HENRYE. WIRTH
2922
Equilibria in Solutions of Tetraalkylammonium Bromides
by Henry E. Wirth Department of Chemistry, Syracuse University, Syracuse, New York
(Received March 8 , 1967)
The observed apparent molal volume of (CH&NBr in aqueous solutions (0-5 m ) can be explained by ion association ( K A = 1.24). I n addition to ion association, formation of dimers (quadruple ions) and micelles can explain the concentration dependence of the apparent molal volumes of (C2H5)4NBrand (n-C3H7)4NBr. For (C2Hj)4NBr,K A was estimated to be 2.40 and KDwas 0.99 (0.1-1.5 m ) ; using K A = 3.1, K D was found to be 2.0 (0.1-1.0 m) for (C3H7)4NBr. Micelle formation is believed probably above 4.0 m in (C2H&NBr solutions and above 1.4 m in (C3H7)4NBrsolutions.
The unusual behavior of the apparent molal volumes of tetraalkylammonium bromides in aqueous solutions has been attributed to solute-water interaction by Wen and Saito.’ Lindenbaum and Boyd2 have explained the osmotic and activity coefficientsof the tetraalkyl halides by enforcement of water structure by the large cations, by “water structure-enforced ion pairing” by bromides and iodides, and by micelle formation. Recently, Levien3 has shown that both the conductance and activity coefficient data for dilute solutions of (CH3)JSBr and (CHB)4NIgive consistent values for ion association constants. It is of interest to see if the apparent molal volume behavior can be explained in a similar fashion.
Apparatus and Materials A mixing dilatometer of the type first described by Geff cken4 and modified by Wirth5 was further modified for this work. A three-way stopcock was introduced into the connection to the Hg cup (Figure 1 of ref 5 ) . The third outlet led to a vertical capillary tube (volume = 0.00206 ml/cm) which was partially filled with Hg during operation. Another capillary tube, partially filled with solution and connected to the tubing joining bulb C with stopcock a, was mounted alongside the first. The other end of this capillary was connected to a 500-ml bulb placed in the thermostat, so that a constant pressure was maintained over the solution. The pressure over the capillary containing Hg was adjustable. Changes in position of the menisci in the two capillaries were measured to *0.005 cm using a scale and vernier from a barometer. I n operation, the stopcock a was opened after temperature equilibrium The Jozirnal of Phy sical Chemistry
was attained and the pressure over the Hg in the capillary adjusted to bring the solution level in the second capillary to a fixed position to within about 0.1 cm. After each mixing operation, the adjustment was repeated. I n this way the internal pressure on the system was maintained constant to within 0.1 mm. Discussion of Errors. The apparent molal volume (4) of the diluted solution is given by I$ = 4~ (Av/n), where 4~ is the apparent molal volume of the reference solution and Av is the observed volume change on adding n moles of solute (contained in y ml of reference solution) to water in bulb A. 4~ was determined by direct density measurements using the sinker method6 with a precision of kO.02 ml/mole. I n the most dilute solutions obtained, n E 4 X mole and the error in estimating Av is about 5 X ml (each value of Av depends on four readings, the height of the Hg in the capillary before and after addition of the solution, and the height of the solution in the second capillary before and after addition of the solution) so the precision is *O.l ml/mole. A precision of 4 X in the determination of density differences would have to be obtained to determine 4 with this precision by direct density determinations.
+
(1) W. Y.Wen and S. Saito, J. Phys. Chem., 6 8 , 2639 (1964). (2) 5. Lindenbaum and G. E. Boyd, ibid., 6 8 , 911 (1964). (3) B. J. Levien, Australian J. Chem., 18, 1161 (1965). (4) W.Geffcken, A. Kruis, and L. Solana, 2. Physik. Chem. (Leip zip), BJ5, 317 (1937). (5) H. E. Wirth, R. E. Lindstrom, and J. N. Johnson, J. Phys. Chem., 67, 2339 (1963). (6) H.E.Wirth and F. N. Collier, Jr., J. Am. Chem. Soc., 7 2 , 5295 (1950).
