218
RICHARD E. LINDSTROM AND HENRY E. WIRTH
data for the methylphenalenyl radical are the large tions, which are positions of negative spin hyperfine splittings for the methyl protons. The are virtually unchanged by the methyl substituent. magnitude of the methyl splitting is approximately the The hyperfine interactions a t the remaining active same as that for the ring protons in unsubstituted positions are altered only slightly by the 1-methyl subphenalenyl. Large methyl proton splittings have been stituen t. observed in methyl-substituted aromatic i o n ~ . ' ~ J ~ The phenyl substituent in I11 effects a slight reducThis effect has been described in terms of a combined tion in the magnitude of the hyperfine interaction at all inductive and hyperconjugation mechanism. The the phenalenyl ring positions. The splittings by the large methyl splitting in I1 demonstrates the importance phenyl protons are in turn quite small, a result which is of these mechanisms in aromatic neutral radicals. consistent with the sterically enforced nonplanar conAn examination of the coupling constant data for I1 formation of the phenyl group. shows only a small perturbation by the methyl group on the unpaired electron distribution in the remainder Acknowledgments. We wish to thank Mrs. S. B. of the molecule. The splittings a t the inactive posiWallon for synthesizing the compounds.
Estimation of the Bisulfate Ion Dissociation in Solutions of Sulfuric Acid and Sodium Bisulfate by Richard E. Lindstrom and Henry E. Wirth Department of Chemistry, Syracuse University, Syracuse, New Y O T ~13210 (Received August 7, 1068)
Young's rule was applied to the observed mean apparent molal volumes of sulfuric acid and sodium bisulfate to obtain estimates of the dissociation quotient (Qv) in the volume ionic strength (g") range 0-4. The results in sulfuric acid solution are given by the equation log Qy log 0.0102 -p 2.036fi,'/2 1.376~" 0.8862~.,s/~0.2171fiv2and in sodium bisulfate solution by the equation Iog Qy = log 0.0102 2.036pV'/$ 1 . 5 4 3 ~ "f 0.8297p,?/2 0.1703gv2. The volume change at infinite dilution ( W )for the process H+ 502- -+ HSOawas found to be 21.6 ml.
+
-
+
+
-
Cz and C3 are the molar concentrations of the dissociated and undissociated species, respectively. I n terms of the degree of dissociation ( a ) , eq 1 becomes
Some years ago Klotz and Eckertl investigated the dissociation of the bisulfate ion in sulfuric acid solutions utilizing apparent molar volumes. Their approach was to assume that a bisulfate solution is a mixture of two electrolytes : the completely dissociated species, H +, H+,SOd2-, and the undissociated species, H+,HSOe-. The observed or mean apparent molar volume, a, could then be expressed as a function of the mole fraction and apparent molar volumes of the two solute specieg. This relationship is essentially that defined more explicitly by Young and Smith2 and tested by Wirth and coworkers.a It is
Simultaneous solution of eq 2 and 3 yields an CY which may be used to calculate the dissociation quotient, Qv, at the given ionic strength where
where CP is the mean or observed apparent molar volume of the solute at ionic strength pv, C#J2 is the apparent molar volume of H+,H+,S042- in a pure solution of the same ionic strength p,., and +3 is the apparent molar volume of H+,HS04- also in a pure solution a t ionic strength p".
(1) I. M. Klotz and C. F. Eckert, J . Amer. Chem. Soc., 64, 1878 (1942). (2) T.F. Young and M. B. Smith, J. Phys. Chem., 58, 716 (1954). (3) H.E.Wirth, R. E. Lindutrom, and J. N. Johnson, ibid., 67, 2339 (1963).
