J. Phys. Chem. 1987, 91, 4123-4127
4123
Heat Capacities of Aqueous Decyl-, Dodecyl-, Tetradecyl-, and Hexadecyltrimethylammonium Bromides at 10, 25, 40, and 55 OC Lynn V. Dearden and Earl M. Woolley* Department of Chemistry, Brigham Young University, Provo. Utah 84602 (Received: December 23, 1986; In Final Form: March 16, 1987)
We have used a flow microcalorimeter and a vibrating-tube densimeter to measure heat capacities and densities of aqueous solutions of decyltrimethylammoniumbromide, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and hexadecyltrimethylammonium bromide at 10, 25, 40, and 55 O C . We have calculated apparent molar heat capacities from the measured heat capacities. From the temperature dependence of parameters obtained from previously measured enthalpy data, we have derived relative apparent molar heat capacities. The apparent molar heat capacities calculated from our measurements are consistent within experimental error with those calculated from the enthalpy data. The application of simple thermodynamic relationships has allowed us to combine the apparent molar heat capacities and the relative apparent molar heat capacities to obtain cpzo values for each surfactant at each temperature.
( I ) Musbally, G.M.; Perron, G.; Desnoyers, J . E. J. Colloid Inrerfuce Sci. 1974, 48, 494. (2) Musbally, G. M.; Perron, G.; Desnoyers, J. E. J . Colloid Interfuce Sci. 1976, 54, 80.
Tetradecyltrimethylammonium bromide (Research Plus) and hexadecyltrimethylammonium bromide (Fisher, Lot 7 16090) were recrystallized three times from a mixture of acetone and less than 5% methanol. The recrystallized surfactants were washed twice with ethyl ether and dried in a vacuum oven at 60 O C prior to use. Solutions were prepared by weight with distilled water. All water used to prepare solutions and used as reference solvent was degassed immediately prior to use. Equipment and Procedure. The heat capacity measurements were made with a Picker flow microcalorimeter which has been described p r e v i o ~ s l y . ~ -The ’ ~ calorimeter was modified to make measurements at 40 and 55 OC. This was done by replacing the Picker thermostat with a Hart Model 5004 constant-temperature bath and a Hart Model 3002 temperature controller. All measurements were made relative to water. The instrument had been calibrated previously by making heat capacity measurements on several NaCl solutions.” This calibration was checked and found to agree with the previous work. The Picker flow microcalorimeter measures a volumetric heat capacity. In order to obtain specific heat capacities, it is necessary to also measure the densities of the solutions. These densities were obtained with a Sodev Model 02D vibrating-tube densimeter coupled to a Hewlett-Packard Model 5326A timer-counter interfaced to an Apple IIe computer. The densimeter system was calibrated as before with pure nitrogen gas and water.’* Model. There are, of course, several possible methods that can be used to interpret data for simple micellar solutions. An advantage of choosing a mass-action model is that it has a simple thermodynamic framework: usually a single reaction with corresponding parameters such as In K, AHo, and ACpo. Analysis of a variety of data with such a model makes it possible for one to observe trends in the parameters and thereby correlate or rationalize a large body of data or make predictions. Of course, physical reality must also be considered along with the simplicity of any model. For example, in a simple mass-action model the assumption that the formation of micelles results in a single micellar species is clearly an approximation. Nevertheless, this assumption yields a model that is readily understood and that is useful in correlating, rationalizing, explaining, or predicting experimental results. However, a simple mass-action model may exhibit (small) systematic deviations from the experimental data. In contrast, purely numerical fitting methods are capable of yielding tables or graphs of smoothed “data” that may more precisely fit the experimental data. However, such methods and
( 3 ) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J . Colloid Interface Sci. 1979. 71. 147. -(4) DiPaola, G.; Belleau, B. Can. J . Chem. 1975, 53, 3452. ( 5 ) Quirion, F.; Desnoyers, J. E. J . Colloid Interface Sci. 1986, 112, 565. (6) Bashford, M. T.; Woolley, E. M. J . Phys. Chem. 1985, 89, 3173. (7) Burchfield, T. E.; Woolley, E. M. J . Phys. Chem. 1984, 88, 2149. (8) Woolley, E. M.; Burchfield, T. E. J . Phys. Chem. 1984, 88, 2155.
