1130
D. L. HILDENBRAND, A. G. WHITTAKERAND C. B. EUSTON
2COOH. This is done to emphasize the fact that intramolecular carboxyls appear to react with copper and not just any two carboxyls from different molecules that get close enough together. Evidence for this is obtained from the fact that the equilibrium constant expression is found to vary inversely with the first power of the acid concentration and not with the square of that concentration. The inverse first power thus implies that the pairs of carboxyls involved come from the same molecule, and that they might even be adjacent. If enough copper has been added to the solution so that self-ionization of the acid is replaced by reaction 1, we can write that 1
[( COO)&U] = 3
[H+]
(3)
Moreover, from the experimental conditions we note that the following approximations can be made for the straight portion of the curves [Cu++] E [cu]T = total copper concn.
(4)
1 [(GOOH),] = equivalent ooncn. of P A A 2
(5)
and
Equation 2 can now be simplified t o
K =
W+I3 [ CU]T[PAA]
Vol. 58 (6)
Since FAA remains essentially constant for the titrations with the higher concentrations of copper nitrate, a log log plot between [H+] and [CU]T should have a slope of approximately 3, as confirmed by experiment. Other salts such as potassium nitrate, strontium nitrate, zinc nitrate and even nickel perchlorate and cobalt perchlorate do not show nearly as strong a tendency for replacement of hydrogen in polyacrylic acid as copper ion does. This behavior is consistent with the behaviors of these ions in forming other complexes. The pH results thus corroborate the polarographic and absorption spectra observations which suggest that a copper polyacrylate complex exists, presumably a chelate structure involving adjacent carboxylate group^.^ Acknowledgment.-Acknowledgment is made for the assistance given by Robert L. Rebertus in obtaining the polarographs. (7) Professor Paul J. Flory recently reported (private communication) that a decrease in viscosity ocours when copper salts are added to polyacrylic acid. This fact can also be explained by the formation, of a complex: see P. J. Flory and J. E. Osterheld, T H I S JOURNAL, 68, 653 (1954).
BURNING RATE STUDIES. I. MEASUREMENT OF THE TEMPERATURE DISTRIBUTION IN BURNING LIQUID STRANDS BY D. L. HILDENBRAND, A. G. WHITTAKER AND C. B. EUSTON Chemistry Division, U.E. Naval Ordnance Test Station, Inyokern, China Lake, California Received June 14, 1964
Fine wire thermocouples (0.0003 inch diameter) carefully prepared by micromanipulative techniques have been used to explore the temperature distribution in several burning liquid systems as an aid in the theoretical approach to liquid combustion. The experimental temperature-time records were combined with simultaneously determined li uid consumption rates to give the steady-state temperature distance curves. Work to date has been chiefly concerned w i 8 the liquid phase profiles and the effect of variables such as li uid viscosity on the shape of the profile. High-speed motion pictures of the burning process have been synchronized with &e temperature-time records to determine the relative positions of the thermocouple and the liquid surface. The three liquid systems studied thus far have been the two component systems 2-nitropropane-nitric acid, metriol trinitrate cooled with triacetin, and ethyl nitrate. Emphasis has been on interpretation of the data and their application to determining surface temperature.
Introduction A knowledge of the temperature distribution in a combustion wave is essential for understanding the mechanism of propagation of the wave. Ideally, the experimental temperature profiles will give such valuable information as the distribution of heat sources and a characterization of the modes of energy flow within the system. These data will, in turn, be helpful in working out the detailed chemical kinetic processes taking place in the combustion wave. This study has been primarily concerned with the liquid phase temperature distribution in the hope of acquiring information about chemical reactions occurring in this region and the possibility of their influencing the over-all rate of burning. The data would also be useful for checking the validity of theoretical treatments such as that developed for solid powders by Rice and
Ginell' which is based on a rate of burning controlled by the surface temperature, However, it is the intent to present only the experimental method and some of the preliminary results in this paper. Details of the results and conclusions reached in this work will be published a t a later date. Experimental Procedure The temperature profiles were obtained with thermocouples prepared from a 0.0003 inch diameter platinum and platinum-lO~o rhodium Wollaston wire. I n the early work, the thermocouples were made by dissolving off about one-half inch of the silver coating and passing the crossed wire ends through a gas-oxygen flame as described by Klein, et aZ.2 Using this method, the size of the bead at the junction could not be closely controlled and the head diameter varied from three to six times that of the wire. When it became apparent from the early records that at least a portion of the temperature-time trace was much steeper (1) 0. K. Rice and R. Ginell, THISJOURNAL, 64, 885 (1950). (2) R. Klein, M. Mentser, G. Von Elbe and B. Lewis, ibid., 64, 877 (1950).
