Table VI. Determination of Cadmium in 1M HNOa (Type I Polarograms) Cadmium taken, mmoles Cadmium found, mmoles 0.0211 0.0210 0.05288 0.0530 0.106 0.105 0 . I58 0.158 0.211 0.214 Std dev (relative) 0.96%
to test this hypothesis was cadmium in 1M nitric acid. Figure 5 shows a comparison of conventional and Type I polarograms for the cadmium analysis; the results are given in Table VI. Although the Kalousek technique does not offer any ad-
vantages over square-wave and pulse polarography for routine applications, this technique appears to have real value in its application to electrochemically irreversible systems. For example, Matsuda (7) has shown that the anodic current observed in Type I polarography is a direct measure of the quantities 01 and kahfor the oxidation process; thus, in principle, these quantities can be directly obtained from the polarogram. As another example, anodic waves have been observed [e.g., for Eu(III), Cr(III), and Ni(1I)I at potentials widely separated from the reduction waves. Analysis can thus be based on measurement of the anodic current in those cases where the reduction waves are ill-defined or masked by the discharge of hydronium ion.
RECEIVED for review May 31, 1967. Accepted August 17, 1967. Work supported by Contract AT(07-2)-1 with the U. S. Atomic Energy Commission.
tentismetric Study of Base Strengths in the Binary Solvent, cid-p-Dioxane Orland W. Kolling and D. Allan Garber Chemistry Department, Southwestern College, Winfield, Kansas 67156 The indicator function of the glass electrode in acetic acid-p-dioxane i s identical to that in anhydrous acetic acid, and the glass-calomel pair is precisely responsive within the mixed solvent mole fraction range from 0.45 t o 1.00 in acetic acid. Increases in the apparent base strengths of strong and weak bases are observed when half-neutralization potentials in the binary solvent are compared to those in pure acetic acid. These changes appear to arise from two sources involving the p-dioxane content of the solvent: a positive shift in the standard potential for the cell; and the repression of ion pair dissociation for both the perchloric acid titrant and the base perchlorate salt with decreasing dielectric constant. Within the solvent mole fraction region considered, the value of KE for both strong and weak bases is independent of the amount of Pdioxane present in the mixed solvent.
NONAQUEOUS TITRATIONS of nitrogen bases in the presence of p-dioxane as the major solvent component or as the medium for the perchloric acid titrant have been analytically important for several years. Early methods of this type included the titration of aliphatic amines by Fritz ( I ) , and the determination of hydrohalide salts of organic bases by Pifer and Wollish (2). An equal molar mixture of p-dioxane and formic acid was found by McCurdy and Galt (3) to be a more effective medium than glacial acetic acid for the conductometric detection of the titration end point for weak bases. More recently, Puthoff and Benedict ( 4 ) demonstrated the suitability of perchloric acid in p-dioxane as a titrant for the potentiometric titration of high molecular weight amines and their salts.
(1) J. S.Fritz, ANAL.CHEM., 22, 578 (1950). (2) C . Pifer and E. Wollish, Ibid.,24, 300 (1952). (3) W. McCurdy and J. Galt, Ibid.,30, 940 (1958). (4) M. Puthoff and J. Benedict, Ibid.,36,2205 (1964). 1562
e
ANALYTICAL CHEMISTRY
The apparent strength of weak bases is increased in p dioxane media compared to that in solvents of higher dielectric constant; however, the solvent parameters responsible for this effect have not been identified. The extensive studies by R. M. Fuoss (5) on the conductance of salts have shown that ion pair association increases nearly predictably with decreasing dielectric constant in binary solvents which are largely p-dioxane. On the other hand, specific solvation of ions by p-dioxane can compete with the influence of the dielectric constant upon association equilibria (6). The intent of the investigation reported herein was to determine what solvent influences are exerted by p-dioxane upon the potentiometrically measured basicity of nitrogen bases and periodic group Ia acetates. Since reliable basicity constants are available for a wide range of compounds in anhydrous acetic acid, the addition of p-dioxane to the solvent permits a more exact evaluation of its effect upon the apparent base strength. Changes in the e.m.f. for the glass-calomel electrodes in acetic acid-p-dioxane were determined for solutions of perchloric acid, as well as for the four common reference bases used in acetic acid : potassium hydrogen phthalate; sodium acetate; sodium salicylate; and 1,3-diphenylguanidine. Additional strong and very weak bases (in acetic acid) included in this work are listed in Table I. For the two-component solvent, the dielectric constant interval extended from 3.7 to 6.24 (acetic acid) at 25" C.