The Journal of Physical Chemistry
ch = a42
+ (1 - a)+3
(2)
The ionic strength a t a total solute molarity (C) is PV =
(1
+ 2a)C
(3)
219
ESTIMATION OF THE BISULFATE ION DISSOCIATION
Apparent molar volumes for solutions of varying bisulfate concentration were obtained using a dilatometric technique.8 I n the present investigation, a calibrated capillary was added to the dilatometer system to provide additional precision in measuring volume changes at low concentration. By careful control of the pressure ( h O . 1 mm) on the system and of the temperature of the thermostated bath (&0.0005”), the experimental uncertainty in the observed volume changes was estimated to be reduced to =k6 X 10-6 ml. This corresponds to an uncertainty of =!=0.06 ml in the molar volumes in the most dilute solution. The apparent molar volume, 0, of a given solution within the mixing chamber of the dilatometer is given by
IJF Figure 1. The bisulfate ion dissociation quotient (QY)aa a function of ionic strength in solutions of sulfuric acid and of sodium bisulfate (solid curves), compared with the results of C. F. Baes, Jr., J . Amer. Chem. Xoc., 79, 5611 (1957), of W. L. Marshall and E. V. Jones, J . PAys. Chem., 70, 4028 (1966), and of Klote and Eckert’ for sulfuric acid. The experimental points are the Raman results of Young in sulfuric acid (0)and in sodium bisulfate ( 0 )quoted by Baes.
Klotz and Eckertl used known values of Qyto establish +a in the concentration range 0-0.14pv. From 0.4 to 3 . 2 they ~ ~ found that values of Qv between 0.01 and 0.09 gave reasondble values for the apparent molal volume of H+,HS04-. They chose Qv = 0.03 as the best value. However, the Raman data of Young* give much higher values of QV in this concentration range (cf. Figure 1) and larger values of Cbs are therefore required. Thus either the slope of 43 vs. I.C,”~ is greater than that of a normal 1: 1electrolyte, or the value of $80 estimated by Klotz and Eckert is too small. In the present work we have found that both a larger slope and a larger value of $aO is required to give reasonable values of Q,. In this investigation the apparent molal volumes of both sulfuric acid and sodium bisulfate were obtained by density and dilatometric methods, with emphasis on the dilute concentration range (0.001-0.OlC).
Experimental Section Stock solutions of sulfuric acid and sodium bisulfate were prepared from CP chemicals. The stock sulfuric acid solution was analyzed by weight titration using a National Bureau of Standards standardized sulfuric acid solution as the reference standard. The stock sodium bisulfate solution was prepared by solution of sodium sulfate, previously dried at llOo, on a mole for mole basis in the stock sulfuric acid. Dilute solutions of both salts were prepared as required by weight dilution of the initial stock solutions. The density of each solutio? thus prepared was determined by the sinker method.6
(5) where 02 is the apparent molar volume of the stock solution, n2is the number of moles of solute in the chamber, and Avol is the volume change noted on mixing the volume of stock solution containing n2mol of salt with a known amount of water. The data obtained are given in Tables I and 11. Figure 2 illustrates the agreement of the experimental results of this investigation with the values obtained by Klotz and EckerL2
Results and Discussion Interpretation of the mean apparent molar volume of
an electrolyte solution by the mixture rule of Young requires knowledge of this property for the contributing salts. Thus it was necessary to evaluate the apparent molar volumes of the dissociated salt, X + , H + , S O P , and undissociated salt, X+,HS04-, as a function of ionic strength. Since direct experimental determination is not possible, the required information was obtained on the assumption that apparent molar volumes of electrolytes are additive, even to relatively high concentration. Evaluation of cp2 for X+,H+,AYO~~-.The apparent molar volumes of the theoretical, completely dissociated bisulfates may be represented by $2(Na+,H+,Sod2-)=
+ dHC1) - $(NaCl)
(6)
+ 24(HC1) - 2$(NaC1)
(7)
