Specific Heat Capacities of ‘Aqueous NaCl
References and Notes (1) H. S.Gutowsky, G.0. Bedford, and P. E. Mac Mahon, J. Chem Phys,, 38, 3353 (1962). (2) R. J. Abraham and H. J. Bernstein, Can. J. Chem., 39, 39 (1961). (3) (a) H. J. Bernstein and E. Pedersen, J. Chem. Phys, 17, 885 (1949); (b) W. W. Wood, W. Fickett, and J. 0. Kirkwood, J. Chem. Phys., 20, 561 (1952);(c) A. Moscowitz, K. Wellman, and C. Djerassl, J. Am. Chem. Soc., 85, 3515 (1963). (4) G. Govll and H. J. Bernstein, J. Chem. Phys., 47, 2818 (1967). (5) E. W. Garbish, B. L. Hawkins, and K. D. Mackay in “Conformational Analysis”, 0. Chiurdoglu, Ed., Academic Press, London, 1971. (6) H. Joshua, R. Gans, and K. Mislow, J. Am. Chem. Soc., 90, 4884
(1968). (7) (a) L. RosenfeM, Z Phys., 52, 161 (1928);(b) M. Born and P. Jordan, “Elernentare Quantenrnechanik”, Verlag Julius Springer, Berlin, 1930, p 250; (c) J. G. Kirkyood, J. Fhem. Phys., 5, 479 (1937). (8)J. P. Mathleu, “Les Theories molecuhiies du powoir rotatoke naturel”, CNRS. Paris. 1946. (9) E. L. EM, “Stereochemistry of Carbon Compounds”, McGraw-Hili, New York, N.Y., 1962. (10) R. R. Gould and R. Hoffmann, J. Am. Chem. Soc., 92, 1813 (1970).
547
(11) C. 0.Beckmann and K. Cohen, J. Chem. Phys., 4, 784 (1936). (12) W. J. Kauzmann, J. E. Walter, and H. Eyring, Chem. Rev., 28, 339 (1940). (13) Starting from commercial (3/+3-methyicyclohexanone, the sygthesig of this compound has been made by I.Douine, These de Specialite (Chimie Organique), Universite de Provence, Marseille, 1974. (14) The experimental data for this compound wiil be published later. (15) From experimental data of N. M. Baghenov and M. V. Volkenshtein, Zh. Fiz Khlm., 28, 1299 119541. (16) A. Francois, These de Speciallte (Chimie Organique), Unlversit; de Provence. Marseille. 1975. (17) A. Francois, 0. PouGrd, F. Vila, and L. Pujol, C. R. Acad. Scl Park, Ser C, 278, 1369 (1974). (18) E. L. Ellel, N. L. Allinaer. S. J. Anaval. and 0. A. Morrison, “Conformational Analyds”, Interscience, New York N.Y., 1965. (19)J. B. Lambert and R. R. Clikeman, J Am. Chem. Soc., 98,4203
(1976). (20) B. L. Hawkins, Ph.D. Thesis, University Microfilms, Ann Arbor, Mich. No. 70-15738. (21) S. S. Kurtz, J. Senta Amon, and A. Sankin, Ind. €ng, Chem., 42, 174 (1950).