(9) Picker, P.; Leduc, P.-A.; Philip, P. R.; Desnoyers, J. E. J . Chem. Thermodyn. 1971, 3, 631. (IO) Picker, P. Can. Res. Deu. 1974, 7(1), 11. ( 1 1 ) Allred, G. C.; Woolley, E. M. J . Chem. Thermodyn. 1981, 13, 147. ( I 2) Picker, P.; Tremblay, E.; Jolicoeur, C. J . Solution Chem. 1974, 3, 377.
Introduction The study of heat capacities of aqueous solutions a t constant pressure can yield useful information. A knowledge of heat capacities over a range of temperatures allows one to calculate the temperature dependence of enthalpies and other thermodynamic quantities at higher and lower temperatures. Values of partial and apparent molar heat capacities also permit a better understanding of molecular interactions in solution. Furthermore, heat capacity data can be used to test various theories or models of reactions in solutions. In this paper we report the systematic study of heat capacities for a series of alkyltrimethylammonium bromides (TABs) in aqueous solution. Previous studies have reported heat capacity measurements for nonyltrimethylammonium bromide (C9 TAB) and decyltrimethylammonium bromide (C10 TAB) at 5, 15, and Heat capacity 25 O C and also at 35 and 45 OC for C9 measurements have been reported recently for hexadecyltrimethylammonium bromide (C16 TAB) from 25 to 50 “C5 We have measured heat capacities of aqueous solutions of decyl-, dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromides at 40 and 55 O C . In addition, we have measured heat capacities of aqueous solutions of the C10, C12, and C14 TABs at 25 “ C and of the C12 and C14 TABs at 10 OC. In a previous report enthalpy data were measured as a function of temperature and used to derive relative apparent molar heat capacities, +J, from the temperature dependence of the parameters that were used to fit the data.6 We have used our heat capacity data to calculate apparent molar heat capacities, &. From the derived +J values and these measured +c values we have obtained e p 2 O values. A mass-action model that includes the effects of activity coefficients to describe the thermodynamic properties of ionic surfactant solution^^^^ has been used to analyze the previously reported enthalpy data6 and the data we report in this paper. Experimental Section Materials. The surfactants were purified before use by previously reported method^.^,^ Decyltrimethylammonium bromide (Kodak, Lot A1 3A) and dodecyltrimethylammonium bromide (Kodak, Lot A8B) were recrystallized three times from acetone.
0022-3654/87/2091-4123.$01.50/00 1987 American Chemical Society
4124
TABLE I: Specific Heat Capacity and Density of Water at 10, 25, 40, and 55 "C from Ke11I4 IO 25 40 55
4.1919 4.1793 4.1783 4.1821
0.999 700 0.997 045 0.992 2 15 0.985 691
TABLE 11: Average Values of the Apparent Molar Heat Capacities and Volumes of Aoueous DecvltrimethvlammoniumBromide Solutions m, mol kg-l @c, J mol-] K-' @v, cm3 mol-[ T = 25 "Ca 0.1 1 5 077 764 258.9 0.150930 708 259.6 0.200 873 670 260.2 0.299612 624 260.8 0.398 409 596 261.0 T = 40 "C 897 883 884 871 829 795 738
0.020 674 0.047 439 0.066 200 0.077 983 0.099 946 0.1 15 077 0.150 930 0.200872 0.299 61 2 0.398 409
645 632
262.7 260.7 261.7 261.6 262.5 262.5 262.9 263.8 264.3 264.9
T = 55 "C 0.1 13 208 0.127 366 0.141 093 0.153 154 0.205 5 1 1 0.291 938 0.409 089
869 840 825 816 770 724 690
266.8 267.2 267.2 267.2 267.8 268.0 268.3
"Values of dv at this temperature are interpolated from data in ref 3.