dNazSOJ $2
(H+, H +,S042-)
=
dNa2S04)
where each $ is the apparent molar volume of the respective salt at a given ionic strength. Utilizing these equations, the hydrochloric acid and sodium chloride data of Wirth6 and the sodium sulfate data of Gibsone T.F. Young, Rec. Chem. Prog., 12, 81 (1961). (6) H.E. Wirth and F. N. Collier, Jr., J . Amer. Chem. SOC.,72, 6292 (1960). (6) R. E. Gibson, J. Phys. Chem., 31, 496 (1927). (4)
Volume 73, Number 1 January 1969
220
RICHARD E. LINDSTROM AND HENRYE. WIRTH
Table I : Apparent Molal Volumes of
Table 11: Apparent Molal Volumes of Sulfuric Acid in Water
Sodium Bisulfate in Water m
C
Q
0 0.001019 0.002010 0.004848 0.011611 0.017461 0.028894 0.057435 0.085643 0 * 10000 0.11340 0.14073 0.22006 0.41510 0.59109 0.75073 0.89607 1.0291 1.1511 1.2636 1.3674 1.4523 1.4637 1.5512 1.5531 1.6365 1.6644 1.7143 1.7956 1.9492 2.1315 2.3514 2.6220 2.9627 3.4058 4.0040
0 0.001016 0.002004 0.004833 0.01 1574 0.017404 0.028792 0.057186 0.085203 0.099446 0.11273 0.13978 0.21803 0.40867 0.57846 0.73062 0.86759 0.99163 1.1043 1.2072 1.3014 1.3778 1.3882 1 4663 1.4679 1.5419 1.5666 1.6104 1.6816 1.8149 1.9707 2.1556 2.3786 2.6521 2 9961 3.4402
(12.86) 14.12 15.23 16.79 19.322 20.769 22.254 24.554 25.909 26.320 26.806 27.486 28.905 30.845 31.955 32.746 33.359 33.860 34.280 34.641 34.956 35.213 35.233 35.483 35.478 35.702 35 * 783 35.903 36.113 36.486 36.898 37.369 37.911 38 539 39.293 40.206
I
I
420
+ Avo
The Journal of Physical Chemistry
0.0 0.001257 0.002485 0.005998 0.009299 0.017159 0.023933 0.029823 0.034997 0.11470
0 0.001254 0.002478 0.005979 0.009270 0.017101 0.023847 0.029710 0.034859 0.11394
(14.08) 17.58 19.07 22.44 24.247 26.726 27.964 28.775 29.327 32.757
0.01347 0.05283 0.1147 0.3442 0.7917 1.4561 2 * 3369
0.01343 0.05259 0.1139 0.3591 0.7674 1.3774 2.1393
25.50" 30.66" 32.78" 35 * 02" 36.36" 37. 21" 38 08"
Q
I
limited ionic strength range, it is then possible to determine 43O for Na+,HS04- and H+,HS04-. Working first with sodium bisulfate, the approach was to pick both a 42a t some ionic strength below 0.04 and an observed apparent molar volume, @, a t a concentration, C, thought to approximate the same ionic strength. Equation 3 then gave an a, which on substitution into eq 2 gave the corresponding 43, The same steps were followed for sulfuric acid, using the identical ionic strength. The entire procedure was repeated as necessary to find 43 values of both solutes giving the best agreement in Av a t that ionic strength. The Av values obtained above were plotted against pV1/*(Figure 4). A line of slope 1.86, that of a 1:1
t
45
-
40
-
0
This uorh
+ Kldr ond Eoheri
(8)
where is the apparent molar volume of X+,H+, Sod2- a t infinite dilution and Avo is the change in apparent molar volume accompanying the process H+ Sod2-+ HS04-. Assuming Avo is independent of the second cation and that eq 8 holds over a
+
C
' Determined by the sinker method.6
were combined to obtain 42 for both theoretical salts. The results are given in Tables I11 and IV and in Figures 2 and 3. Because similar data for the HSOd- ion are not experimentally available, the direct approach could not be used for the undissociated species, Naf, HS04- and H+, HSO,-. Instead, the (b3 us. pvl/a curves were obtained by first determining the probable intercept of such a curve for each salt, then completing the evaluation using data for salts with analogous apparent molar volume properties. Determination of Avo. The apparent molar volume of X+, HS04-, a t infinite dilution qho, is given by 48' =
m
Figure 2. Experimental values for the mean apparent molal volume of sulfuric acid (a) us. the square root of the molarity and vs. the square root of the calculated volume ionic strength (dashed curve). These ionic strengths (,uv = (1 2a)C) are consistent with the values of a obtained from eq 11.
+
221
ESTIMATION OF THE BISULFATE IONDISSOCIATION Table 111: Ionization of HSO4- in Sodium Bisulfate
0 0.05 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0 0.0008681 0.003737 0.01695 0.04163 0.07890 0.1921 0.3532 0.5580 0.8045 1.086 1.411 1.772 2.169
Observed dissociation quotient.