EXPERIMENTAL Apparatus. All emf measurements were made with a Leeds & Northrup model 7401 pH meter equipped with the standard calomel and glass electrodes. Because of the slow response of the electrodes in p-doxane media, equilibrium ( 5 ) T. Fabry and R. Fuoss, J. Phys. Chem., 68,971 (1964). ( 6 ) J. B. Hyne, J. Am. Chem. SOC.,85, 304 (1963).
Table I. Dissociation Constants of Bases in Acetic Acid at 25°C (CE = 0.0040M)
-2
0 c3 0
-.I
-3 300
400 MV
Figure 1. Effect of sodium acetate concentration (C) upon the emf of the glass-calomel electrode pair in mixed solvents having acetic acid mole fractions of: (1) 1.00; (2) 0.931; (3) 0.894; (4) 0.692; and (5) 0.599
potentials were obtained only after 40 to 60 minutes. Solutions were stirred intermittently before each measurement, and the temperature was 25" f 1" C. Mean potential values listed in the tables are derived from at least three measurements on individual solutions and have a maximum uncertainty of =tl mV. Results on duplicate solutions of the same solute-solvent composition are reproducible to = t 2 mV. All of the emf values for the electrode pair are negative in acetic acid-p-dioxane. Solvents. Reagent grade glacial acetic acid was dehydrated with acetic anhydride by the method of Tappmeyer and Davidson (7). The center 7 5 % cut of distillate had a corrected boiling range of 117.5"-118" C. Water and peroxides were removed from reagent grade p-dioxane by the alumina column chromatographic procedure of Dasler and Bauer (8). The maximum water content of the solvents determined by Karl Fischer titration was: 0.002% in acetic acid and 0.0012% in p-dioxane. The presence of water at this concentration level is without significant effect upon the potentiometrically determined pH(H0Ac) for solutions of bases alone and base perchlorate salt mixtures in acetic acid media (9). Solutions. Stock solutions of reagent grade bases were prepared at the 0.1M level in acetic acid and standardized potentiometrically, except for the three weakest bases. (Solutions of the latter were prepared determinately.) The acetic acid solution of perchloric acid was made anhydrous by the usual method (IO), and, after standing at room temperature for six weeks, it was standardized against potassium hydrogen phthalate. The half-neutralized bases and the perchlorates of lithium and sodium were obtained in solution by exact titration with standard perchloric acid. Solutions of the solutes in the mixed solvent, acetic acidp-dioxane, were prepared volumetrically at 25" C., using burets protected with drying tubes, and emf measurements were made immediately after dilution. The basicity constants of all bases were re-determined, using the comparative method of Kolling and Lambert (11). (7) W. Tappmeyer and A. Davidson, Inorg. Clzem., 2, 823 (1963). (8) W. Dasler and C. Bauer, IKD. ENG. CHEM.,ANAL.ED., 18, 52 (1946). (9) I. M. Kolthoff and S.Bruckenstein, in "Treatise on Analytical Chemistry," Pt. I, Vol. 1, Interscience, New York, 1959,pp. 524-8 and 506-8. (10) J. S. Fritz, "Acid-Base Titrations in Nonaqueous Solvents," G. Frederick Smith Chemical Co., Columbus, Ohio, 1952, p. 13. (11) 0. Kolling and J. Lambert, Inorg. Chem., 3,202 (1964).
Base emf (mV) PKB 49 1 10.50 Acetamide 500 10.96 Acetanilide N,N-Dimethylaniline 395 5.55 387 5.15 1,3-Diphenylguanidine 420 6.79 Lithium acetate 489 10.40 1-Naphthylamine 405 6.10 Potassium acetate 415 6. 58a Sodium acetate 384 5.00 Triethylamine 479 9.89 Triphenylphosphine 486 10.24" Urea 4 Dissociation constants used as standards and reported from potentiometric measurements by S. Bruckenstein and I. M. Kolthoff (13).