their results (including derivatives and integrals) are not as readily applied to the prediction or explanation of data for the same systems under different conditions or for other surfactant systems. For these reasons we have chosen to analyze our data using the mass-action model that has been previously This mass-action model is summarized by eq 1-9. A glossary of symbols is given at the end of this paper. nBBr-
+ nTAB+ = Brn,TAB,"(l-~)
(1)
K = [ a / n (1 - Pa)",( 1 - a ) " ~ ~ ( " ~ + ~ ~ ) (2) ]r log
r
Dearden and Woolley
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
= -n[&~(i - p ) z - p - i ] ~ , P / ~ / (+i b V ) + Bl,[nm(2Pa - P - 1)1 + B,,[m(l - 2Pa)l (3)
+
+
+
log y* = - A , W / ( 1 b W ) (1 /2) log (1 - a ) (1/2) log (1 - P a ) + B,,[m(2 - a - Pa)/21 + Bn,[ma/2n1 (4)
4 = 1 - a(1 + P - I / n ) - (In 10)A,13~2a(bP/2)/3m+ B,,[(l - a ) ( l - Pa)m(ln 10)/2]
+ B,,[a(l Pa)m(ln 10)/2nI ( 5 )
TABLE III: Average Values of the Apparent Molar Heat Capacities and Volumes of Aqueous Dodecyltrimethylammonium Bromide Solutions m,mol kg-' &, J mol-' K-l cm3 mol-' T = 10 OC 0.030 062 902 287.5 0.040 436 862 288.0 0.050512 813 287.9 0.009 554 0.0 12 202 0.013 776 0.019720 0.024 728 0.030 297 0.035 028 0.039 474 0.044 28 1 0.050 339 0.060 7 18 0.070 059 0.079 457 0.100 980
T = 25 OC 1060 1077 1065 1024 957 918 89 1 868 850 823 805 788 778 758
290.6 287.4 289.0 289.0 290.6 291.6 292.1 292.4 292.8 293.0 293.4 293.9 294.0 294.1
0.029 237 0.039473 0.050625
T = 40 O 989 908 860
295.9 296.6 296.8
0.029516 0.040 458 0.050013
T = 55 OC 1066 973 925
C
299.2 300.9 301.7
TABLE IV: Average Values of the Apparent Molar Heat Capacities and Volumes of Aqueous Tetradecyltrimethylammonium Bromide Solutions m,mol kg-' @c,J mol-' K-' &, cm3 mol-] T = 10 "C 0.013047 319.0 743 712 0.01 5 096 321.5 717 0.016999 321.0
T = 25 "C 0.009 955 0.012 972 0.014 998 0.016963
914 902 847 818
321.3 324.3 325.0 324.1
0.009 964 0.012817 0.015 03 1
T = 40 "C 972 950 930
330.9 329.5 330.8
0.010003 0.013 051 0.015037 0.016885
T = 55 "C 1152 1050 99 1 984
335.5 335.0 336.9 336.3
Results and Discussion The apparent molar heat capacities and apparent molar volumes were calculated from the equations & = ( M * + 1000/m)cp - (1O0O/m)cpO (10) @v = ( M ,
+ 1000/m)/d-
(lOOO/m)/do
(11)
In these equations cp and d are the experimental specific heat capacity and density of the solution, cpo and do are the specific heat capacity and density of the pure solvent, M z is the molar mass of the solute, and m is the stoichiometric molality of the surfactant. The values used for the specific heat capacity and density of pure water given in Table I are from KelI.l4 The configuration of the instrument is the same as that used in a previous study, and the correction factorfwas not applied because of its negligible effect (13) Woolley, E. M.; Burchfield, T.E. J . Phys. Chem. 1985, 89. 714.