EQUILIBRIA IN SOLUTIONS OF
TETRAALKYLAMMONIUM BROMIDES
In an experiment to determine the effect of change in internal pressure on the volume of the system, it was found that the volume change was - 5 X ml/cm. ml is due to the compresOf this change, 3 X ml can be sibility of water in solution and 2 X attributed to the volume change of the glass apparatus, since the compressibility of the Hg is negligible. Since the internal pressure on the solution was held constant to 0.1 mm, no error was introduced from this source. I n another experiment, the volume was observed for a long period of time while the atmospheric pressure was changing. The effect of external pressure was found to be about 4 X ml/cm. A possible error of 1 X ml was introduced in experiments conducted befort: this source of error was recognized. The thermost ated bath containing the apparatus could be held constant to *0.0002” for periods up to 1 hr, as measured with a sensitive thermistor. The average temperature of the solution and Hg in the apparatus was believed to be constant to *O.OOO1°, since the heating-cooling cycle was 10-30 sec. The observed volume change was 2 X m1/0.001” (calculated for the solution and Hg: 1.4 X After a disturbance to the bath, such as the additional heat input to the bath from the solenoids used to operate the magnetic stirrer, the equilibrium bath temperature sometimes changed by 0.0005”. Before this error was recognized and corrected for, an additional error of 1 X ml was introduced. Eastman (C2H5)4NBr was recrystallized from a chloroform-ether mixture and dried in a vacuum oven. The reference solutions were analyzed by gravimetric determination of bromide as AgBr. The molalities found were 1.0859 and 0.4815.
Results and Discussion Tetramethylammonium
Bromide. The apparent molal volumes of (CH3)4NBrin aqueous solution reported by Wen and Saito,’ by Hepler, Stokes, and Stokes,’ and by Conway and VerralP are given in Figure 1. I n drawing the smooth curve, most weight a t low concentrations was given to the data of Hepler, Stokes, and Stokes.’ The extrapolated value of the apparent molal volume at infinite dilution (4”) is 114.18 ml/mole as compared to 114.25 obtained by Hepler, Stokes, and Stokes and to 114.29 obtained by Conway, Verrall, and D e ~ n o y e r s . ~ If Young’s rule’o is applied to this system, it becomes
where
4obsd
is the experimental apparent molal volume,
2923
/
Limltlnp Slepr
llu*o~ L
4“
Me4NBr
/
114.6
0 Haplor, Slokoe b S l o k w X Conway L Varroll + W a n L Saito 0
0.5
1.0
1,s
p 2
Figure 1. Apparent, molal volume of tetramethylammonium bromide as a function of the square root of the volume concentration. Data taken from the literature.
4i is the apparent molal volume of the dissociated salt in a solution in which the molality of the ions is mi ( = m ~ a )and , +,., is the molar volume of the undis1.862/ci sociated salt. It is assumed that 4i = +io and that +u is independent of concentration.” In the preliminary treatment, various values of KA (eq 2) were used to calculate 4”. That value of K A which gave constant values for +u was considered to be best. It was observed that the value of 4” (ca. 114 ml) was very close to that obtained by extrapolating a plot of 4obsd us. l/m to l / m = 0 (Figure 2). The degree of dissociation decreases rapidly with increasing concentration, so the extrapolated value may be taken to represent the molar volume of the completely associated (liquid) salt. This value is 13% greater than the molar volume (100.7 ml) for the crystalline salt calculated from X-ray datal2 and is within the normal range of volume expansion on fusion.13 Similar
+
~
~~
~
~
( 7 ) L. G. Hepler, J. hI. Stokes, and R. H. Stokes, Trans. Faraday SOC.,61, 20 (1965). (8)B. E. Conway and R. E. Verrall, J. Phys. Chem., 70, 3952
(1966). (9) B. E. Conway, It. E. Verrall, and J. E. Desnoyers, Trans. Faraday SOC.,62,2738 (1966). (10) T. F. Young and hl. B. Smith, J. Phys. Chem., 58, 716 (1954). (11) The apparent molal volume of a nonelectrolyte increases linearly with concentration (cf. Harned and Owen, “Physical Chemistry of the Electrolyte Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. T., 1958, p 368). The experimental apparent molal volumes for electrolytes are generally represented by the equation +, = 1.86.\/6 bc,. The agreement obtained in this work implies that the error in assuming that du is constant is compensated for by the neglect of the term in c , for the dissociated electrolyte. (12) R. W.G.Wyckoff, “Crystal Structures,” Vol. I, 2nd ed, Interscience Publishers, Inc., New York, N. Y., 1963, p 107. (13) E. A. Moelwyn-Hughes, “Physical Chemistry,” 2nd ed, The Macmillan Co., New York, N. Y., 1961,p 748.
