NOTES
2348
ride ions n o = 1 and 7 2 ' = 18.60 and may be seen in Figure 1 where they have been plotted vs. the atomic number 2, since the use of crystalline ionic radii is not a very good criterion for the interpretation of properties of species in solution. The solvation number increases somewhat irregularly from 8.5 for La3+to 11 for Dy3+, Ho3+, and Era+, agreeing with the coordination number 9 for the rare earth ions from La3+ t o Nd3+ but not with the coordination number 8 given2 for Gd3+to Er3+. It is interesting to note that both sets are obtained from the same partial molar volume data. However, since the ionic partial molal volume at infinite dilution does decrease smoothly with the intrinsic ionic radii,8 re, in solution, these have been calculated and are shown in Figure 1. The ionic radii of the hydrated volumes were computed by either Stokes and Robinson's expressiong
as a differentiating solvent toward acids. The purpose of the present work is to elucidate the behavior of and HC10, in pyridine through HCl, HBr, HI, "03, potentiometric measurements using a PtlH2(g) electrode (DS. a Zn(Hg)(ZnC12(s) reference electrode) and to establish the relative order of their dissociation constants. Assuming that an acid dissociates in pyridine according to
+
H + X(1) the over-all dissociation constant, KHX,is given by
HX
a H +axKHX = aHX
Accordingly, using the notations used previo~sly,~ the emf values of cells I and I1
__ V H= 4.35rS3
reference electrode (pyridine) I I
or from the relation of Conway, Verrall, and Desnoyerslo
reference electrode (pyridine) 11
VH
=
+
~ ( C H X(pyridine)lHJ't )
(8) J. Padova, J . Chem. Phys., 39, 1552 (1963). (9) R. H. Stokes and R. A. Robinson, Trans. Faraday SOC.,53, 301 (1957). (10) B. E. Conway, R. E. Verrall, and J. E. Desnoyers, 2. Physik. Chem. (Leipzig), 230, 157 (1965). (11) Y. Marcus, M. Givon, and G. R. Choppin, J . Inorg. Nucl. Chem., 25, 1457 (1963). (12) I. Abrahamer, Ph.D. Thesis, Jerusalem, 1966.
The Relative Dissociation Constants of Hydrochloric, Hydrobromic, Hydriodic, Nitric, and Perchloric Acid i n Pyridine.
(I)
+ H X ~ ( C H X , ) ~ H ~(11), P ~
2.51rC3 3.15rC2
and are plotted on the same graph. The trend is similar for r,, T,, and no and slightly different for re, and clearly shows the variations observed in other properties."~'~
(14
HXI(CHXJ
at 25' can be represented by eq 2 and 3, respectively, provided the activity coeficients of all ionic species
EHX=
Eref
+ + Elj
+ 0.02956 log [HX]
0.02956 log KHX
E H X ~ ,= H EXr e~t
+ +
(2)
Elj
0.02956 log (KHx~[HXI] K H X ~ [ H X ~ (3) ])
are considered equal and those of the uncharged molecules set equal to one. Furthermore, if the over-all dissociation constants are small, the equilibrium concentrations of the undissociated species can be replaced by the corresponding total analytical concentrations. Thus, eq 2 and 3, under such a situation, reduce to
EHX=
Eret
+ + Elj
+ 0.02956 log CHX (4)
0.02956 log KHX
A Hydrogen Electrode Study by L. M. Mukherjee and John J. Kelly Chemistry Department, Polytechnic Institute of Brooklyn, Brooklyn, Neu York 11801 (Received December 27, 1966)
Previously reported potentiometric investigations of the acid-base equilibria in pyridine are extremely -inadequate.' It has been shown, however, from ply+ vious conductance measurement^^^^ that pyridine acts The Journal of Physical Chemistry
(1) (a) H. Angerstein, Rocznik. Chem., 30,855 (1956); (b) J. S. Fritz and F. E. Gainer, Talanta, 13, 939 (1966). (2) A. Hantzsch and K. S. Caldwell, 2. Physik. Chem. (Frankfurt), 61, 227 (1908). (3) (a) M. M. Davies, Trans. Faraday ~ o c . 31, , 1561 (1935); (b) D. S. Burgess and C. A. Kraus, J . Am. Chem. SOC.,7 0 , 706 (1948). (4) (a) S. Bruckenstein and L. M. Mukherjee, J . Phys. C h m . , 66, 2228 (1962); (b) L. M. Mukherjee, 8. Bruckenstein, and F. A. K. Badawi, ibid., 69,2537 (1965).