0 0.02946 0.06113 0,1302 0.2040 0.2809 0.4383 0.5943 0.7470 0.8970 1.042 1.195 1,331 1.473
(34.46) 34.56 34.58 35.26 35.88 36.52 37.76 39.02 40.28 41.54 42.80 44.06 45.32 46.58
(12.86) 13.16 13.49 14.10 14.73 15.34 16.59 17.79 18.99 20.19 21.39 22.57 23.73 24.89
O(NaHS03
a
Q"
Qb
14.54 16.48 20.90 23.60 25.64 28.50 30.40 31.84 33.10 34.20 35.32 36.38 37.42
0.940 0.838 0.679 0.581 0.514 0.437 0.406 0.396 0.395 0.402 0.407 0.414 0.422
0.0128 0.0162 0.0243 0.0335 0.0430 0,0652 0.0980 0.145 0.207 0.293 0.394 0.518 0.668
0.0128 0.0158 0.0229 0.0319 0.0422 0.0679 0.1010 0.145 0.204 0.287 0.396 0.530 0.661
' Calculated using eq 15.
Table IV: Ionization of IIso4- in Sulfuric Acid +(H+,
+(H+,H",
PVlll
C
Ciia
HSOr-)
804'3
@(Hasor)
a
Qa
Qb
0 0.05 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0 0,0009038 0.004184 0.02186 0.05703 0.1093 0.2586 0.4591 0.7022 0.9756 1.279 1.618 1.990 2.387
0 0.03006 0.06468 0.1479 0.2388 0.3307 0.5085 0.6776 0.8380 0.9877 1.131 1.272 1.411 1.545
(35.68) 35.78 35.88 36.48 37.00 37.56 38.62 39 * 99 40.68 41.72 42.70 43.70 44.68 45.66
(14.08) 14.40 14.72 15.32 15.91 16.48 17.56 18.57 19.54 20.47 21.38 22.27 23.17 24.09
16.90 21.16 27.70 30.90 32.66 34.50 35.50 36.20 36.66 37.02 37.46 37.92 38.36
0.883 0 695 0.415 0.289 0.232 0.196 0.197 0.212 0.238 0.266 0,291 0.314 0.338
0.0128 0.0162 0.0219 0.0299 0.0407 0.0754 0.135 0.229 0.377 0.587 0.857 1.20 1.63
0.0128 0.0159 0.0233 0.0329 0.0451 0.0791 0.132 0.240 0.356 0.576 0.894 1.27 1.56
" Observed dissociation quotient.
Calculated using eq 14.
electrolyte, extrapolated through these points gave Avo = 21.6 ml, a value 1.4 ml greater than that reported by Klotz and Eckert.' Equation 8 gave 4 3 O for Na+, HSOI- and H+, HS04- as 34.46 and 35.68 ml, respectively. Evaluation of $3 for X + , HSOd-. Having established 4 3 O for H+,HSO4- and Na+,HS04-, it was expected that 43 at higher concentrations could be obtained by using HC104or HCI and NaC104 as model electrolytes (ie., a t a given ionic strength, 4(H+,HS04-) = 40(H+,HS04-) [#(HC104) - $o(HC104)]. Values of 43 thus obtained were found to approach the experimental values for sulfuric acid and sodium bisulfate at the highest concentrations studied, indicating very little dissociation. To be in agreement with the work of the slope of the (p3 vs. pV1l2curve must be three to four times that usual for a 1:1 electrolyte. A similar ,phenomenon was observed by Wirth and Shapiro' in their work with potassium dihydrogen
+
I
phosphate, KH2P04. After correcting for possible hydrolysis and dissociation, they found that the apparent molar volumes of this salt, in the 0.25-1.6 ionic strength range, varied nearly linearly with pvl", with a slope of 5.88. No explanation is apparent for this observation, but it does parallel the relationship indicated for the undissociated bisulfate salts. This prompted the choice of HzP04- as the model for the bisulfate ion. A qualitative appraisal of the over-all 43 us. pV1'* relationship would then show a transition from the limiting slope of 1.86 in dilute solution to the larger slope predicted by the HzP04- model. Curves for both solutes a t ionic strengths above 0.02 were constructed, using the relations
+
$(Na+,HzP04-) = t$(K+,H2P04-) +(Na+,Cl-) - +(K+,Cl-)
(9)
(7) H. E. Wirth and S. Shapiro, unpublished work, 1964. Volume 73,Number 1
January 1989
222
RICHARD E. LINDSTROM AND HENRYE. WIRTH
L
-
IO
I
I
I
I
I
0
Ob
1.0
15
2.0
C"20r
I1c"
Figure 3. Experimental values for the mean apparent molal volume of sodium bisulfate (a) us. the square root of the molarity and vs. the square root of the calculated volume ionic strength (dashed curve). These ionic strengths (pV .(1 2 a ) C ) are consistent with the values of (Y obtained from eq 11.