+
Volume 71, Number 9
August 1967
HENRY E. WIRTH
2924
233tn
oi2
P$NBr Scala oi4
Oi6
, ,
0 Wlrfh Conway 8 V a r r a l l Conwoy,Varrall 8 Datnoytr@
+
\
Pr,NBr
232
-0-
\\
/
+\
174.0
0
\
\
\
N
5
\
0
i
\
\
(D
-
\
c9
\
I
+
0
0.1
0.2
I
I
173.0
0.05
C
0
0.10
Figure 3. Estimation of the apparent molal volume of (C2Hs)dNBr a t infinite dilution by extrapolation of the function d, 1 . 8 6 6 to infinite dilution.
-
0.3
I /rn
culated from eq 3. Using the equation of Robinson and Stokes,15 the value of y (the stoichiometric activity coefficient
Figure 2. Estimation of 6” [(CHs)4NBr]and d,,[(C*H&NBr and (CaH7)aNBr]by extrapolation of the apparent molal volume to infinite concentration ( l / m = 0).
miyi y = a y i = __
extrapolations were also used to estimate the molar volumes of the predominant species present in concentrated solutions of (C2H5)4NBrand (C3H7)4NBr. Since Young’s rule is given in terms of molality, the smooth curves of Figure 1were transferred to a working plot Of 4obsd and 4i us. Table I gives the results of the calculation of K A , where
+
the equilibrium constant for the reaction (CH3)4N+ Br- Ft (CH3)&Br. The mean activity coefficient for the ions was calculated using the relation -log yi =
0.509 1l/nzi 1 o.328adiG
+
+ log (1 + 0.036mi)
(3)
with 12 = 4.5 (Levien3 used d = 4.4-4.6to determine KA from activity and conductivity data) and yu was taken to be unity. An iterative procedure was used. An estimated value of +i was used to calculate (Y from eq 1; this value was used t o obtain mi, from which a refined value of 4i was obtained. This procedure was repeated until self-consistent values of (Y and $i were obtained. The activity coefficient yi was then calThe Journal of Physical Chemistry
mT
calculated on the assumption that the electrolyte is fully dissociated) was obtained and compared with the experimental activity coefficients given by Levien3 and by Lindenbaum and Boyde2 Between 0.2 and 1.2 m, a constant value was obtained for K A and the calculated activity coefficients were in excellent agreement with the experimental results of Levien. The average value of K A found is 1.24, in reasonable agreement with the values 1.45 (activity) and 1.42 (conductivity) found by L e ~ i e n . ~ Above 1.2 m, the values of KA increase. This is ascribed to a failure of eq 3 at high concentrations, so K A was assumed to be constant, and the values of yi and y were calculated (Table 11). The calculated activity coefficients are in better agreement with the experimental values of Lindenbaum and Boyd2 than with those of Levien3 a t the high concentrations. A single dissociation constant is therefore sufficient to interpret the observed concentration dependence of (14) When apparent molal volumes are available, molalities and volume concentrations at 2 5 O are readily interconverted by means of the relations c = 1000n/(1002.93 m+) and m = 1002.93c/ (1000 c+) where 1002.93 = 1000/dH,n. (15) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Academic Press Inc., New York, N. Y., 1959, p 38.