(14) Kell, G. S . In Water-A Comprehensioe Treatise; Franks, F., Ed.; Plenum: New York, 1972.
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 4125
Heat Capacities of Alkyltrimethylammonium Bromides TABLE V: Average Values of the Apparent Molar Heat Capacities and Volumes of Aqueous Hexadecyltrimethylammonium Bromide Solutions m, mol kg-' bC, J mol-' K-' bv, cm3 mol-' T = 40 "C 0.01 0 000 837 364.4 0.012227 824 364.9 0.015 132 784 364.7 0.009 357 0.010 41 3 0.012435 0.014 989 0.049 702
T = 55 "C 992 946 892 874 813
920 l
o
55
z
0
F
Y
366.7 369.6 369.5 368.1 369.1
I
I
0.1
0.2
0.3
I
I
0.4
0.5
m. m o l / k g
in accordance with the discussion of that study." Tables 11-V contain the average values of C # J ~for each of the four surfactants in water at their indicated temperatures. These values represent the average result of from two to four separate comparisons between a given solution and pure water. Values of cp and d corresponding to the average +c and dVvalues given in Tables 11-V can be calculated by using eq 10 and 11, along with the values of cp" and do given in Table I. The standard deviations of the replicate determinations of & at each concentration were averaged for each surfactant to give the following values: 9 J K-' mol-' for C 10 TAB, 12 J K-' mol-' for C 12 TAB, 39 J K-' mol-' for C14 TAB, and 45 J K-l for C16 TAB. The actual experimental uncertainty is likely to be greater than these values. It has been noted in an earlier paper that differences in methods of purification of surfactant and/or in the mode of measurement can result in differences of up to 20 J K-' mol-' in apparent molar heat c a p a c i t i e ~ . ' ~ Tables 11-V also contain the average values of +v for each of the four surfactants at the indicated temperatures. In this paper we have chosen to focus on the analysis of specific heat capacity data. The apparent molar volumes are based on densities that have average deviations that are nearly always less than 0.001%, although a few values had average deviations as high as 0.004%. It can be shown that uncertainties of this magnitude in the densities cause uncertainties of 0.004% in the specific heat capacity. Therefore, our reported densities are adequate for determination of specific heat capacities having an uncertainty of 0.004% or greater. Calculations also show that densities must be precise to a few parts per million to obtain reliable apparent molar volumes. The apparent molar volumes reported in this paper are in reasonable agreement with the variations with structure and temperature in previously reported data.335 Direct comparison of values for q5v is only possible for hexadecyltrimethylammonium bromide at 40 "C. Our values agree with those of Quirion and Desnoyers within about 0.3 cm3 m01-l.~ This difference could be due to slight differences in purities of the surfactants as suggested in an earlier paper. l 3 The relatively small amount of density/volume data given in this paper does not allow for its effective analysis using the mass-action model. This same statement could also be made regarding the heat capacity data, except that enthalpy data measured as a function of temperature6 allows the effective use of the model in analyzing even a small set of heat capacity data. In those cases where we have measured sufficient volume data we have analyzed that data with the mass-action expression for & from ref 8, analogous to eq 8 and 9 in this paper. This treatment gives the following values: for C10 TAB at 40 OC, = 260.8 cm3 mol-I and A P / n = 4.0 cm3 mol-'; for C10 TAB at 5 5 "C, Vzo= 262.9 cm3 mol-' and A P / n = 2.6 cm3 mol-'; for C12 TAB at 25 OC, = 288.6 cm3 mol-' and A P / n = 6.1 cm3 mol-'. There are no values in the literature for direct comparison. However, the values of these parameters are in reasonable agreement with the trends observed with variations of structure and temperature for other surfactant^.'^ The values of n, @, 6, B1,, Bny,b, and the Debye-Huckel constants A,, AL, and Ac used in all the calculations for this paper are the same as those used in an earlier study of the enthalpies