0
+
9(HfJHzP04-) = dJ(K+,H2PO*-)
- s$(K+,Cl-)
(10)
The sodium chloride, hydrochloric acid, and potassium chloride data of WirthSJ and the potassium dihydrogen phosphate data of Wirth and Shapiro were used for the calculations. These curves were then adjusted to fit the t&O values determined earlier for Na+,HS04- and H+,HS04-. This fitting established the final 93 us. pV1I2 relationships used in the remainder of this investigation. The results are given in Figures 2 and 3 and in Tables I11 and IV. Estimation of Dissociation Quotients, Qv. It was now possible to proceed with a determination of CY as a function of ionic strength. $2 and 93 values for the salts a t a given ionic strength were read from 9 us. pv'/' plots to k0.02 ml and introduced into the equation
*
93 a=-------
93
- 92
where CP was an observed apparent molar volume estimated to be near the correct value. Substituting this a into eq 3 gave C which was used to obtain a second CP. This process was repeated until the C obtained in eq 3 corresponded to the CP used in calculating a. At this point, Q,, the dissociation quotient a t ionic strength p, was calculated using the equations CY2C Qv(NaHS04) =: l-CY
The results are summarized in Tables I11 and IV. The Journal of Physical Chemistry
0.2
C1'20r rJy2
Figure 4. Upper curve: volume change (Av) for the process Il+ SOP- -c HSOd- at low ionic strengths, calculated for sulfuric acid (0)and for sodium bisulfate (I) (the size of the symbols represents the error in the estimated value of Au); lower curve: experimental values of @ - @O for sulfuric acid and for sodium bisulfate us. the square root of the molarity and us. the square root of the calculated ionic strength (dashed curves). The values of 01 used in calculating /I" are consistent with the modified form of eq 11 (a = [(& - & O ) -
+
+
4(H+,CI-)
0.I
(a
- ao)1,'A~I.
The results of this investigation are compared in Figure 1 with those of Baesg and those of Marshall and Jonesl10 as well as the original estimates of Klotz and Eckert.l The agreement with the recent results is considered to be satisfactory in view of the number of assumptions necessarily made in this work. The experimental results can be represented by the equations
+
log 0.0102 2.036pv'/*log Qy 1.376,~" 0.8862p,p/2- 0.217pv2 (in HzS04) (14)
+
log Qv
log 0.0102
+ 2.036pV'/2- 1 . 5 4 3 ~+~
0.8297pv'/2- 0.1703pv2 (in NaHS04)
(15)
The quantity 0.0102 is the thermodynamic dissociationconstant ( K ) a t 2 5 O , which we have taken from B a e ~ . ~ This value is in good agreement with the results of Dunsmore and Nancollasll (K = 0.0103 f O.OOOl), Covington, Dobson, and Wynn-Jones12( K = 0.0106
*
(8) H. E. Wirth, J . Amer. Chem. Soc., 59, 2549 (1937). (9) C.F. Baes, Jr., ibid., 79, 5611 (1957). (10) W. L. Marshall and E. V. Jonea, J . Phys. Chem., 70, 4028 (1966). (11) H.S. Dunsmore and G. N. Nanoollas, ibid., 68, 1579 (1964). (12) A. K. Covington, J. V. Dobson, and W. F. K. Wynn-Jones, Trans. Faraday SOC.,61, 2057 (1965).