Sodium acetate and urea served as standards, and the mean values based on three results for each base are listed in Table I. Although measured at a higher concentration than previously, the ~ K values B for the bases reported before (LiOAc and KOAc) agree within k0.05 unit. RESULTS AND DISCUSSION
Any interpretation based upon the measured emf from a cell composed of the calomel reference electrode, a test solution, and the glass electrode, in any nonaqueous solvent requires the identification of: the nature of the indicator electrode response, solute effects upon the cell potential, and the solvent influences on the total cell reaction. Electrode Response. In glacial acetic acid, the indicator function of the glass electrode has been shown to be equivalent to the hydrogen or chloranil electrodes (12), and the appropriate form of the Nernst equation for a solution of a base is Equation 1 derived by Bruckenstein and Kolthoff (13).
EB
=
(E'Gc f EJ f RT 7 In Ks
- RT - In KECB 2F
(1)
refers to the total E" for the electrode pair, and the other symbolism is that of the latter authors in which K, is the autoprotolysis constant of the solvent, Ej the liquid junction potential, CE the total molarity of base, and KB the basicity constant. The prediction that EB is a linear function of the In CB provides a convenient test of the electrode response in acetic acid media. The corresponding dilution cs. emf plots for sodium acetate were determined in four acetic acid-pdioxane solvents of fixed compositions, and these lines shown in Figure 1 have the slope of 0.0295 f 0.0005 volt per tenfold dilution at 25" C. Because solvent mixtures high in p-dioxane were quite sensitive to static charge effects in the room, reproducible potential readings could not be obtained for solvents having a mole fraction greater than 0.55 in p-dioxane. Thus, the low dielectric constant range to which the glass-calomel electrode pair was restricted includes the interval 3.7 to 6.24 (14). Base Solutions. The inflection portions of potentiometric titration curves for halide salts of organic bases in acetic E"GC
(12) J. Higuchi, M. Danguilan, and A. Cooper, J . Phys. Chem., 58, 1167 f,1954). ~ . .,. .
(13)s. Bruckenstein and I. M. Kolthoff. J. Am. Chem. Soc.. 78. . 2974 (1956). (14) 0. Kolling and C. VanArsdale, Trans. Kansas Acad. Sci., 68, 65 (1965). I
VOL. 39, NO. 13, NOVEMBER 1967
a
,
1563
-1
600
1
11
[
*
#
I
,
,
,
,
,
I
,
,
I
1.0
X
.I
0.5
I.0
0.5
X
Figure 2. The change in cell potential for 0.0040M bases with mole fraction (X) of acetic acid in the binary solvent
Figure 3. Trend in the half-neutralization potential (HNP) for 0.0067M bases and their perchlorate salts with changing mole fraction ( X ) of acetic acid
The bases are: (1) acetanilide; (2) acetamide; (3) urea; (4) triphenylphosphine; (5) lithium acetate; (6) sodium acetate; (7) potassium acetate; (8) N,N-dimethylaniline; (9) 1,3-diphenylguanidine; and (10) triethylamine
'The bases are: (1) acetanilide; (2) acetamide; (3) urea; (4) lithium acetate; (5) sodium acetate; (6) N,N-dimethylaniline; (7) 1,3-diphenylguanidine; and (8) triethylamine
acid-p-dioxane are lengthened and made more abrupt with increasing p-dioxane content (2). Since the H X from the salt is initially removed by forming covalently bonded HgXz in this method, the titration reaction is that of the free base with perchloric acid. [p-Dioxane is an inert solvent toward mercury(I1) halides, so that no consideration needs to be given to these solutes (l5),] One interpretation of the observed sharpness of the end point is that p-dioxane increases the apparent strength of the weak bases. However, according to Equation 1 above, at a given CB the measured potential of a base solution will reflect the effect of the solvent composition upon K,, E3,and E o , as well as upon KB. It is probable that K, and E* will be the least variables of the four in acetic acidrich mixtures. The gross influence of the mole fraction of acetic acid in the solvent upon the emf of the glass-calomel electrodes at a fixed concentration (0.0040M) of the base is shown in Figure 2. The plots are all linear with an essentially constant slope of 179 + 2.1 mV., and the systematic shift in potential is in the same direction as that found by Pifer and Wollish ( 2 ) from titration curves. Since the alterations in titration curves with increasing p dioxane content can include the influence of the solvent upon equilibria involving perchloric acid as well as the base, the cell potential was measured as a function of solvent composition for a constant concentration of acid (0.0040M). The appropriate form of the Nernst relation for pure acetic acid as the solvent is Equation 2 (13).