v2"
rzo
Figure 1. Apparent molar heat capacities of decyltrimethylammonium bromide solutions at 25 "C (0),40 OC (*), and 55 "C (A). The dashed lines are least-squares fits using eq 9 with the parameters in Table VI. The solid lines are predictions with ACp" fixed using method 2 as discussed in the text. For clarity, values for the lines and data at 25 "C are shifted downward by 50 J K-' mol-' and those at 55 OC are shifted upward by 50 J K-' mol-'. TABLE VI: Parameters for Fitting Eq 9 to Apparent Molar Heat Capacity Data for Aqueous DecyltrimethylammoniumBromide Sohtions"sb cpzo,J ACpo/n,J rmsd, J T , "C In K mol-' K-' mol-' K-' mol-' K-' Method 1 25 171 878 f 9 -330 f 13 5 40 171 874f 4 -298 f 9 9 55 170 887 f 6 -245 f 11 6 25 40 55
171 171 170
Method 860f7 875 f 8 919 f 13
~
2 -302 -302 -302
7 8 13
"All values of In K and the values of A C p o / n used with method 2 were taken from ref 6. See discussion in the text. brmsd is the rootmean-square deviation of the fit to eq 9. The f values listed with each parameter are the statistical root-mean-square deviations. We estimate that the total uncertainties may be larger than these by as much as a factor of 2 or 3.
of dilution of water + T A B s . ~ The values of (dB,,/aT),, (aB,,,/aT),,, and AH" were also taken from ref 6. Equation 9 AC,,", (aZBl,/aT2),, and contains four fitting parameters: Cpzo, (a2B,,/dP),,. It was found that the latter two parameters were not required in order to fit adequately to the data reported in this study. The data were analyzed by using eq 9. This was done by using two methods. In method 1 eq 9 is fit to the apparent molar heat capacities to determine ACpo and C P 2 O . In method 2 a prediction, based on parameters obtained from fitting enthalpy data as a function of temperature,6 was used with the apparent molar heat capacity data to obtain Figure 1 shows results of applying these two methods to our data for decyltrimethylammonium bromide at 25, 40, and 5 5 "C. In this figure the symbols represent the measured apparent molar heat capacities. The dashed lines represent the fits where ACpo and Cp2" are determined by using method 1. The solid lines represent the fits where C P 2 O is determined by using method 2. A summary of the parameters obtained by using the two methods is given in Table VI. Figure 1 and Table VI tend to emphasize certain factors that need to be considered when treating heat capacity data to determine ACpo or cP!O. For example, method 2 uses a ACpo that was derived by fitting AHo from ref 6 as a function of temperature. The value of ACpo obtained was considered to be constant over that temperature range. A careful inspection of Table VI and Figure 1 indicates, along with consideration of the analysis of previously reported heat capacity data, that ACpo is probably changing with temperature. Figures 1 also illustrates that it is necessary to have premicellar data in order to determine ACpo quantitatively by using method 1 and to establish the
cpzo.
4126
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
TABLE VII: Parameters for Fitting Eq 9 to Apparent Molar Heat Capacity Data Using Method 2a,b ACpoln, J T, ' C In K C,', J mol-' K-' mol-' K-' Dodecyltrimethylammonium Bromide IO 380 I104 f I 1 -406 25 37 1 1092 f 21 -406 40 37 1 1123 f 2 -406 55 361 1123 f 8 -406 10 25 40 55
Tetradecyltrimethylammonium Bromide 709 1131 f 9 -499 686 1228 f 20 -499 -499 678 1247 f 29 66 1 I267 f I 1 -499
40 55
Hexadecyltrimethylammonium Bromide 1079 1339 f 15 -573 1047 1396 f 28 -573
"Values of In K and the values of ACpo/n were taken from ref 6. See discussion in the text. *The f value listed with each parameter is the root-mean-squaredeviation of the fit to eq 9. We estimate that the total uncertainties may be larger than these by as much as a factor of
Dearden and Woolley 1550,
*
(15) Leduc, P.-A,;Desnoyers, J . E. Can.J. Chem.1973,51, 2993. (16) DeLisi, R.; Perron, G.; Desnoyers, J. E. Can.J . Chem. 1980,58. 959.