2349
NOTES
Table I: Potentiometric Study of Acid Mixtures (cf. eq 6) PKHXI CHXI,
HCl
CHXrr
M
2.87 X 4.32 X 6.64 X 1.48 X 3.95 x
HNOa
1.52 X 1.52 X 1.52 X 1.98 X 1.98 x
AE, v
M
0.051 0.056
lo-* lo-* lo-* 10-o 10-2
-
PKHX~
1.44 1.43 1.49 1.495 1.48
0.063 0.041 0.053
Av 1 . 4 7 f 0 . 0 2 HBr
0.31 0.34 0.41
0.020 0.031 0.038
1.43 X lo-* 3.67 X lo-' 5.58 X
HNOs
7.83 X lo-* 7.83 X 7.83 X
Av 0.35*0.04 HNOs
2.01 x 10-9 3.12 X lo-' 4.07 x 10-8
HI
1.41 X lo-* 1.41 X 1.41 X lo-*
0.022 0.031 0.036
0.50 0.66 0.73 Av 0.63*0.09
HNO,
2.79 X lo-* 5.84 x 10-4 7.04 x lo-'
HC104
2.12 X lo-* 2.12 x 10-2 2.12 x 10-8
0.74 0.72 0.71
0.027 0.035 0.037
Av 0 . 7 2 i 0 . 0 1
0.70
I-
I
Table II : Summary of the Relative p K Values of Acids P K H N O-~
HX
PKHX
-1.74" -1.47b
HCl
AV -1.60 i 0.13 HBr
-0.24" -0.35b AV -0.30
HI
* 0.05
+0.66" +0.63b Av +0.64 f 0.01 +0.84"
I
-
2 LOGC"
4
3
+
B Figure 1. Plot of eq 4. Data fitted to E m = A log CHX. Least-squares constants given in the format HX, A, B are: HC1, 0.616, 0.0263; HBr, 0.660, 0.0337; HI, 0.687, 0.0305; HNOa, 0.668, 0.0301; HClOd, 0.692, 0.0277. Least-squares lines are shown in the figure.
where the CHXterms denote analytical concentrations. After substitution of HX by HXI in eq 4 and assuming that Elj remains constant, one obtains eq 6 from the difference between the emf values of cell I and cell I1
+0.72b Av + 0 . 7 8 f 0 . 0 6
" Cell I (using eq 4).
' Cell I and cell I1 (using eq 6).
where both cells contain the same concentration CRX, of Hxl.