The values of E'GCand the dissociation constant KHC~O, would be expected to be the most responsive to the addition of p dioxane, and the representative data are included in Table 11. Although not shown herein, a plot of emf us. mole frac(15) A. Tourky et al., J. Phys. Chem., 64,565 (1960).
1564
*
ANALYTICAL CHEMISTRY
tion of p-dioxane is definitely nonlinear and the slope of the tangent becomes smaller with increasing p-dioxane. (The maximum limiting slope in solvent compositions approaching pure acetic acid is 95 mV.) Half-Neutralization Potentials (HNP). An empirical correlation between the pKB values for nitrogen bases in aqueous media and their half-neutralization potentials in nonaqueous solvents of lower dielectric constant has been established for both protonic and aprotic solvents. Representative studies (16) in which the glass indicator electrode has been used with perchloric acid as the titrant include these solvents: acetic anhydride (D = 2 2 ) ; glacial acetic acid (D = 6.2); acetone (D = 20.7); acetonitrile (D = 3 6 ) ; and nitromethane (D = 38). Generally, potentials are reported as differences with respect to diphenylguanidine as the reference base. In glacial acetic acid the HNP's can be a valid measure of the PKB's of a series of bases only if the stoichiometric concentrations of the titrated bases are the same. Also, Equation 3 derived by Bruckenstein and Kolthoff (13) demonstrates that the potential of a cell containing a base and its perchlorate salt is dependent upon the dissociation constant (KBc~o~) of the salt. RT EB,BC= I O(E'w ~ Ed InK, f
+ +y RT
- In
(KBCB
F
KBCIO CBC10a)1'2 ~ KB CB
(3)
At the condition of half-neutralization of the base (CB = CB~lOa), Equation 3 reduces to Equation 4.
RT
- In
F
(KB
+ K B C ~ O J-" ~-RT 2F In C B KB
(4)
(16) C. A. Streuli, ANAL.CHEM., 30, 997 (1958); LW.,31, 1652 (1959); L. Chatten and L. Harris, Zbid., 34, 1495 (1962); R. L. Adelman, J. Org. Chem., 29, 1837 (1964); H. K. Hall, J. Phys. Chem., 60, 63 (1956).
Table 11. Potentials for Some Solutions of Perchloric Acid and Salts in Acetic Acid-p-Dioxane Solute (0.0040M) He104 LiC104 NaClOd KHPhthalate Na salicylate
XHOAo
= 1.00
752 mV 548 556 402 414
0.967 749 541 549 393 404
0.894 740 527 537 377 387
For strong bases, KB = KBcIo4,and EEXPbecomes proportional to In KB. On the other hand, weak bases have KB < KBoi06, and EHNP contains the contributions of both constants. The addition of p-dioxane to an acetic acid solution of a base and its perchlorate can alter the EHXP through the changes in the values of both KB and KBcIo~, as well as through influences upon E", E,, and Ks. However, in contrast to solutions of bases alone, the influence of the solvent composition upon EHxp is not identical for all base-salt pairs, but depends upon the relative magnitudes of the dissociation constants of the solute pair. The net effect is shown by Figure 3 in which E H N p DS. X H O A ~is plotted. The curves are not linear (except for acetanilide), and for the stronger bases, the slopes of limiting tangents to the curves in the low p-dioxane solvents are similar or slightly lower in magnitude to the slope of the lines in Figure 2. For the half-neutralized very weak bases, EHNPdecreases only slightly with increasing p-dioxane content of the solvent. Therefore, it appears that the solvent is greatest where KB and KB01o4 effect on the measured EHNP are comparable and least where the dissociation constant for the base is the smaller one. The net result on the titration curves is that the differences in the apparent basicity between the strong and weak bases are enhanced by the addition of p-dioxane through the concomitant influence of KBoio4 and KB upon EB,BGIO~. Significant changes in the emf for 0.0040M solutions of salts alone occur with increasing p-dioxane in the mixed solvent. (Data are listed in Table 11.) The potentials are more negative than EHNP and are influenced in a similar manner to EHNP with increasing p-dioxane content. Solvent-Solute Interactions. The acetic acid-p-dioxane solvent is a protonic acid-Lewis base pair, having the proton donor as the more polar component. Although restricted to a short and low dielectric constant range, this mixed solvent is the formal analog of the system, water-p-dioxane. Consequently, it is appropriate to examine the emf data for parallel influences from the less polar solvent. In such cases theoretical treatments for aqueous mixtures have correlated a given solvent parameter to the changes in the E" value. Because of the several unknowns involved, no attempt was made to evaluate E" in p-dioxane-acetic acid; however, as noted above, the effect of the solvent upon this quantity is one term contributing to the measured potential of the glass-calcomel electrode pair. The hydrogen electrode with HC1 in the p-dioxane-water solvent system has been discussed by Amis (17), using the Born relationship which requires that E" decrease linearly with l/D. The failure of the predicted change in E" to be exactly followed in the low dielectric constant region has been attributed to the selective solvation of the solute ions by the more polar component. However, the simple "sphere in (17) E. S. Amis, J . Electroanal. Chem., 8,413 (1964).