I
1
1250 Y
i i
e"' 050 950
C a50 75
8.L
~
o.bi
0.102
0.b3
0.b4
0.05
0.L
m. m o l / k g
Figure 2. Apparent molar heat capacities of decyl- (O), dodecyl- (0), tetradecyl- (*), and hexadecyltrimethylammonium bromide (A)solutions at 40 'C. The lines are based on parameters from ref 6 and the values given in Tables VI and VII.
cP2"
2 or 3.
concentration dependence of dc. However, Figure 1 shows that it is possible to obtain reasonable estimates for C P 2 O using enthalpy data with only a few heat capacity measurements. Moreover, when it is impossible to obtain sufficiently accurate premicellar specific heat capacity data by direct measurement because of a small cmc, the use of method 2 described above is likely to be the best alternative in the determination of C P 2 O values. The cmc's for the C12, C14, and C16 TAB surfactants occur at quite low concentrations. It is difficult to measure specific heat capacities in those low-concentration regions with sufficient accuracy to obtain meaningful $c values. For this reason and because of the inverse relationship between concentration and apparent molar heat capacity in eq 10, we suggest that it is better to analyze the heat capacity data for these surfactants using the second method described above. The values for e p 2 O obtained from this analysis are given in Table VII. Direct comparison of our results with values in the literature is possible in only a few instances. For decyltrimethylammonium bromide our value of C P 2 O obtained by using method 1 differs from that given by De Lisi et aL3 by 5 J K-' mol-I at 25 OC. Woolley and B ~ r c h f i e l d also ' ~ analyzed the data of De Lisi et aL3 to give a value of C P 2 O that is the same as our value obtained by using method 1. Our value of C P : O obtained by using method 2 differs and by 18 by 13 J K-I mol-] from that given by De Lisi et J K-' mol-' from that calculated by Woolley and Burchfield13using the data of De Lisi et aL3 For hexadecyltrimethylammonium bromide we have fit the dC data of Quirion and Desnoyers5 at 40 "C from 0.005 to 0.052 mol kg-' using method 2 to obtain a C P 2 O of 1366 f 54 J K-' mol-', which is 27 J K-' mol-' higher than our value. We have also treated their data at 50 OC from 0.09 to 0.30 mol kg-' using method 2 to obtain a C P 2 O of 1424 5 J K-' mol-'. Our value at 5 5 OC is lower than this value by 28 J K-' mol-'. The trends in C P 2 O with T for the four surfactants appear to be in reasonable agreement with those exhibited in earlier studies.3,8-13In the earlier studies a maximum at about 2 5 O C is observed in the temperature dependence of CP2"for surfactants of alkyl chain length of 10 or less. This maximum appears to shift to higher temperature with surfactants of alkyl chain length greater than 10. We have also examined the differences between values of C p 2 O at a given temperature. The average incremental change in CpZo per CH2 group at 25 OC is 92 J K-' mol-' for the C10, CI 2, and C14 TABs. This compares with values of 83, 8 5 , and 95 J K-l mol-' at 25 OC for the C9 and C10 T A B s , ~C8 and C10 sodium a l k a n o a t e ~ , ' ~and J ~ C8, CIO, and C12 sodium alkyl sulfates,'
1
1400
1
-I
1200
&ooo 800
I O ---
I
I
60,sdOO
0.005
0.010
0.015
0.020
m. mol/kg
Apparent molar heat capacities of tetradecyltrimethyl25 OC ( 0 ) 40 , OC (*), and ammonium bromide solutions at 10 ' C (O), 55 O C ( A ) . The lines are based on parameters from ref 6 and the C p 2 O values given in Table VII. Figure 3.