Determination of the Specific Heat Capacities of Aqueous Sodium Chloride Solutions at High Pressure with the Temperature Jump Technique K. G. Liphard, A. Jost, and G. M. Schneider’ Institute of Physical Chemistv, University of Bochum, Bochum, German Federal Republic (Received Novetnber 9, 1976)
In this work specific heat capacities have been measured by the temperature jump technique. Electrical energy stored in a high voltage capacitor is discharged through the electrically conducting solution; this causes a rise in temperature which is measured indirectly by the optical absorbance change of a buffered indicator system. cv data are reported for aqueous sodium chloride solutions in the concentration range from 0.1 to 2.0 mol kg-’ at 293 K at 1and 2 kbars. All cv values decrease with increasing pressure. A t 1bar and 1kbar cv decreases monotonously with increasing salt concentration whereas at 2 kbars a maximum appears. Using data for compressibility and cubic expansion coefficients c v was converted to cp; its dependence on pressure and salt concentration, respectively, is similar to the behavior of C V . The data obtained are discussed with respect to structural effects. From the volume dependence of cv and the pressure dependence of cp, the temperature dependence of (ap/aT)v and of (aV/aT),, respectively, is calculated; with increasing salt concentration the temperature dependence of both decreases,
I. Introduction Among the thermodynamic properties of electrolyte solutions the heat capacity is of primary importance. Several heat capacity studies on aqueous solutions of NaC1, a most important electrolyte in nature, have already been made during recent years1” but there are no measurements at high pressure up to now. Such high pressure heat capacity data on NaCl and other electrolytes, however, would be of considerable interest not only for practical applications, e.g., for oceanography such as for the storage of heat in the deep sea; for mineralogy especially for geysers, hydrothermal syntheses etc.; for salt industry etc., but also for theoretical research, e.g., for the thermodynamics of electrolyte solutions, for the investigation of structural changes, etc. In the laboratory heat capacities are mostly measured calorimetrically. The usual calorimetric methods, however, show some disadvantages for high pressure measurements: The mass of the autoclave is usually much more than a factor of 10 larger than that of the species investigated so that precision measurements are very difficult; heat losses through pressure connections also have to be considered. These effects can be avoided using the temperature jump technique because here the measuring time is on the order of 1ms. In the temperature jump technique a high
voltage capacitor is discharged through an electrically conducting solution. The electrical energy We,absorbed causes a temperature increase AT according to
WO1= c m A T
’/2CU2 = cpVAT where c is the specific heat capacity in J K-l g-l, rn the mass in g, AT the temperature difference in K, C the capacity in F, U the loading voltage of the capacitor in V, p the density in g ~ m -and ~ , V the effective volume in cm3. For the present investigations the change of temperature (temperature jump) AT is measured indirectly by means of the light absorption change of a colored pH indicator (here phenol red) dissolved in very low concentration in the buffered solution under test. 11. Experimental Section A. Temperature Jump. The measurements of the heat capacities were carried out in a temperature jump apparatus that has been developed for the investigation of fast reactions in solutions under high pressure. The measuring cell with optical windows for spectroscopic measurements was mounted in a high pressure autoclave. Details of the experimental device have been described The Journal of Physical Chemistiy, Vol. 81, No. 6, 1977
K. G. Llphard, A.
548 10,
TABLE I: Specific Heat Capacities of Aqueous Sodium Chloridea
,
- - - 1 kbar
- 2 kbar OD
Jost, and G. M. Schnelder
mNaC1,
mol kg-’
~
0.1 0.5 1.0 2.0
C51
C V ,J g-’ K-’ 1 kbar 2 kbars
3.84 3.80 3.72 3.59
3.59 3.63 3.56 3.46
cp, J g - ’ K-’ 1 kbar 2 kbars 3.92 3.89 3.82 3.75
3.78 3.83 3.77 3.71
a c v and c . Data taken at different pressures and molalities. $he digits have been given beyond significant figures to avoid accumulation of roundout errors. 01.
O0
L ~ G
500
600
hlnm
Flgure 1. Spectrum of phenol red at different temperatures and pressures: 2 X mphenol red, 9 X lo4 mTris buffer, 0.1 mNaCI, pH 7.4 at 20 O C , OD = log &/I = optical density.