-
+
EQUILIBRIA IN SOLUTIONS OF TETRAALKYLAMMONIUM BROMIDES
Table I : Calculnt,ion of K A for (CHa)aNBr (+"
2925
= 113.9 ml) Yobad
mT
dobsd
U
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.5
114.70 114.83 114.93 115.02 115.08 115.12 115.16 115.18 115.20 115.22 115.22 115.18
0.94 0.88 0.85 0.845 0.820 0.800 0.780 0.765 0.750 0,735 0.700 0.640
KA
Yi
1.1 1.31 1.39 1.16 1.19 1.20 1.22 1.23 1.23 1.25 1.35 1.56
0.775 0.732 0.705 0.683 0.669 0.658 0.649 0.639 0.631 0.625 0,614 0.604
Av (0.2-1.2 m )
Table 11: Calculation of
UYl
0.728 0.644 0.599 0.575 0.541 0.526 0.504 0.486 0.474 0.459 0.429 0.380
Yobad
(Levied3
(L and B)2
0.720 0.645 0.598 0 . ,564 0.538 0.516 0,497 0.483 0.469 0.458
0.746 0.672 0.624 0.587 0,558 0.533 0.513 0.497 0.483 0.471 0,450 0.429
0.443
= 1.24
yi and y for (CH3)dNBr ( K A = 1.24) Yobad
Yobsd
mT
'#Jobad
4
Yi
UYi
(Levien) 8
(L and B)*
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
115.18 115.10 l l j .01 114.92 114.84 114.76 114.67 114.60
0.640 0.565 0.500 0.445 0.403 0.364 0.326 0.295
0.689 0.738 0.800 0.859 0.916 0.981 1.06 1.14
0.440 0.416 0.400 0.395 0.370 0.357 0.346 0.336
0.443 0.438 0.436 0,436 0.437 0.440 0.444 0.448
0.429 0.406 0.391 0.381 0.372 0.365 0.360 0.354
the apparent molal volume of (CH3)4NBr over the concentration range 0.1-5.0 m. Tetraethylammonium Bromide. The apparent molal volumes of (C2H6)4NBrdetermined by Wen and Saito' in the concentration range 0.1-10 m were extrapolated to infinite dilution by these authors, using the experimentally observed negative slope. They chose to ignore the possibility that in dilute solution the slope of all uni-univalent electrolytes must approach a positive value of 1.86, as has been shown by Redlich.16 This work was started to investigate the behavior of apparent molal volumes of (C2HJ4NBrin more dilute solutions than those used by Wen and Saito.' Since then, Conway, Verrall, and Desnoyersg have published data for the concentration range 0.01-0.20 M which extrapolate to a lower value for $', but which is still higher than that obtained here. The value of h in the equation 4 - 4'
=
1.86fi
+ hc
(4) was inconsistent, (too high by a factor of 2) with values obtained by them for other tetrnalkylammonium bromides.
The results of the present work are given in Table 111. Values of 4 - l.86+ us. c for dilute solutions are given in Figure 3. It is evident that the slope (h = 3.5) is less than that obtained by Conway, Verrall, and Desnoyers, but it is consistent with slopes found by them for the other alkylammonium salts. Also, the values found here are in excellent agreement, except in the most dilute sample, with the results of Conway and Verrall. The extrapolated value of the apparent molal volume of (C2H5)JVBrat infinite dilution (4') is 173.60 i 0.10 ml as compared to 174.3 found by Conway, Verrall, and Desnoyersg and 175.3 reported by Wen and Sait0.l An attempt was made to interpret these data on the basis of the single association equilibrium which was so successful in the case of (CHD)(NBr. The plot of 4 us. l / m was extrapolated to l / m = 0 to give an estimate of c$,, (Figure 2 ) . The ionic activity coefficients were calculated using d = 5.2, obtained from Levien's value for d for (CHa)4NBr and the estimates of the effective radii of tetraalkylammonium salts given (16) 0 . Redlich and D . M. Meyer, Chem. Rev., 64, 221 (1964).
