July, 1958
KINETICS OF THI CARBONIC ACID DEHYDRATION
809
counted for by the repulsion of both H+ and c104- the slow electrochemical desorption.15 The authors wish to express their thanks to Prof. ions which is experimentally observed a t the eathodic branch of the electrocaKdlarv curve. On con- A. R. Tourkv for his interest in this work. c1udi%, may note that fbr in acid (15) B. Conwiy and J . O’M. Bockris, J . Chem. Phys., 26, 532 the slow proton discharge is more probable than (1957).
AN APPARATUS FOR THE INVESTIGATION OF RAPID REACTIONS. THE KINETICS OF THE CARBONIC ACID DEHYDRATION1 BY PAULG. SCHEURER, ROBERT M. BROWNELL AND JAMES E. LUVALLE~ Technical Operations, Arlington Laboratory, Arlington, Mass. Received January 16, 1968
A brief description of a flow machine constructed for the investigation of rapid reactions of photographic interest is given. Details are given of those parts of the instrument which are different from other machines that have been described in the literature. The latter portion of the paper presents data obtained on the dehydration of carbonic acid. This reaction was utilized to test the performance of the machine. The energy of activation was found to be 16.1 kcal./mole, A S * = 36 e.u. and AF* = 5.9 kcal./mole. Fir& ionization constants and the heat of ionization were computed for carbonic acid a t each temperature. The computed heats showed good agreement with Roughton’s measured values.
I. Introduction
against fluid pressure. A circular gland nut allows for initial and subsequent adjustment due to wear. The bearings Reactions with half-lives of one minute or less and glands are machined from “Rulon,” a self-lubricating may be investigated by the capacity flow method material. Roller trip microswitches prevent over-run of of Denbigh,3 the continouus flow method of Hart- the carriage. The motor is powered from a separate line to interaction with the electronic equipment and the ridge and Roughton4 or the accelerated and stopped avoid control console. Rotation of the lead screw operates a flow methods of Chance.6 The capacity flow “Metron” tachometer head, while acceleration of the dismethod is excellent for reactions with a half-life of placement driver plate is recorded by a rack-driven potena few seconds to several minutes. The stopped tiometer and associated electronic circuitry. Tubing running to the cylinders and solenoid valves is fabricated from flow method may be used for reactions with a half- 0.125” 0.d. and 0.062” i.d. full-annealed type number 304 life down to 0.4 to 0.7 millisecond. The methods stainless steel. Weatherhead “Ermeto” swedge type used for solution kinetics can, of course, be used for fittings are used on all transitions to valves and cylinders. gaseous kinetics with suitable modifications.6 A The Skinner solenoid valves have stainless steel bodies and synthetic rubber inserts which are spring loaded in the flow machine for solution kinetics with some new plungers the three way valves. It was necessary to features has been constructed and tested. This break the ofstainless tubing connections between the solenoid paper will give a brief description of the flow valves and the mixing chamber with a short length of polymachine and discuss the data obtained with it on ethylene tubing to absorb mechanical shock to the observation cell. the dehydration of carbonic acid.