0.857 739 521 530 368 379
0,782 732 513 520 352 365
3,692 730 505 513 334 349
0.599 725
...
507 320
336
continuum" electrostatic model of Fuoss and Onsager has been verified for ion pair association of salts in ideal binary solvents containing p-dioxane and having dielectric constants as low as 4 (18). If the influence exerted by the solvent medium upon solutions of perchloric acid (as a strong acid) is predominantly an electrostatic contribution to E" for the glass electrode, then the measured E H C ~ should O ~ be approximately linearly related to l / D . Although the graph is not included here, no correspondence was found for these two quantities in acetic acid-p-dioxane. This is not unexpected, since nonideal dielectric constant and total polarization us. mole fraction curves indicate that complex solvent-solvent interactions occur in this medium (14). One consequence of these interactions is that the the macroscopic dielectric constant has decreased by only 0.34 unit when the p-dioxane mole fraction reaches a value of 0.20, and D is essentially unchanged from that of pure acetic acid when p-dioxane is added up to 0.10 mole fraction. Therefore, within the upper, nearly constant Drange from 5.9 to 6.24 (XHOA~, = 0.80 to l.OO), it is a reasonable assumption that p-dioxane has no significant electrostatic influence on ion pair dissociation constants of HClO,, BClOd, and HOAc. Feakins and French (19) have concluded that the Born relation is not followed by the Hz-HClelectrode in most aqueousorganic solvents having low water contents. They have derived an alternate equation correlating the change in E" to the mole fraction or volume fraction of water in the mixed solvent. Their treatment is a thermodynamic one that assumes the difference in the partial molar free energy of the solvated ions of the solute in the two solvents depends only on the ionic concentrations, and the partial molar free energy of the more polar solvent component (water) is adequately expressed by its mole fraction (or volume fraction), Since the model for the solvated ion requires that only the more polar solvent is firmly coordinated to the solute ions, the predicted proportionality between E" and log Xxz0 does not apply to those solvent mixtures approaching the condition of x H 2 O = 0. The upper D-range for acetic acid-p-dioxane solutions of perchloric acid in contact with the glass electrode parallels the model used by Feakins and French for the hydrogen electrode in water-g-dioxane. The appropriate form of the Feakins-French equation is Equation 5 in which X is the mole fraction and (E")srefers to the standard potential in the mixed solvent.
+
= (E')HOA~ RT In XHOA~
F
Since the total E"OCfor the glass-calomel electrode pair in a (18) R. Fuoss and C. Kraus, J. Am. Chem. SOC.,79, 3304 (1957); A. D'Aprano and R. Fuoss, J . Pltys. Chem., 67,1871 (1963). (19) D. Feakins and C. French, J. Chem. Soc., 1957,2581. VOL. 39, NO. 13, NOVEMBER 1967
1565
Table 111. Potential Differences Corrected for (E'Gc Ej) in Solvent Mixtures
+
I
AEENP
7004
D (25")" 6.13 6.02 5.91 5.43 4.85 4.55 4.08 3.70 a Dielectric constants values were determined from D calibration curves, using data published earlier (14). XHOAa
rl
I
(DiphenylA E H c ~ omV ~ , guanidine), mV 4 0 8 1 10 2 22 5 31 11 38 ... 19 61 25
0.857 0.817 0.782 0.692 0.599 0.550 0,478 0.446
.