Dec., 1954
TEMPERATURE DISTRIBUTION IN BURNING LIQUIDSTRANDS
than anticipated, it was decided to use micromanipulative techniques in preparing the thermocouples. I n this way, the bead could be kept at a small, uniform size, thereby reducing thermal lag to a minimum. A deFonbrune Micro-forge was modified slightly and used as a micromanipulator. The thermocouples were then made in the following manner. About '/4 inch of the silver coating was dissolved from a short length of platinum Wollaston wire. The 0.0003 inch diameter platinum wire was then brazed to a 0.004 inch diameter platinum lead wire with a gas-oxygen microtorch and the small wire cut off to the appropriate length. The process was repeated for the platinum-10% rhodium wire. The two large lead wireR were then mounted in opposite arms of the micromanipulator and brought together until the tips of the 0.3 mil wires were just touching. By bringing the tip of the microtorch into the field of the microscope, the welding operation could be very carefully controlled; the flame was removed as the two wires just fused together. Using this method, essentially a butt-weld was obtained with the junction about 70% larger in diameter than the wire. T o remove any uncertainties regarding the temperature-e.m.f. relation, one of the 0.3 mil diameter couples was compared with a Bureau of Standards calibrated platinum, platinum-lO% rhodium thermocouple in the temperature range 25-1000°. The behavior of the fine thermocouple was entirely normal and it followed the standard couple within *lo over the whole range. For most of the work, bare thermocouples were used. However, a few runs made using couples coated with a very thin Teflon film gave profiles identical to those obtained with bare couples, indicating a lack of catalytic activity by the platinum. The thermocouples were mounted in Pyrex tubes by drilling two holes with a hot tungsten wire and stretching the couple diametrally across the tube using additional micromanipulators. A wax seal held the thermocouple firmly in position, with the junction located as closely as possible in the center of the tube. Conduction errors were minimized by this type of mounting since the couple lay essentially in an isothermal region. For the temperature profile measurements, the liquid filled tube was placed in a two-window bomb and preesurized with nitrogen gas. Thermocouple leads and igniter wires were brought out through the bomb head by high-pressure insulated connectors. The liquid was ignited by passing a current through a length of iron wire on which was threaded a small piece of ballistite. By locating the thermocouple sufficiently far down the tube, any igniter effects were completely damped out by the time the combustion wave reached the vicinity of the couple. As the liquid burned pa& the thermocouple, the temperature rise was recorded. A mask could be at,tached to the tube to provide reference marks a known distance apart for measuring consumption rates. The thermocouple output was amplified with a Tektronis Type 112 direct coupled amplifier and fed to an Electronic Tube Corp. Model H-21 dual beam cathode ray oscilloscope; the scope pattern was photographed on continuous strip film with a Fairchild Type 314 Oscillograph Record Camera. One of the scope beams was modulated a t 250 C.P.S. and used as a baseline while the other was modulated at 1000 C.P.S. and used to record the thermocouple signal. At the same time, motion pictures of the combustion wave traveling down the tube wer? taken with an Eastman high-speed camera at a rate of about 400 frames per second. Signals from a time base pulse generator were used to Z-axis modulate the oscilloscope and to actuate the high-speed camera timing light in order to synchronize the two film records and provide a common zero time reference. By means of appropriate lenses, the high-speed camera covered a field of view about '/z inch square in which the thermocouple could be clearly seen. Before and after each run several known voltages were impressed on the oscilloscope to calibrate the record. The sensitivity of the instrument was usually such that a full scale deflection corresponded to a temperature rise of about 600'. A traveling microscope was used for assessing the temperature record. Separate experiments showed the time lag in the electronics of the temperature measuring system to be less than two milliseconds, which was entirefy negligible in this work. The actual frequency response of the thermocouple waa not determined. However, since the couple readily recorded changes of fifty to one hundred thousand degrees centrigrade per second obtained 8;s described later, it was felt that
1131
the response would be adequate for recording the rise in the liquid preheat zone which had a maximum rate of change of one to three thousand degrees per second.