Volume 7 1 , Number 9
August 1967
HENRYE. WIRTH
2926
Table 111: Apparent Molal Volumes of (C2Hs)aNBr nz, moles of salt added
122.7
Au, ITll
-
C,
Au/nr
4
moles/l.
Reference Solution (m = 0.4815, +R = 173.20) Added to 183.25 g of HzO 0.0004384 0.00012 0.27 173.47 0.002373 0.0008764 0.00036 0.41 173.61 0.004719 0.002197 0.00106 0.48 173.68 0,01164 0.003956 0.00243 0.61 173.81 0.02053 0.005714 0.00387 0.68 173.88 0.02905 0.01013 0.00695 0.69 173.89 0.04902 0.01631 0.0110 0.68 173.88 0.07394 Reference Solution ( m = 0.4815) Added to 105.62 g of H 2 0 0.0004380 0.00020 0.46 173.66 0.004097 0.0008784 0.00049 0.55 173.75 0.008141 0.00220 0.00143 0.65 173.85 0,0199 0.006614 0.0044 0.67 173.87 0.05348 0.01279 0.0082 0.64 173.84 0.09488 0.01897 0.0117 0.61 173.81 0.1275 0.02514 0.0146 0.58 173.78 0.1546 Reference Solution ( m = 1.0859, +R = 171.99) Added to 103.99 g of H204 0.009009 0.00148 1.64 173.63 0.008547 0.003620 0.00628 1.73 173.72 0.03344 0.0131 0.007240 1.81 173.80 0.06451 0.01634 0.0288 1.76 173.75 0.1337 0.0478 0.02906 1.64 173.63 0.2134 0.0636 0.04178 1.52 173.51 0.2783 0.05450 0.0769 1.41 173.40 0.3322 0.06722 0.0882 1.31 173.30 0.3776 0.07994 0.0978 1.22 173.21 0.4164 0.09266 0.1060 1.14 173.13 0.4500 0.1054 0.1133 1.07 173.06 0.4793 0.1181 0.1196 1.01 173.00 0.5051
1oo.s 1oo.e
0
OS
0. I
chyZ Figure 4. Fuoss plots for tetraalkylammonium bromides, using data of Evans and Kay,IO and d = 4.5 [(CHS)aNBr], 5.2 [(C2H&NBr], and 5.7 [ ( C ~ H T ) ~ N BA’ ~]= . A 8 4 ; - Ec log c, and J is a parameter which includes 6. The slope of A’ - Jc us. CAY* gives K* (see Robinson, Stokes, and Stokes18 and R. &I.Ruoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Inc., New York, N. Y., 1959, Chapter 16).
+
a Values not corrected for possible changes in temperature or atmospheric pressure.
In order to test this assumption, it is necessary to evaluate K A by some other procedure. For this purpose the conductivities of dilute solutions of (C2H5)4NBr as determined by Evans and Kaylgwere employed. These authors considered d to be a parameter to be determined from the conductivity data and found no evidence of ion association in any of the tetraalkylammonium bromides. If, however, d for (CHa)4NBr is taken to be 4.5, their data a t low concentration give a value for K A = 1.5, in good agreement with the value found by Levien by conductance. Similarly, if d for (C2H5)4NBris assumed to be 5.2, K A is found to be 2.4 (Figure 4).
by Conway, Verrall, and D e s n ~ y e r s . ~Constant values of K Awere not obtained.” It was next assumed that an equilibrium of the type 2(C2H&NBr $ [(C2H5)4NBr]2 is involved. Such an association was used by Robinson, Stokes, and Stokes1* to interpret the behavior of solutions of potassium hexafluorophosphate.