I
.
us. X H O A ~
tensive ( K 1: lo2), according to nmr measurements (20), and, by analogy to the p-dioxane-water system, the result is a 300 decrease in the value of Ks. However, since Ks in pure acetic 0 - 0.3 LOG X acid is small (E 1O-l6), this is a minor variable compared to the dissociation of the acid. Solvent exchange of the type in Figure 4. Trend in cell potential for solutions as a function of Equation 7 has been identified in p-dioxane-water solutions the logarithm of the mole fraction of acetic acid in the binary of protonic acids ( 2 4 , and the p-dioxane-solvated acid has the solvent smaller Kd value. The combined effect of such decreases in The curves are for the solutes: (1) perchloric acid (0.0040M); and K,, K H C ~and O ~ ,KBclo4is to decrease the contributions from half-neutralized bases (0.0067M), (2) acetamide, (3) urea, (4) lithium these terms with increasing mole fraction ofp-dioxane. These acetate, (5) sodium acetate, (6) N,N-dimethylaniline, (7) 1,3-diphenylguanidine, and (8) triethylamine. Dashed lines are the limitinfluences act independently Qf E'GC to give a smaller EHCIO~ ing slopes or EHHP than that predicted by the proportionality between the standard potential and log XHoaC. This is the trend found in Figure 4 as the mole fraction decreases below about 0.85 two-electron process is involved in the measured E, Equation in acetic acid. 2 now becomes Even though the solvent-solvent interaction in Equation 8 produces a negligible change in dielectric constant for solvent mixtures containing little p-dioxane, the central solvent composition region (XH0a,from 0.30 to 0.75) exhibits a regular, nearly ideal, increase in D with increasing mole fraction of the more polar component (14). It is within this solvent range that one might expect to identify any influence from the If the ion pair separation constant, KETcloI, is not the major variable in the isodielectric constant range, then E H Cwill ~ ~ ~ dielectric constant alone upon solute ion pair equilibria. The perchloric acid in acetic acid-p-dioxane system is the least be proportional to log XHOA~. The graph of the two variables complex equilibrium investigated and is suitable for this is given in Figure 4 for the total acetic acid mole fraction range. purpose, For a given solvent composition, S , a correspondThe limiting tangent to the curve in the X H o ~interval , from A E ~ c i ocan ~ be calculated as the difference between ing 0.86 to 1.00 has a slope of 0.026 volt rather than the expected (EHC~O~)HOA~ (EHcI~,), by applying Equation 6 to each solu0.0295 volt. Although the related salts listed in Table 11 tion. At a constant solute concentration show the same general qualitative trend in emf as does HC104, the application of the Feakins-French relationship to basebase perchlorate solutions is more relevant. The mean value of the limiting slope of EHNP GS. log XHOA~ (as XHOA~ + 1) is 0.0306 i 0,0011 volt for the five stronger base-perchlorate pairs. and it follows from Equation 9 that A E H c ~iso ~ proportional Beyond the nearly isodielectric constant region in acetic to Aln K H ~ 1 0 4 . The term, (EoGC E,)$ in Equation 6 was acid-p-dioxane, the changes in E H C I and O ~ EHNP reflect the determined graphically from the extension of the Feakinscomposite influence of p-dioxane upon both E'GC and the disFrench theoretical tangent to a curve like that in Figure 4. sociation constants. Competitive solvation may take place Representative data for the most precise set of potentials are as the p-dioxane content increases. This can be illustrated listed in Table 111. by two possible equilibria in perchloric acid solutions. According to the Fuoss-Onsager-Bjerrum theory (18), the logarithm of the association constant (KA)for the ion pair x(HOAc). HLC104y O-(CHrCH2)rO derived from a 1-1 electrolyte increases by proportion to the [O(CHn-CH&O]y* H'C104xHOAC (7) reciprocal of the dielectric constant. When applied to EquaHOAC O-(CH~-CHZ)~Q ;t O(CH-CH~)~-O*HOAC (8) (20) N. Muller and P. Rose, J . Phys. Chem., 69,2564 (1965). (21) E. Grunwald et al., J. Am. Chem. SOC.,82, 5801 (1960); The solvent-solvent association reaction appears to be exD. J. Glover, Ibid.,87,5275 (1965).