Results and Discussion Thus far, profile data have been obtained for three liquid systems-the stoichiometric mixture (for complete combustion) 2-nitropropane-95% nitric acid, metriol trinitrate3" (820/,)-tria~etin,~~ and ethyl nitrate. The temperature records for all three systems have the same general shape. The various features of the profile appear to be related to the combustion wave in the following way. As the burning surface approaches the couple, there is a rapid exponential rise of 100300°, depending on the system, which is from 0.1 to 0.3 millimeter in depth. High-speed motion pictures show that the couple is visible beneath the liquid surface in this region. This is followed by a very gradual rise of some 20-50" extending over a region 0.3 to 1 millimeter in length in which the couple is no longer visible. The length of this plateau was not entirely reproducible and was shown by the motion pictures t o be caused by the thermocouple pulling up a film of liquid as it works against the surface forces. At the end of the plateau there is a n extremely abrupt rise of over 1000" in about 10 milliseconds. The start of the abrupt rise was shown to coincide exactly with the breaking of the liquid film as seen in the highspeed pictures. Because of this filament pull-out effect, the couple finds itself well up into the hot gases above the surface when the film breaks. There is a further gradual rise until the thermocouple reaches the hottest portion of the flame. Only a part of the gas phase profile can be obtained, of course, if the flame temperature exceeds the melting point of platinum, as it did in the case of the nitropropane-nitric acid mixture. I n this study, however, the liquid preheat region and the surface temperature were of primary interest. It is clear that because of the filament pull-out effect, the present method does not yield the correct gas phase profile in the region directly above the surface. However, the effect is helpful in determining the actual liquid surface temperature. The thermocouple is interpreted as reading the "true" surface temperature when it becomes tangent to the liquid surface and just begins pulling up the liquid film. This corresponds to the point on the profile a t which the exponential rise breaks over into the gradual plateau, as indicated a t point A of Fig. 1. I n calculating the temperature-distance curves from the experimental data, the temperature distribution was assumed to move down the tube at the steadystate consumption rate and only enough points were included to show the shape of the curve. By comparing data obtained from a series of runs made under identical conditions it was found that the exponential liquid phase temperature rise was reproducible to well within f10" and that surface temperatures may likewise be obtained within the same limits. High-speed photographs pointed out a striking (3) (a) Methyl trimethylol methane trinitrate; acetate.
(b) glycerol tri-
D. L. HILDENBRAND, A. G. WHITTAKER AND C. B. EUSTON
1132
Vol. 58
photographs showing only a very thin region of extremely mild convection currents in the preheat zone. This would seem to indicate that with the two nitrate esters any liquid phase reactions must be occurring to a much lesser extent than in the nitropropane-nitric acid system and they must be occurring in a region much closer to the surface if they occur a t all.
I
I
- 0.5
0 MILLIMETERS,
Fig. 1.-Temperature versus distance from burning surface for ethyl nitrate burning at 100 p.s.i.g.; consumption rate 0.052 cm./sec.
feature in the combustion behavior of the 2-nitropropane-nitric acid system. There is a great deal of random motion or turbulence in the liquid preheat region beneath the surface, presumably due t o convection currents caused by the large thermal gradients and possibly by heat generated in exothermic chemical reactions near the surface. Because of these disturbances the profiles for this system were quite erratic in the liquid preheat region as shown in Fig. 2. Addition of 0.5%
I
- 0.5
I
MILLIMETERS. 0
Fig. 3.-Temperature versus distance from burning surface for 2-nitropropane-95% nitric acid plus 0.55% lucite burning at 300 p.s.i.g. ; consumption rate 0.132 cm./sec.
A detailed theoretical treatment of the combustion process cannot be made until more is known about the chemistry involved. However, some useful information may be gained from an analysis of the experimental profiles according to treatments such as that developed by Reid.4 He has proposed an expression for the steady-state temperature distribution in a burning liquid or solid resulting from heat conduction and radiation absorption by treating a region sufficiently far below the surface so that heat generated by chemical reaction is negligible. Exclusion of the chemical reaction term, of course, allows the heat flow equation to be solved analytically. The temperature distribution may then be expressed by the equation
300 P 2oo I-
100
- 0.5
0 MILLIMETERS,
where v is the steady-state consumption rate, T and T , are temperature recorded by the thermocouple and initial temperature, respectively, h2 is the Lucite by weight increased the viscosity from 0.7 thermal diffusivity, t is time, A is the radiation to 18 centipoises and damped out completely the intensity a t the burning surface, p and c are irregularities in the profile as seen in Fig. 3. Un- density and specific heat, a is the radiation abfortupately, the Lucite itself did not burn completely sorption coefficient and r is the distance below the and a considerably higher surface temperature was surface a t which T and bT/dt are measured. All recorded, probably because of a polymer-rich film but A , a and h2 are known from the experiment. on the surface. The experiment does serve to From three sets of data taken at three different show, however, that the “thermal noise” can be times, simultaneous solution of the resulting three damped out by increasing the viscosity sufficiently. equations will yield these quantities. As an exPhotographs of the burning Lucited mixture ample, the following values for these parameters tended to confirm this by revealing a greatly were obtained from an analysis of a metriol trireduced amount of activity in the preheat zone. nitrate-triacetin liquid phase profile: a = 121 The other two liquid systems, metriol trinitrate cm.-’, A = 17 cal./cm.2 sec. and h2 = 3.6 X and ethyl nitrate, with viscosities of 25 and 0.6 cm.2/sec. None of these quantities have been centipoises, respectively, both yielded smooth and determined independently so that a comparison very reproducible liquid phase profiles with the (4) W. P. Reid, THISJOURNAL, 67, 242 (1953). Fig. 2.-Temperature v e r ~ u sdistance from burning surface for 2-nitropropane-95yo nitric acid burning a t 300 p.s.1.g.; consumption rate 0.160 cm./sec.