respectively, as reported by Woolley and B~rchfie1d.I~ The average incremental change in CPz0per CH, group at 40 and 55 OC is 77 and 80 J K-' mol-' for all four TABs. For each temperature it should be noted that there is apparently a decrease in the incremental change per CHI group with increasing alkyl chain length. However, the data are too uncertain to describe this effect quantitatively. The systematic study of a homologous series of surfactants emphasizes certain properties of surfactant solutions. Figure 2 shows our apparent molar heat capacities for all four surfactants at 40 "C. The lines were constructed by using eq 9 with parameters obtained from fitting enthalpy data as a function of temperature.6 The intercept, C P 2 O , was fixed with our measured apparent molar heat capacities by using method 2. The figure shows that the cmc decreases with increasing chain length. Also, we see that the magnitude of the "hump" increases with increasing chain length and that there is a larger overall decrease in $c with increasing chain length. The hump arises from the perturbation in the micellization equilibrium induced by the temperature change that is inherent in a measurement or calculation of heat capacity. for formation The decrease arises because of the negative X P o of micelles. A recent heat capacity study of hexadecyltrimethylammonium bromide suggests evidence for a postmicellar t r a n ~ i t i o n . However, ~ the measurements reported in this study have not been made at high enough concentrations to detect such transitions. In Figure 3 we show the apparent molar heat capacities for tetradecyltrimethylammonium bromide at 10, 25, 40, and 55 O C . Once again the lines were generated as described above for Figure 2 and the apparent molar heat capacities were used to determine C P 2 O by method 2. In the figure we can see that the size of the hump increases with increasing temperature. The concentration
J. Phys. Chem. 1987, 91, 4127-4131 b
at which the hump occurs also increases with increasing temperature. This results from the increase in the absolute value of AHo that occurs with increasing temperature. In conclusion, we have measured densities and specific heat capacities of the C10, C12, C14, and C16 TABS. These data have allowed us to calculate 4c values. We have combined these 4~ values with previously derived 6,values to determine values of C P 2 O . We suggest that, when possible, measurements should be made in the pre- and postmicellar concentration regions for surfactant solutions in order to determine quantitatively C P 2 O and ACpo values. However, in cases where this is not feasible, we suggest that enthalpy data obtained as a function of temperature can be used in conjunction with measured heat capacity data to determine ACpoand C P 2 O . W e also suggest that the 4c values to be used in this manner be determined at concentrations where C # J ~ is not changing rapidly.
c cp" 9
Ep20
cmc d, do AHdil
I
K kix
m
M2 n v20
Ax0 01
P 6
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
r
Y*
d 4C
Glossary A,
B,,, B ,
dr
constant in Debye-Hiickel expressions ion interaction parameters
Dynamics of the Reactions of CH,',
dL
4V
CH,',
4127
ion-size parameter specific heat capacity of solution and solvent standard partial molar heat capacity of solute critical micelle concentration expressed in molality density of solution and solvent integral enthalpy of diluting a solution from an initial concentration to a final concentration m ionic strength, mol kg-l thermodynamic equilibrium constant of eq 1 based on mo-
lalities coefficients in eq 8 and 9 defined in ref 8 total or stoichiometric molality of surfactant molecular weight of solute aggregation number standard partial molar volume of solute change in a thermodynamic property X (X= H , C,, V) for forming micelles at infinite dilution mole fraction of surfactant in micellar form fraction of counterions "bound" to the micelle shielding factor to give effective micellar charge activity coefficient product mean stoichiometric activity coefficient osmotic coefficient on a stoichiometric basis apparent molar heat capacity relative apparent molar heat capacity relative apparent molar enthalpy apparent molar volume
and CH+ with Acetylene
R. B. Sharma, N. M. Semo, and W. S . Koski* Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21 218 (Received: July 29, 1986; In Final Form: February 20, 1987) The reactions of CH3+, CH2+,and CH+ with acetylene to produce C3 ionic products were investigated by measuring the angular distributions of ion product velocities, reaction cross sections, and deuterium isotope distributions. The reactions appear to be proceeding by two different mechanisms. The lifetimes of the intermediate complexes as judged from the deuterium distributions are significantly smaller than the rotational periods of the systems. Measurements of the energies of the ionic reactants and products show that a large amount of internal energy can be present in the C3H3+ion.