+
+
+
1566
e
ANALYTICAL CHEMISTRY
+
Table IV. Solute
I
LiC104
NaC104 Diphenylguanadinium perchlorate
50
w
Changes in Cell Potential for Perchlorates (C = 0.0040M) in Acetic Acid-p-Dioxane A E B c ~ omV ~ , in solvents having X H O A=~ 0.967 0.894 0.857 0 782 0.692 7 21 27 35 43 7 19 26 36 43
22
6
I
29
38
0.599
43
... 49
52
0.030 volt for all 10 bases. Therefore, from Equation 10 obtained by applying the Feakins-French relationship to Equation l ,
EB = (E'ac
+ E ~ ) H o+A ~
(1
10 0.2 0
0.2 5
Figure 5. The change in cell emf (AE) in mV, after correction for (E'Gc Ej), with decreasing dielectric constant ( D ) . Curve (1) is the data for perchloric acid and (2) is that for half-neutralized l,3-diphenylguanidine
+
tion 9, this relationship predicts that A E H c ~ will o ~ be proportional to l/D. Figure 5 represents this function over the total p-dioxane-acetic acid dielectric constant range included in the present study, and it will be noted that the plot is linear over the broad interval from about 3.70 to 5.91 in dielectric constant. The change in the dissociation of HCIOl can be illustrated, using data for X H ~ = ~ o0.692 and 0.446 (on the linear portion of Figure 5) ; the experimental results substituted in Equation 6 give a -Aln K H C ~ofO1.08 ~ unit. The same theoretical approach cannot be used for the solutions of salts alone without qualification, because the measured E includes the solvent influence upon the unknown contribution from acetolysis. On the other hand, although acetolysis will not be the principal variable involved in EHXP for baseperchlorate salt solutions, the situation is still quite complex because of the effect of the solvent uEon the dissociation constants in Equation 4. A partial simplification of the latter solute system can be achieved by taking the special case in which KB and KBcio4 are similar, but both are much greater than K,. It follows from Equations 4 and 9 that AEHNPis proportional to Aln (2KBC~~a)llZ/KB, since BC104 is usually the stronger electrolyte. Half-neutralized diphenylguanidine fulfills these restrictions, and the plot of AEHNP us. 110 in Figure 5 is linear over the same dielectric constant region as is the corresponding function for perchloric acid. If the data from Figure 2 are plotted in the form E B us. log XHOA~, the series of parallel lines have a constant slope of
it is clear that the ratio, KS/KB1", is unchanged by the addition of p-dioxane to a solution of fixed molarity of base. Likewise, the shift in AEanp with solvent composition noted O~, the magnitude above reflects the change in K B C ~ although of the net effect on EHNP is still determined by the relative values of KB and KBOIO~. Another approach to testing this conclusion involves the shift in the potential of the electrode in solutions of salts with solvents having variable p-dioxane content. Kolthoff and Bruckenstein (9) have shown that acetolysis of perchlorate salts in pure acetic acid is insignificant and that the proton activity is independent of the salt concentration. For this case, Equation 11 applies.
In a manner analogous to the treatment that was used on a perchloric acid solution above in the mixed solvent, it can be shown that the quantity, AEBc~o~, is proportional to A h KHclo4for a given perchlorate. The important consequence of this is that AEBc~04 will have the same value for all perchlorates at a fixed solvent composition only if K,IKB is ino~ dependent of the p-dioxane content. The A E B D ~ values obtained from (EBCIO~)HOA~ - (EBCIOJS for three representative unsolvolyzed perchlorates are listed in Table IV, and, for a given X E O AAEB01o1 ~, is a constant quantity. Athough it follows from Equations 9 and 11 that A E B o ~ O ~ and A E ~ c l owill ~ be the same at a constant X H ~ Athe ~ ,agreement between these two quantities is not close. However, this does not invalidate the conclusion concerning the Ks/KB ratio, nor the effect of solvent composition upon the halfneutralization potential.
RECEIVED for review June 23, 1967. Accepted August 22, 1967. We are indebted to the National Science Foundation for financial support of this project by a Supplementary Grant to GE-2744, Academic Year Extension of the Research Participation for College Teachers Program.
VOL. 39, NO. 13, NOVEMBER 1969
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