by P i t ~ e rwho , ~ ~obtained a reasonable fit up to 1.8 rn using the following constants: PoMx = 0.1960
P0NX =
P1Mx = 0.3564
PINX
-0.0580
= -0.4510
C@Mx= 0.00827 C@NX= 0.0469
-0.3
-0.2
/
- 0.1
After substitution, the resulting equation employing these values becomes f(@O)
+ 0.8074 exp(-2m”)
= 0.2540 - 0.03863m
(14) The results off(+”),0, a12(from Table I, with the first three values from the linear plots and the remaining four from the nonlinear plots), at each molality, are listed in Table 111. It is known7that the emf of cell I is a function of Om. Hence, the weighted average value of O(apparent) = -0,3428 has more significance at higher molalities than the unweighted average. It is interesting to note from Table 111,that the values of O for the present study decrease with an increase in m, whereas those for the HBr-NH4Br-H20 system show that this trend is reversed. This decrease in O a t higher concentrations implies the existence of less hard-core contact between the pairs of (PrI4N+and H+. It is also of some significance to calculate ~y~~ and compute the trace activity coefficients, y?, from the following expressions (using the value of O(actual) = -0.17 obtained from eq 18), where 9 is taken in account:
+
-2.3026~121= ( B M X - B@Nx) m(C@Mx - C@Nx) 8 and
+
(15)
log (%YYOJ = -ma12 (16) Equation 16 is obtained with the condition that y2 = 1 and hence y1 = ylt’ as in the linear form of eq 1. The values of aZ1and AGE (which are computed from eq 17) are also presented in Table I11 A G E = 2yly2RTm28 (17) where y1 = y2 = 0.5 and O = -0.17. As expected, the excess Gibbs free energy of mixing is significantly higher for the HBr-(Pr)4NBr-H20 system than that for the HBr-NH4Br-H20 system. This difference is due to cation-cation, cation-anion-cation, and hydrophobic interactions. All of the calculations discussed thus far were based on B ~ It - seems appropriate the premise that \ ~ H C , ( ~ ~ ) ~ N=+ ,0.
0.4 Figure 2.
A
1.2
0.8
1/2m,+QrI
+
In y l m , vs. the parameter ‘/&nH+ mBr-).
to compute e M N and \kMNX in the case where QMNX (a measure of the ternary interactions) is not equal to zero. P i t ~ ehas r ~ derived ~ the following equations, which enable one to do this: A In
yHBr/m(Pr),N+ = @H+,(Pr)aN+ ~H+)+H+,(~)~N+.B;
+
‘/z(mBr-
+
(18)
in which A In y H g r = In yexpt- In ycdd. The values for In yexptwere those obtained from eq 3, whereas those for In yc&d were evaluated from
In 7kBr = f Y + m iBYMX + Y2(B@NX - B%X)l + m 2[C’MX + Y2(c@N”,, - c @ M X ) l
(19)
where f’
= -A@[m”/(l
+ 1.2m”)l
+ 1.2m’h) + (2/1.2) In (1 (20)
and
A@= l / 3A7 = 0.392 (for H 2 0 a t 25 “C)
(21)
B d ~ and x B$M(are the same as those previously shown in eq 13 =
3/2c@MX
(22)
and BYMX = 2f1°MX + ( 2 f 1 1 ~ x / 4 m[ 1 ) - exp(-2m” )( 1 2m” - 2m)l (23)
+
Figure 2 represents the plot of the left side of eq 18 against the Q coefficient on the right. A straight line graph The Journal of Physlcai Chemistry, Vol SI, No. 5, 1977
394
D. Attwood
with the intercept 0 = -0.17 and slope \k = -0.15 was obtained. This is a useful result and verifies Pitzer’s equations, in that there should be a single value of 6 and \k which become nearly constants at higher molality. As evident from Figure 2, the values of A In THBr/mz are neglected in the molality range m = 0.05 to 0.5, since A In 7 H B r is small due to very little ternary interactions in this dilute region. As expected, the effects of the ternary interactions are greater with an increase in m, whereas the trend for 6 is just the opposite (i.e., less prominent at higher molalities). The cosphere effects are considered by Ramanathan, Krishnan, and Friedmanz6to have a larger role for aqueous solutions of tetraalkylammonium halides. The relatively high values of 6 at low m in the present study reflect the fact that interactions (which include interpenetration and entangling of the propyl chains) between H+ and (Pr)4N+are of increasing intensity. The value of 6 ~ + , ( p ~ ) ~decreases N+ from a higher value at low molality to a relatively constant value at high molality, whereas that for 0Ht,”pt6 indicates that the trend is reversed. The triple interactions \ ~ M M M , \k”~, and ~ X X Xare believed to be exceedingly small, but 9 m is of reasonable significance when (Pr)4N+,H+,and Br- ions come together at higher concentrations, since the propyl chains may be pushed aside to permit the closer approach of the Br- and H+ ions to the center of the substituted N+. Interpretations of this type of large-sized tetraalkyl hydrophobic cation-anion systems have been made by Rasaiah,%Frank and Evans,27 and Wood and Anderson.28 The tetraalkylammonium salts tighten the structure of water around them in a way simlar to some aliphatic hydrocarbons. Thus, there will be a large structural effect of (Pr)4N+(as compared with NH4+)in aqueous solution, which is dependent upon the structure-making properties of the (Pr)4N+ion.29930Similar studies for HBr + (Et),NBr + H 2 0 are currently in progress to gain more insight on the complex behavior of mixed aqueous electrolytic solutions.