Introduction The reactions of hydrocarbon ions with neutral hydrocarbons play an important role in the buildup of ionic chains in combustion processes.' They also play a key role in hydrocarbon polymerization by radiation2 and in recent years they have received considerable attention from scientists interested in explaining the origin of hydrocarbon molecules observed in ~ p a c e . ~ Most - ~ of these applications are based on laboratory work which, in the main, has been devoted to the measurement of rate constants and branching ratios." Considerably smaller number of investigations have been involved in measuring the energy and angular distribution of the products produced in hydrocarbon ion-molecule reactions. Such measurements give one a deeper insight into the dynamics and mechanism of these ion-molecule reactions than one can obtain by most other studies. They give information on the existence or nonexistence of a persistent intermediate complex which has been a point central to chemical kinetics and in turn they shed light on the nature of condensation reactions which are (1) Calcotte, H. F. Combust. Flame 1981, 42, 215. (2) Foldiak, G., Ed. Radiation Chemistry of Hydrocarbons; Elsevier: New York, 1981. (3) Herbst, E.; Adams, N. G.; Smith, D. Astrophys. J . 1983, 269, 329. (4) Schiff, H. I.; Bohme, D. K. Astrophys. J . 1979, 232, 740. (5) Smith, D.; Adams, N. G. Astrophys. J . 1977, 217, 741. (6) Szabo I.; Derrick, P.J. int. J. Mass Spectrom. Ion Phys. 1971, 7 , 5 5 . (7) Fiaux, a.; Smith, D. L.;Futrell, J. H. Int. J. Mass Spectrom. ion Phys. 1974, 15, 9. (8) Kim, J. K.; Anichich, V. G.; Huntress, W. T., Jr. J. Phys. Chem. 1977, 81, 1798.
0022-3654/87/2091-4127$01.50/0
important in carbon chain build up. In this later type of measurements reference should be made to the work of Herman et ale9 In the reaction of C2H4' (C2H4, CH3, H2) C3H3+they measured velocity and angular distribution of the ionic product and concluded that the reaction was proceeding through a persistent complex. On the other hand, work from the same laboratory showed that the reaction CH3+ (CH,, H2) C2H5+was proceeding by a direct process.1° Very recently an interesting crossed beam study was reported on the dynamics of the reaction of C+ with CHI to produce CH3+, C2H3+, and C2H2+." The production of CH3+involved a direct rebound collision mechanism in which hydride ion abstraction took place. C2H3' and C2H2+ proceeded through unimolecular decay of long-lived collision complexes. In the work being reported here we measured cross section and angular and energy distribution of the ionic products from the reactions of CH+, CH2+,and CH3+ with acetylene and because of the ubiquitous nature of C3H3+we have tended to emphasize reactions producing this ion and related ions.'* The ion C3H3+ is one of the abundant ions present in C2H2/02flames, in mass spectra of hydrocarbons, and in products of irradiated hydrocarbons, and it was felt that a study of the dynamics of these (9) Herman, 2.;Lee, A.; Wolfgang, R. J . Chem. Phys. 1969, 51, 452. (10) Herman, 2.;Hierl, P.; Lee, A.; Wolfgang, R.J . Chem. Phys. 1969, 51, 454. (11) Curtis, R. A.; Farrar, J. M. J . Chem. Phys. 1983, 85, 2224. (12) Smyth, K. C.; Lias, S.G.; Ausloos, P. Combust. Sci. Technol. 1982, 28, 147.
0 1987 American Chemical Society