(17) If the calculated value of yi is combined with the observed activity coefficients of Lindenbaum and Boyd* using the relation Q = Y o b d Y i , a constant value of K A ( = 2.15) is obtained for the concentration range 0.1-1.8 m. The same value is obtained from the apparent molal volumes in the same concentration range if + i = 174.3 1.86+., where 174.3 is the value of + O observed by Conway, Verrall, and Desnoyers.9 If my values are correct, a single equilibrium constant cannot explain the data. (18) R. A. Robinson, J. M. Stokes, and R. H. Stokes, J . Phye. Chem., 65, 542 (1961). (19) D. F. Evans, and R. L. Kay, ibid., 70,366 (1966).
Water Added to 102.62 ml of Reference Solution ( m = 1.0859, TZZ = 0.09366) W t of Hi0 added, g
13.90 27.79 41.69 55.58 69.48 83.38 97.27
0.0259 0.0463 0.0626 0.0759 0,0867 0.0956 0.1033
0.28 0.49 0.67 0.81 0.93 1.02 1.10
172.27 172.48 172.66 172.80 172.92 173.01 173.03
0.8034 0.7181 0.6482 0.5912 0.5433 0.5026 0.4676
~~~
The Journal of Physical Chemietry
+
EQUILIBRIA IN SOLUTIONS OF TETRAALKYLAMMONIUM BROMIDES
2927
Table IV : Estimation of K2 for (CzHa),NBr.' Yobmd
mT
hbsd
mi
mu
mx
KZ
Yoeled
(L and B)'
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 3.0 4.0 5.0 7.0 10.0
173.80 173.67 173.49 173.30 173.10 172.92 172.72 172.53 172.34 172.16 171.2b 170. 4b 169. 2b 168.3* 167. 7b 166. 6b 165. gb
0.0881 0.1616 0.225 0.283 0.334 0.381 0.423 0.462 0,499 0.532 0,656 0.75 0.87 0.91 0.95 0.95 0.95
0.0116 0.0354 0.065 0.099 0.132 0.167 0.202 0.237 0.271 0.306 0.444 0.56 0.73 0.79 0.85 0.85 0.85
0.0003 0.0030 0,010 0.018 0.034 0.052 0.075 0.101 0.130 0.162 0.400 0.69 1.40 2.30 3.20 5.20 8.20
1 1.2 1.2 0.92 0.98 0.93 0.92 0.90 0.89 0.87 1.02 1.1 1.3 1.8
0.695 0.610 0.550 0.509 0,470 0.441 0.415 0.393 0.374 0.357 0.287 0.242 0.185
0.716 0.631 0.575 0 . 536 0,505 0.479 0.458 0.441 0.427 0.414
K z (0.2-1.5 a
K A = 2.4,
+ic'
= 173.60,
= 171.50,
@x
= 164.40.