ELECTROLYTE-SOLVENT INTERACTION
223
0.0009), Marshall and Jones’O ( K = 0.01028 i 0.0002), and Klotsl3 ( K = 0.01015). However, Wallace14 found K = 0.0131 f 0.0002 in his Donnan membrane equilibrium studies. The coefficient of pv1/2is the Debye-Hiickel limiting slope. Other authors9-l2 have used the equationl5
B. I n dilute solutions, our equations correspond to an A value of ca. 0.7.
(16)
Acknowledgment. The authors gratefully acknowledge the facilities, time, and funds provided by the Frank J. Seiler Research Laboratory, Office of Aerospace Research, United States Air Force Academy, Colorado, where the greater portion of the research for this investigation was accomplished.
with A values ranging from 0.4 (Baes) to 0.94 (RIarshall and Jones) with B = 0, while Covington, Dobson, and Wynn-Jones use A = 1.0 and 1.7 with a finite value of
(13) I. M. Klota, Chem. Rev., 41, 373 (1947). (14) R. M. Wallace, J . Phys. Chem., 70, 3922 (1966). (15) It should be noted that a plot of log Q vs. p’/s (on a molal basis) coincides within experimental error with a plot of log QV vs. pvl/e (molar basis) even in concentrated solutions.
log Q = log K
+ 12.036p1’2 + AP”~+ BP
Electrolyte-Solvent Interaction.
XIX.
Solvation by Molecular Picric Acid
by Alessandro D’ApranoI and Raymond M. Fuoss Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut
06660
(Received August 26, 1968)
The conductances in acetonitrile at 25” of solutions of tetrabutylammonium picrate and tetramethylammonium picrate and tetramethylammonium bromide to which picric acid was added have been measured. The conductance of the salts is decreased by the picric acid. If a specific preferential solvation of the anions by picric acid molecules, to give a complex with lower mobility, is assumed, the data can be quantitatively described in terms of an equilibrium between ions solvated by picric acid and ions surrounded only by acetonitrile. In purifying the acetonitrile, it was found that traces of ammonia can give spurious conductances for picric acid solutions, due to formation of ammonium picrate. For ammonium picrate in acetonitrile, the limiting conductance is 174.4 and the association constant is 185. A 1-ppm concentration of ammonia in acetonitrile of upon addition of picric acid. conductance of the order of 10-5 gives a specific conductance‘of 1.5 x I n order to account for the decrease in conductance produced by the addition of p-nitroaniline (PNA) to solutions of various electrolytes in acetonitrile, we proposed that PNA, with its larger dipole moment, displaced acetonitrile solvate, thereby forming a bulkier and slower ionic species. Other cases of specific ion-solvent interaction have since been reported.8 With the nitro phenol^,^ much larger effects than for PNA were observed for the meta and para isomers, while o-nitrophenol caused only a very slight decrease. Picric acid (trinitrophenol) decreased the conductance of tetrabutylammonium bromide even more than pnitrophenol did. Since PNA and p-nitrophenol have about the same dipole moment, the greater effect of the latter must be due to a difference between the hydroxyl and the amino group. These results suggested that hydrogen bonding, rather than ion-dipole attraction, was the mechanism of solvation in the case of the nitrophenols; we therefore investigated the effect of adding picric acid to several other electrolytes
and again found markedly decreased conductances. I n the course of the work, it became clear that the conductance of picric acid in pure acetonitrile is extremely low and that what we (and others) have used as the specific conductance of picric acid in acetonitrile is actually the conductance of dilute solutions of picrates of basic impurities in the acetonitrile, ammonia and water being the most probable. We present here a summary of a study of the conductance of picric acid in “dry” acetonitrile, in “pure” acetonitrile, and in acetonitrile containing controlled amounts of water or ammonia. A 1-ppm concentration of ammonia will (1) NATO Postdoctoral Research Fellow, 1966-1967. On leave of absence from the University of Palermo, Palermo, Italy. (2) A. D’Aprano and R. M. Fuoss, J . Phys. Chem,, 67, 1722, 1871 (1963). (3) W. R. Gilkerson and J. B. Ezell, J . Amer. Chem. Soc., 87, 3812 (1965); W. R. Gilkerson and E. K. Ralph, ibid., 87, 175 (1965); J. B. Ezell and W. R. Giikerson, ibid., 88, 3486 (1966). (4) C. Treiner, M. Quintin, and R. M. Fuoss, J . Chim. Phvs., 63, 320 (1966).
Volume 73, Number 1 January 196.9