EHX,,HX, - EHX~ = AE = 0.02956 log (1
+
HXI HXI
Volume 71, Number 7 Juw 1987
2350
NOTES
In the present case, eq 4 appears valid for each of the tiona12 and vibrational3 temperature of the NH radical five acids studied, as shown by the linearity of the plot observed by kinetic spectroscopy. The utilization of the thermal effect in flash photolysis has been disof E H X vs. log C H X (Figure 1) having slopes in good cussed.4 , 5 agreement with the expected value of 0.02956 v a t 25”. In Table I the results of the mixture experiThe adiabatic flash heating of hydrazine has been considered2Jin terms of the reactions ments together with the calculated ApK values for various acid pairs (cf. eq 6) are given. Table I1 NzH4 +2XH2 (1) presents a summary of the relative pK values (vs. ”0,) calculated from the least-squares constants of NHz NzH4 +NH3 NzH3 (2) the plot of eq 4 and those obtained from the experiKzH3 +NH NHz (3) ments on acid mixtures using eq 6. The order of acid strengths HC104 > H I > HN03 > HBr > HC1, as with reaction 3 taking place at high temperatures to shown by the present hydrogen electrode study, is the explain the observation of K H under these conditions. same as that found in earlier conductance studies2t3 The final products were considered3 in terms of the and it further corroborates the “differentiating” effect reactions of pyridine toward acids. However, our measurements 2NzH3 + Kz 2NH3 (4) with the pure acids (eq 4) and with the HNO3-HI and HN03-HC104 mixtures (eq 6) yield (Table 11) NHz NzH3 +Nz H2 “3 (5) 0.64 and 0.75 for the average value of pK”Oa - ~ K H I Reaction 4 represents the combination of NzH3 radicals and pK”Os - pKHCIOa, respectively, as compared and probably proceeds via the intermediate formation to the available conductometric value3of 1.07 and 1.18. of tetrazane (NIHB). Based on the results of the oxiAcknowledgment. Acknowledgment is made to the dation in solution of hydrazine enriched with hydrazine’5N, combination of NzH3 radicals results in 50-10070 donors of the Petroleum Research Fund, administered randomization6q7 in the isotopic nitrogen produced by the American Chemical Society, for partial support depending on the mechanism of N2 elimination from of this research. tetrazane. Cross-disproportionation of NH2 and N2H3 (reaction 5 ) probably proceeds via intermediate formation of diimide (NzHz) Adiabatic Heating of Hydrazine by Flash NH2 NzH3 +NH3 X2Hz (W Photolysis. Nitrogen Formation with Hz NzHz +Nz (5b) Integrity of the N-N Bond This would not lead to isotopic mixing in the nitrogen since the Nz formed comes from a single molecule of by L. J. Stief‘ and V. J. DeCarlo hydrazine by successive dehydrogenation. Disproporti~nation’e~ of NZH3 Research Division, Melpar, Inc., Falls Church, Virginia
+
+
+
+
+ +
+
+
(Received JanuaTy 6, 1967)
NzH3
+ NzH3 NzHz
The recent demonstration’ that approximately 80% of the nitrogen formed in the direct photolysis of hydrazine results from reactions which do not involve the fission of the N-N bond has prompted us to examine the thermal decomposition of hydrazine for a similar effect. The photochemical experiments employed mixtures of hydrazine and hydrazine-J5N and showed that the isotopic nitrogens formed in the photochemical decomposition were only 13% randomized. The thermal nature of the reaction in the flash photolysis of hydrazine has been reported by Ramsay2 and verified by Husain and N o r r i ~ h . ~The temperature attained in these systems was estimated to be in the range 1200-2000°K based on measurement of the rotaT h e Journal of Physical Chemistry
+
+
NzHz
+ Nz
+
+ NzH4
+ Hz
(6)
(jb)
would be an equally plausible source of Nz and would also lead to a lack of mixing of isotopic nitrogen. Thus, an examination of the distribution of the isotopic ni(1) L. J. Stief and V. J. DeCarlo, J . Chem. Phys., 44, 4638 (1966). (2) D. A. Ramsay, J. Phys. Chem., 57, 415 (1953). (3) D. Husain and R. G. W. Norrish, Proc. Roy. SOC.(London), A273, 145 (1963). (4) G. Porter in “Techniques of Organic Chemistry,” Vol. V I I I , Part 11, 2nd ed. John Wiley and Sons, Inc., New York, N.Y.,1963, p 1055, Chapter 19. (6) R. G. W. Norrish, Chem. Brit., 1, 289 (1965). (6) W. C. E. Higginson and D. Sutton, J . Chem. SOC.,1402 (1953). (7) J. W. Cahn and R. E. Powell, J. Am. Chem. SOC.,76, 2568 (1954).