11. The Flow Machine Figure 1 is a block diagram of the stopped flow apparatus. The machine may be separated for convenience into three parts; the mechanical drive, the mixing and observation cells and the electronic observation system. The mechanical drive consists essentially of a variable speed lead screw drive’ powered by a 1/2 h.p. enclosed motor which pro els four fluid displacement pistons in cylinders of twenty-lve, twenty-five, fifty and one hundred milliliter capacity, respectively. The inside diameter of the cylinders slightly exceeds the diameter of the pistons. The pistons have selfaligning end connectors and ride in spaced bearings one of which is a tapered gland ring for sealing the cylinder head
SOLENOID EXIT ViPLVE VIEWING CELL-
SOURCE
PISTONS
GRATING MONO. CHROMATOR
INLET . . VILVES
WISE
rTHERMISToR
u RELAY
(1) This research waa supported by the United States under Contract AF 18(600)-371 monitored by the Office of Scientific Research. Fig. 1.-Block diagram of stopped flow apparatus. Reproduction in whole or in part is permitted for any purpose of the United States Government. A schematic diagram of the motor and solenoid controls (2) To whom inquiries concerning this paper should be sent. is given in Fig. 2. The single phase Doerr motor was coupled to the displacement pistons through a hydraulic (3) (a) K. G. Denbigh. Trans. Faraday Sac., 40, 352 (1944); (b) B. Stead, F. M. Page and K. G. Denbigh, Discs. Faraday Sac., 2, 263 speed control. Three double-pole-double-throw relays (REI, RE2 and REI,) were used for the forward and reverse (1947); (e) K. G. Denbigh, M . Hicks and F. M. Page. Trans. Faraday Sac., 44, 479 (1948); (d) F. M. Page, ibid.. 49, 1033 (1953). connections and also were utilized in the control of the sole(4) (a) H. Hartridge and F. J. W . Roughton, PTOC. Roy. Soe. noid valves. The normally open pair of contacts of RE2 close (London),8 1 0 4 , 376 (1923); (b) H. Hartridge and F. J. W. Roughton. during reverse motion to ensure that solenoid valves SV1, Proc. Cambridge Phil. Sac., 23, 450 (1926); (c) G. A. Milliken, PTOC. SV2, SV3 and SV4 connect their respective pump cylinders Roy. SOC.(London), 8166, 277 (1936). to the reservoirs. A normally closed pair of contacts of the (5) (a) B. Chance, J . Frank7in Inst., 229, 455, 613, 737 (1940); forward relay, REI, maintains the exit solenoid valve, SV5, (b) Rev. Sci. Insfs., 18, 601 (1947); ( e ) ibid., 22, 619 (1951). closed a t all times other than during forward motion. The (6) (a) F. Raachig, 2. angew. Chem., 18, 281 (1905); (b) T. D. solenoid valves are operated from a d.c. supply using a germanium diode bridge and a resistance-capacitance filter. Stewart and E. R. Edlund, J. A m . Chem. Sac., 48, 1014 (1923); (c) H. 6. Johnston and D. M . Yost, J . Chem. P h f p . , 17, 386 (1949). This ensures high speed closure of the valves and reproduci(7) W . R. Ruby, Rev. S c i . I ~ s ~ T 26, . , 460 (1955). bility of closing time. The speed of closure is increased by
810
PAULG. SCHEURER, ROBERTM. BROWNELL AND JAMESE. LUVALLE
VoI. 62
208V 60-
DELAY 300 V DC FROM RELAY RACK-
10 w
150 rnfd -150 WV
L PILOT LAMP
22 v2v
of motor and solenoid controls. are energized only during motion of the displacement pistons. / BLOCK The programming switches enable the operator to set up the desired sequence of operations. If necessary, three mixers OBSERVATION may be cascaded. Upon the usual operational procedure, only the mixing unit immediately connected to the observation cell is used. The mixing cell and the observation cell were assembled as one unit (Fig. 3), with the mixing cell below the observation cell. The mixing cell, Fig. 4, was made in three parts from Lucite and press fitted. The 60" cone section, 1, was inserted from below into the main section, 2, with the four tangential jets and the base of the cone a t the same level. Section 3 with a 60" cone shaped hole was inserted from the top so that the lower cone was centered in the upper conical shaped hole. The dimensions of the mixing cell could be LOWER SECTION varied easily by changing the dimensions of the upper and &-MIXING CEbL lower sections. The mixing cell in current use has a volume of 0.018 cm.* The volume between the mixing cell and the observation cell was 0.032 ~ m and . ~the volume of the oba t a flow of 7.4 servation cell was 0.078 ~ m . ~Thus . sec. it would take 15.1 milliseconds after mixing to fill the Fig. 3.-Exploded view of mixing and observation cell observation cell. The time of travel for an element of fluid, dz, from the exit of the mixing cell to the center of the slit assembly. would then be ten milliseconds. An excellent discussion of errors arising from different types of fluid flow, slit length and distance from the point of mixing already has appeared in the literature.4~68*The observation cell was of stainless steel with quartz windows. The dimensions of the observa0.67 tion cell were 2.00 mm. deep by 3.95 mm. wide by 9.82 mm. high. The optimum design wohld have the cross sectional area of the observation cell just equal to the cross sectional area of the exit t o the mixing chamber. However, a t least ten mixing cells were constructed before a unit that mixed properly was obtained; hence the observation cell is too large for the final mixing unit. The first mixing cells were Fig. 4.