Dec., 1954
THERMODYNAMIC FORMATION CONSTANTS OF COORDINATED COMPOUNDS
can be made, but the calculated values do appear to be reasonable. By applying the treatment to other systems, it may be possible to classify them accord-
1133
ing to certain models, e.g., a radiation and conduction model or a conduction only model. Work of this type is planned.
STUDIES ON COORDINATION COMPOUNDS. XII. CALCULATION O F THERMODYNAMIC FORMATION CONSTANTS AT VARYING IONIC STRENGTHS1 BY REEDM. IZATT, CHARLES G. HAAS,JR.,B. P. BLOCK AND W. CONARD FERNELIUS Contribution from the College of Chemistry and Physics, The Pennsylvania State University, State College, Pa. Received June 16, 1864
Molarity quotients determined potentiometrically a t varying ionic strengths have been converted to stepwise thermodynamic formation constants in aqueous solution for the reactions of Zn++, Ni++, Cea+, and Pr3+(as the perchlorates) with the acetylacetonate ion a t 30” by means of activity coefficients calculated from the Debye-Huckel equation. Agreement of the several thermodynamic constants calculated for each metal ion is good. The molarity quotients in the lit,eraturefor the Pb++-citrates and the Cu++-, Ni++-, Cd++-, and Mg++-malonate4 systems may be satisfactorily converted to thermodynamic constants by the same procedure.
Introduction Much of the quantitative work in the determination of formation “constants” of coordination compounds has been done in solutions containing a large excess of neutral salt, which was added to maintain the activity coefficients of the various species constant throughout the determination. This procedure allows comparisons to be made among different metal ions, if the same medium is employed in each case. Unfortunately, however, work on different coordination systems has been done a t various ionic strengths and often with different anions. It would be more desirable if the “constants” were true thermodynamic constants and therefore theoretically comparable. The present investigation was undertaken to determine for a given chelating agent, the acetylacetonate ion, the practicability of obtaining thermodynamic constants by correcting molarity quotients with theoretically calculated activity coefficients. The data obtained also indicate the range of ionic concentration in which such a calculation procedure yields concordant values. A further object of the investigation was to illustrate the desirability of the use of the method by applying it to data for molarity quotients already available in the literature and noting the agreement obtained. Theoretical.-The calculation of thermodynamic formation constants requires that the activity coefficient term of equation 1 be known.
where K f = the thermodynamic formation constant,
Qr = the molarity quotient y = the molar activity coefficient of the ionic species, as indicated, present in the soln. x and y refer to the number of ligands, Ch, attached to Mn+ and the charge on the ligand, respectively
It may be learned by (i) making determinations (1) From a dissertation presented by Reed M . Izatt in partial fulfillment of the requirements for the degree of Doctor of Philosophy, August, 1954.
near infinite dilution (as in conductivity methods) , (ii) determining Qf a t several ionic strengths and extrapolating the plot of ionic strength or square root of ionic strength os. Qf to infinite dilution, or (iii) calculating activity coefficients from theoretical relationships (e.g., the Debye-Huckel theory). Procedure (i) yields thermodynamic constants so that no correction is necessary. Procedure (ii) gives accurate values if one is able to determine the &I values a t sufficiently dilute concentrations so that the error involved in the extrapolation from the last point to infinite dilution is minimized. This error is usually large since the curve is steepest at the last points measured. Procedure (iii) eliminates the necessity of making the large number of determinations required to define the curve because the activity coefficients enable one to determine the value of the thermodynamic constant from the molarity quotient a t some concentration, C. Ionic strength is defined by Lewis and Randall2 as 1.1 = ‘/aZmiZi2
Harned and Owen3 give the expression for the activity coefficient of an ion, f j , based on the DebyeHuckel theory as where (a) all terms have their usual significance (for a complete definition of terms see ref. 3) (b) the expression in the parentheses is constant for a given solvent and temperature, and is referred to hereafter as H (c)
r
= 2p
Equation 2, then, makes possible the calculation of the activity coefficient of an ion in dilute solutions. Since the work reported in this paper was performed in fairly concentrated solutions, it was (2) G. N . Lewis and M . Randall, “Thermodynamics and The Free Energy of Chemical Substances,” 1st ed., McGraiv-Hill Book Co., Inc., New York, N. Y . ,1923, pp. 373-74. (3) H. S. Harned and B. B.Owen, “Physical Chemistry of Electrolytic Solutions,” 2nd Ed., Reinhold Publ. Corp., New York, N. Y., 1950, pp. 35-42, equation 3-4-4, 117-121.