where #x is the equivalent volume of the dimer and m, is its equivalent concentration. qji is given by 173.60
+ 1+862/Ci
... ... m ) = 0.99
Dat of Wen and Saito.1
The apparent molal volume observed by extending eq 1will be given by
=
... 0.346 0.331
(6)
As before, values of ~$i and I#Jobsd were taken from a smooth curve of 4 us. d iand replotted vs. m for convenience in calculation. & is taken to be the extrapolated value of &bsd (l/m 0) (Figure 2). 4u can be estimated from the apparent molal volume of dilute solutions ( K Aknown) where the concentration of dimer is low. It was possible to find, by an iterative procedure, values of mi, mu, and m, which satisfied eq 2, 3, 5 , and 6. These values, along with the calculated dimerization constant
(7) are given in Table IV. It is assumed that the activity coefficient of the monomer is equal t o that of the dimer. The average value of K z is 0.99 (0.2-1.5 m ) . Above 1.5 m, K z increases and above 5.0 m the concentration of ions and of monomer is constant, while m increases rapidly. This indicates that micelle formation occurs, as has been assumed before.2 The implicit assumption
involved here is that the equivalent volume of the (CzH5)4NBrin the dimer is the same as in the micelles. The calculated values of the activity coefficient (Ycalod = miyi/m.r) are uniformly lower than the observed values of Lindenbaum and Boyd, but the difference is not much greater in dilute solution than the difference between the observed values of Levien and those of Lindenbaum and Boyd for (CH3)4NBr. Above 1 nz, however, there is definite evidence of more ions in the solution than can be accounted for by the equilibria assumed here. Perhaps the dimer or the micelles are slightly ionized. Tetrapropylammonium Bromide. The data of Wen and Saito' and Conway and VerralP were combined (Figure 5 ) to give a value of 239.60 ml/mole for $ I O , the same value as was estimated by Conway, Verrall, and Desnoyers. The value ford for use in eq 3 and for use in interpreting the conductance data was taken to be 5.7. K A was found to be 3.1 (Figure 4) and dJu was taken as 232.5 ml/mole. The value of dJx was estimated to be 228.6 (Figure 2), where the increasing values of 4 above 4 m were ignored. Table V gives the calculated values of K Z and of the activity coefficient. K z is reasonably constant between 0.1 and 0.9 m and there is evidence for micelle formation above 1.5 m. A further equilibrium involving formation of ions is also indicated and this may account for the increase in apparent molal volume above 4 m. Structure of Water Inferred from Apparent Molal Volume 71, Number 9 A ugusf 1967
HENRYE. WIRTH
2928
Table V : Estimation of KZfor (n-CaH7)4NBra
mT
dobid
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6
238.9 238.2 237.6 237.1 236.7 236.3 235.8 238.4 234,9 234.5 233.8 233.2 232.6 232.2 231.8 230.7 230.4
1.8 2.0 3.0 4.0
mi
0.0848 0.154 0.205 0.254 0.292 0.329 0.354 0.379 0.393 0.403 0.426 0.435 0.435 0.435 0.435 0.435 0.435
m.
mu
0.0142 0.043 0.072 0.106 0.138 0.171 0.196 0.221 0.237 0.247 0.274 0.285 0.285 0.288 0.285 0.285 0.285
0.0010 0.004 0.023 0.040 0.070 0.10 0.15 0.20 0.27 0.35 0.50 0.68 0.88 1.08 1.28 2.28 3.28
Kz (0.1-1.0 m )
Yobid
Kz
Ycalod
(L and B)'
2.5 1.1 2.2 1.8 1.8 1.7 1.9 2.1 2.4 2.9 3.3 4.2 5.4
0.676 0,585 0.508 0.462 0.422 0.391 0.359 0.335 0.307 0.282 0.248 0.216 0.189
0.708 0.620 0.560 0.517 0.486 0.461 0.441 0.424 0.411 0.400 0.382 0.373 0,366
= 2.04
two equations can be written for the total volume ( V ) of solution containing m moles of solute per 1000 g of water
v
= 55.51C1
+ mfi2 = %.jlfil" + m42
(8)
where fil is the partial molal volume of the water in the solution, ijl0 is the molar volume of pure water, and ti2 and 42 are the partial and apparent molal volumes of the solute. Solving 81 =
fi1"
+ [m(@Z- 82)/55.51]
(9)
For most ''normal" electrolytes fi2 is greater than 42, so ti1 is less than ole. This decrease in volume can be attributed to the breaking of the water structure by the electrolyte, With the tetraalkylammonium bromides, g2 is less than $ J ~throughout most of the concentration range,' fil is therefore greater than &", and an increased structuring of the water is implied. This interpretation has been used for HCIOI solutions.6 However, if the solutions contain other species, as postulated here, eq 8 becomes C"= Figure 5. Apparent molal volume of (n-CaH7)rNBr a s a function of the square root of the concentration. Data from the literature.