-Mixing cell (side view) dimensions are given in mm. designed similar to those of W. R . Ruby.' All of these Cell has been drawn 5 X actual size. failed to give good mixing. The test for complete mixing was very simple. A 10% the momentary application of overvoltage to the solenoid as ammonium sulfate solution was mixed with water. Failure it discharges a 150 microfarad condenser. The solenoids to obtain complete mixing caused the index of refraction to are held closed by their rated voltage. A current-limiting vary throughout the this variation appearing as an lamp in series with each solenoid holds the power dissipation apparent difference incell, light absorption. A t 200 r.p.m. of each solenoid below its rated maximum. Diodes are (1.8 cm.B/sec.) and all higher velocities of flow, mixing was used in series with the solenoids to prevent interaction. completed before the fluid reached the observation cell. REBalso operates REa. During the forward thrust of the drive the programmed valves open and close in accordance (8) 9. L. Friess and A. Weissberger, Editors-"Technique of with the operation of REa. It was important that the in ut Organio Chemistry," Vol. V I I I , "Investigation of Rates and Mechasolenoid valves be operated discontinuously so that !ety would not get hot and raise the temperature of the reactants. nisms of Reactions," Interscience Publishers, Inc., New York, The time delay relay RE4 is used to ensure that the valves N. Y..1953, Chapter X. Fig. 2.-Schematic
CLAMPING
July, 1958
KINETICSOF
THE
CARBONIC ACIDDEHYDRATION
111. Electronics and Optics A Sorenson Nobatroii power supply was modified by the addition of an auxiliary choke, 0.04 henry, 30 amperes, to reduce the noise level. This supply furnished the power for the tungsten lamp. The Bausch and Lomb hydrogen arc was supplied by a bridge selenium rectifier which fed a voltage regulator with six type 6080 series regulator tubes and a 5651 reference tube. A flow switch was inserted in the water line t o the hydrogen arc to protect the arc in case of water pressure failure. The E.M.I. 6256B and 6295B photomultiplier tubes were supplied by a power supply rather than batteries. I n order t o keep the signal output of the photomultipliers in the high seiisitivity range of the C.R.O. during the reaction, it was necessary to buck out the initial output voltage at the start of a reaction, or the final ouptut voltage a t the end of the reaction. Figure 5 shows the circuit utilized. Adjustment of R1 for a given reference light level is used to bring point A to zero potential. This then becomes the C.R.O. reference point. The reference light level is expressed as a voltage referred to point A.
i -
811
I
'L.-. OSCILLOSCOPE -. -. -. -. Fig. 5.-Circuit for bucking photomultiplier current for initial and final light levels.
1.5 1.4
1.1 ,
3.20
where D is the vernier reading on the 1500 division Helipot, R1and V is the voltage. The light from the tungsten lamp or the hydrogen arc was passed through a Bausch and Lomb grating monochromator with a dispersion of 33 A./mm. The over-all sensitivity varied with wave length and was of the order of 0.01 t o 0.02 optical density unit per centimeter of oscilloscope deflection with the tungsten lamp a t a slit opening of 0.1 mm. (380 to 640 mp). The sensitivity with the hydrogen arc was of the order of 0.004 t o 0.005 optical density unit per centimeter of oscilloscope deflection with a slit opening of 1.58 mm. (240 to 400 mp). The sensitivity of the apparatus could be increased by employing a Tektronix differential preamplifier (Tektronix Type 53/54D) provided the noise level in the present apparatus could be lowered. Obviously, operation of the photomultiplier at liquid nitrogen temperature would be one way to decrease the noise level. Preceding stopped flow measurement, a variable timing device (see Fig. 2), periodically energized the solenoid valves, causing them to deliver reactant solutions at convenient time intervals alternately to the mixing cell and the reservoir bottles. When the solenoid valves are energized to shift flow from the mixing cell to the reservoir bottles, the sweep mechanism of the oscilloscope is triggered so that the sweep of the C.R.O. starts prior to the closing of the valves. Thus a small portion of the continuous flow curve is always observed prior to the stopped flow curve. Several traces could thus be observed during one full discharge cycle of the displacement pistons.