elsewhere.6 With only slight modifications this apparatus was used for the measurements presented in this paper. In order to prevent dissolution of the pressure transmitting medium, nitrogen, in the solution under test a small flexible tube filled with solution was attached to the top of the cell and the pressure was transmitted to the solution from the pressurizing medium through the elastic walls of the tube. The temperature in the cell was measured by a steelsheathed thermocouple introduced into the cell through a capillary tube. The pressure was measured with Heise gauges. B. Spectrophotometry. The relation between the optical absorption change and the rise in temperature was measured separately by a static method described in detail el~ewhere.~ Here the pressure transmitting medium was also nitrogen. It was excluded from the cuvet to be dissolved by an open-ended tube filled with solution avoiding a quick mixing by a long diffusion path. C. Substances. Sodium chloride was purchased from Baker Chemicals, Deventer (Holland), as “Analysed Reagent”, and phenol red and tris(hydroxymethy1)aminomethane (Tris) by Merck AG, Darmstadt (Germany). These substances were used without further purification. The water used was triply distilled. All solutions were carefully degassed before measurement. 111. Results Measurements have been carried out for solutions of NaCl in water in the concentration range from 0.1 to 2 mol kg-l at 1 and 2 kbars. The temperature before the temperature jump was T = 293.2 K for all measurements. The concentration of the indicator phenol red was always 2 X mol kg-l in a solution of 9 X lov4mol kg-l Tris buffer. Thus the concentration of both indicator and buffer was more than two orders of magnitude lower than that of the smallest salt concentration measured; thus any influence on the heat capacity could be neglected. A. Results of Spectrophotometric Measurements. Absorption spectra of aqueous phenol red solutions were measured at different salt concentrations and pressures. One series of spectra is shown in Figure 1. The salt concentration is 0.1 mol kg-l, the pressures are 1 and 2 kbars. The absorption maxima at X 557 and 432 run belong to the deprotonated and protonated form, respectively, of the indicator. The spectra were recorded at four different temperatures. I t can easily be seen that the equilibrium is shifted toward the protonated form of the indicator with increasing temperature. From these spectra the temperature dependence of absorption (at constant waveThe Journal of Physical Chemistry. Vol. 81, No. 6, 1977
length) can be calculated for each pressure and salt concentration. B. Results of Temperature Jump Measurements. The heat capacity can be calculated according to e=-
cu2
V 2 p AT Here the effective volume V is most difficult to measure because of the complicated geometry of the measuring cell. Thus the ratio C/V was determined by calibration of the cell with solutions of different salt concentrations at normal pre~sure.l-~ All density data were taken from the literature.21s For the determination of specific heat capacities several temperature jumps were made starting from the initial temperature T = 293.2 K, the temperature jumps being in the range from 0.5 to 5 K. The resulting temperature differences AT (calculated from the optical absorption changes) were plotted vs. U.The slope of the resulting lines were extrapolated to zero temperature jump and the heat capacity values were obtained from these limiting slopes. The error of this extrapolation is small since within the accuracy of the present measurements essentially straight lines were found. The accuracy of the specific heat capacity data obtained is estimated to be &l%. C. Heat Capacity Data. Another advantage of the temperature jump technique for heat capacity measurements is the alternative determination of specific heat capacity at constant volume or constant pressure, cv and cp, respectively. When the solution is heated normally thermal expansion occurs. For very short heating times (e.g., on the order of 1ps) the heating takes place under essentially isochoric conditions, i.e., dV = 0, producing a shock wave which runs through the solution. For much slower heating times the pressure is balanced at each time. Thus at short heating times cv values and at longer heating times cp values can be measured. The heating times can easily be changed by the appropriate choice of the discharge unit, mainly by changing the capacity of the high voltage capacitor. In this paper only measurements of cv data are presented. The resulting cv values are listed in Table I. The dependence on the molality m of the salt at 1bar, 1kbar, and 2 kbars is shown in Figure 2; here the data at normal pressure were taken from the literature.2 The cv values of pure water were calculated from cp values taken from ref 9 using data for compressibilities and cubic expansion coefficients taken from ref 10. Table I and Figure 2 show that the cv values decrease with increasing pressure. At 1bar and 1kbar the cv values decrease monotonously with concentration but at 2 kbars a maximum appears. The dependence on the square root of the molality of the salt is approximately linear above about 0.5 mol kg-l for all pressures measured. The measured cv values can be converted to c p values using
540
Speclflc Heat Capacities of Aqueous NaCi
*.
01
05
10
/mol’” kg-”2
Figure 2. Specific heat capacity at constant volume cvas a function of the square root of the molality mof NaCI: T = 293.2 K, p = 1 bar, 1 kbar, and 2 kbars.
0
..
1 bar 1 kbar 2 kbar
( 1.L2
1.0
05
kg-”2
rn:iCl
Flgure 4. Plot of (&&/la = 293.2 K.
r
v)rVS. the square root of the molailty mof NaCI:
1
I