Volumes. If the solutions of tetraalkylammonium bromides are considered to be completely ionized, The Journal of Physical Chemistry
V
=
55.51fil
+ mitii + mUO, + mXDx= 55.5101' f
mT4obsd
(10)
If 4 o b s d is replaced by its value from eq 5 and setting 4, = fi,, ox = f i x since 4, and 4x are assumed independent of concentration, eq 11 is obtained 81 = 9"
+
[mi(+i
- fii)/55.51]
(11)
CARBON ISOTOPE EFFECTS IN
THE
DECOMPOSITION OF OXALIC ACID
From this viewpoint, the effect of a tetraalkylammonium bromide on the partial molal volume of water is that of a normal electrolyte and increased structuring of water does not occur. Acknowledgment. This work was supported by the
2929
Office of Saline Water (Grant No. 14-01-0001-623). Certain preliminary work was done by K. A. Brown and R. A. Bellantone under the sponsorship of the Undergraduate Research Participation Program of the National Science Foundation.
Carbon Isotope Effects in the Decomposition of Oxalic Acid in Glycerine Solution
by Warren E. Buddenbaum, M. A. Haleem, and Peter E. Yankwich Xoyes Laboratory of Chemistry, University of Illinois, Urbana, Illinois 61801
(Receiued March 10, 1967)
The C13 kinetic isotope effects in the decomposition of oxalic acid in glycerine solution have been studied a t 98-135". Direct measurements were made of the intramolecular isotope effect; it was found to increase with increasing temperature, being about 1.2% a t 98" and about 2.4% at 135". Of the two derived intermolecular isotope effects, one is of the order of 1% and so strongly temperature dependent as to suggest inversion in sense near 200-250°, while the other is 2.5-3.0% and nearly (subject to considerable experimental error, however) independent of temperature. The results are examined in light of simplified calculations on eight-atom models and an analysis of abnormal temperature effects in kinetic isotope fractionation, both published previously. Seither the conventional nor the isotope kinetics results support a multiple-path mechanism; both are consistent with operation of the cross-over phenomenon in the temperature-dependent factors of the isotopic rate constant ratios-for which, however, there is as yet no direct evidence.
Introduction This paper is a report on experiments designed to establish the magnitude and temperature dependence of Cla kinetic isotope effects in the decomposition of oxalic acid in 96% glycerine. The kinetics of the reaction in this solvent were the subject of an earlier report from this laboratory,l and were of special interest because of the similarity of the activation parameters t o those observed in the decomposition in the gas phase.2 The hydrogen3 and carbon4J isotope effects in the gas phase decomposition were found to be so strongly temperature dependent as actually to reverse in sense over a range of barely 50" ; on the other hand, the carbon isotope effect associated with the decom-
position (to different products, however) in concentrated sulfuric acid6 exhibited only a moderate positive7 temperature dependence abnormality. The in(1) M. A. Haleern and P. E. Yankwich, J. Phys. Chem., 69, 1729 (1965). (2) G. Lapidus, D. Barton, and P. E. Yankwich, ibid., 68, 1863 (1964). (3) G. Lapidus, D. Barton, and P. E. Yankwich, ibid., 70, 407 (1966). (4) G. Lapidus, D. Barton, and P. E. Yankwich, ibid., 70, 1575 (1966). (5) G. Lapidus, D. Barton, and P. E. Yankwich, ibid., 70, 3135 (1966). (6) A. Fry and M. Calvin, ibid., 56, 897 (1952). (7) P. E.Yankwich and W. E. Buddenbaum, ibid., 71,1185 (1967).
Volume 71, Number 9 August 1967