Acknowledgment. The authors gratefully acknowledge the personal guidance and assistance provided by Professor K. S. Pitzer at the University of California (Berkeley),who not only supplied most of the various parameters required for many of the calculations contained herein, but also furnished several private communications without which this paper could not have been written. Thanks are also
extended to Professor R. H. Wood for his kind comments and constructive criticisms.
Supplementary Material Available: Tables I and I1 containing additional details concerning the evaluation of the emf data for individual total molalities of HBr (Pr)4NBr + H20 (3 pages). Ordering information is available on any current masthead page.
+
References and Notes (1) K. (2) K. (3) K. (4) K. (5) H.
S. Pitzer, J. Phys. Chem., 77, 268 (1973).
S. Pitzer and G. Mayorga, J. Phys. Chem., 77, 2300 (1973). S. Pitzer and G. Mayorga, J. Solution Chem., 3, 539 (1974). S. Pitzer and J. J. Kim, J. Am. Chem. Soc., 96, 5701 (1974). S. Harned and R. A. Robinson, “Multicomponent Electrolyte Solutions”, Topic 15,Vol. 2,“International Encyclopedia of Physical Chemistry and Chemical Physics”, Pergamon Press, Oxford, England,
1968. (6) R. N. Roy and E. Swensson, J. Solution Chem., 4, 431 (1975). (7) R. A. Robinson, R. N. Roy, and R. G. Bates, J. Solution Chem., 3, 837 (1974). (8) R. N. Roy, J. J. Gibbons, C. Krueger, and T. White, J. Chem. Soc., Faraday Trans. 7, 72, 2197 (1976). (9) S. Llndenbaum and G. E. Boyd, J. Phys. Chem., 64,911 (1964). (10) W. Wen, K. Miyajima,andA. Otsuka, J. Fhys Chem, 75, 2148(1971). (11) A. K. R. Unni, L. Elias, and H. I. Schiff, J. Phys. Chem., 67, 1216 (1963). (12) k. G. bates in “Determination of pH”, 2nd ed,Wiiey, New York, N.Y., 1973,pp 283,331. (13) H. B. Hetzer, R. A. Robinson, and R. 0. Bates, J. Phys. Chem., 66, 1423 (1962). (14) R. A. Robinson and R. H. Stokes in “Electrolyte Solutions”, 2nd ed, Butterworths, London, 1959, pp 481,438. (15) G. N. Lewis and M. Randall in ‘Thermodynamlcs”, revised by K. S. Pitzer and L. Brewer, McGraw-Hill, New York, N.Y., 1961,Chapter 23. (16) E. A. Guggenheim and J. C. Turgeon, Trans. Faraday Soc., 51, 747 (1955). (17) W. Wen and C. L. Chen, J. Chem. Eng. Dafa, 20, 384 (1975). (18) G. Scatchard, J. Am. Chem. Soc., 83, 2636 (1961). (19) H. A. C.McKay, Trans. Faraday Soc., 51, 903 (1955). (20) H. L. Friedman in “Ionic Solution Theory”, Interscience-Wiley, New York, N.Y., 1962. (21) E. A. Guggenheim, Trans Faraday Soc., 62, 3446 (1966). (22) P. J. Reilly, R. H. Wood, and R. A. Robinson, J. Phys. Chem., 75, 1305 (1971). (23) K. S. Pitzer, private communication. (24) K. S. Pitzer, J. Solution Chem., 4, 249 (1975). (25) P. S. Ramanathan, C. V. Krishnan, and H. L. Friedman, J. Solution Chem., 1, 237 (1972). (26) J. C. Rasaiah, J. Chem. Phys., 52, 704 (1970). (27) H. S. Frank and M. W. Evans, J. Phys. Chem., 13, 507 (1945). (28) R. H. Wood and H. L. Anderson, J. Phys. Chem., 71, 1871 (1967). (29) W. Y. Wen and S. L. Saito, J. Phys. Chem., 66, 2639 (1964). (30) R. L. Kay, T. Vituccio, C. Zarvoyski, and D. F. Evans, J. Phys. Chem., 70, 2336 (1966);R. L. Kay and D. F. Evans, ibid., 70, 2325 (1966).
Monomer Concentrations in Binary Mixtures of Nonmicellar and Micellar Drugs D. Attwood Pharmacy Depatfment, University of Manchester, Manchester MI3 9PL, England (Received September 15, 1976)
Aqueous mixtures of (a) two nonmicellar antiacetylcholine drugs (propantheline bromide and methantheline bromide) and (b) a micellar antiacetylcholinedrug (adiphenine hydrochloride) in combination with a nonmicellar drug (propanthelinebromide) have been examined by light scattering methods. Limiting monomer concentrations, mLon,were determined either from inflections in the light scattering plots or by integration of the light scattering - 1)d In c (where M and Mappare the monomer and apparent aggregate data according to In x = JOC{(M/Mapp) weight, respectively,and x is the weight fraction of monomers). The variations of mLonwith the composition of propantheline-methantheline mixtures could be predicted using equations derived for ideal mixing of micellar surfactants. Appreciable nonideality of mixing was indicated for the adiphenine-propantheline systems. Studies of mixtures of ionic hydrocarbon chain surfactants in aqueous solution have led to the general conclusion that the mixed micelle may be regarded as an ideal solution of its component~.l-~Critical micelle The Journal of Physical Chemistv, Vol. 8 1, No. 5, 1977
concentrations (cmcs) of the mixtures fall between values of the pure components and the variation of cmc with solution composition may generally be predicted on the assumption of ideality of mixing.