IV. Performance An investigation of the dehydration of carbonic acid9 was made to determine the performance of
3.24
Fig. 6.-Effect
3.28 3.32 3.36 3.40 3.44 l / T x lo+. of temperature on the rate of dehydration of carbonic acid.
the flow machine prior to utilizing it on some reactions of photographic interest. The stopped flow method was used for these experiments. The data obtained with this instrument have been compared with the results of Dalaielg*and Roughto@ in Fig. 6 and Tables I and 11. The data of Fig. 6 were used to obtain the energies of activation given in Table I. The energies of activation agree within the experimental error. The values calculated from the equilibrium constants for the first ionization given in Table I1 were computed from the rate constants and pHo by the methods outlined by Dalzielga and Roughton.gh The heats of ionization were computed by the method of Harned and his eo-workers, lo using the equat,ionsl0 log K~ = log K,,, - p ( t - e)* (1) AH, = - 4 . 6 p ~ ~ z (-t
e)
(2)
TABLE I COMPARISONOF ENERQY OF ACTIVATION AE kcal./&le
This work Roughtongb Dalziel'"
16.1 16.5 16.9
(9) (a) K. Dalziel, Biochem. J . , 66,79 (1953); (b) F. J. W. Roughton, J . Am. Chem. Soc.. 63, 2930 (1941); (c) A. R. Olson and P. V. Youle, i b i d . . 62, 1027 (1940); (d) F. J. W. Roughton, Proc. R o y . SOC. (London), 1666, 269 (1936); (e) R. Erinkman, R. Margolia and F. J. W. Roughton, P h i l . !!'Tan& Roy. Soc., A232, 65 (1933); (f) F. J. W. Roughton. Proc. Roy. Boc. (London), l26A,474 (1930); (g) M. N. J. Dirken and H. W. htook, J . Physiology, 7 0 , 382 (1930); (h) R. N. J. Saal, Rec. trau. chim., 47, 264 (1928). (10) (a) H. S. Harned and N. D. Embree, J . Am. Chem. Soc., 66, 1050 (1934): (b) H. S. Harned and R. A. Robinson, T r a n s . Favaday Soc.. 36, 973 (1940).
R. H. ARANOW, L. WITTENAND D. H. ANDREWS
812
Vol. 62
TABLE I1 37.3 62.1 3.81 1 . 3 (1.35) 490 DEHYDRATION SPECIFIC RATE CONSTANTS, FIRST 37.5 70.8 3.76 1 . 5 (1.51) 480 Thg-values in parentheses were used for the calculation IONIZATION CONSTANTS AND THE HEATSOF IONIZATION FOR Of: - A H . CARBONIC ACID k.
to,
sea. -1
OC.
(pHlo
1.979b
...
17.90 23.0
14.69b 18.1
3.56
23.5 25.5' 26.3' 27.0' 29.0' 30.2 31.5 32.0 34.8 35.6 35.6 36.67
19.0 23.0 25.6 31.Ogb 32.0 37.7 37.0 38.6 49.6 50.1 55.0 80.0'~
0.0
... 3.69 3.72 3.69 3.80 3.76 3.79 3.81 3.85 3.85 3.82
KH~co~~
-AH,
where p is a constant for any given acid and 0 is the temperature corresponding to Kma,. Roughton has estimated Kma, t o occur at 55' for carbonic Assuming Roughton's value of 55" for 0, a plot of (t was made against log K1 and the slope of the best straight line was used as a value for p (p = 3.18 X lo-+). This value of p was used in equation 2 to compute values of AH. The values of AH obtained directly by Roughton are also included in Table 11. The agreement is certainly within the experimental error. The results of these experiments' show that this flow machine may now be utilized for the investigation of previously unstudied reactions. Acknowledgment.-The electronics were designed and built by R. Smythe and D. Forrant. The mechanical system was designed by E. Gariepy.
cal.
(2.5 f 0.3)'b 1710 f 1059b x 10-4 ... 1240 i50' 2.4(2.4) X 800 10-4 1 . 8 (1.78) 800 1.7 (1.66) 890 1.8 (1.78) 760 960 f 130gb 1 . 4 (1.38) 680 1 . 5 (1.52) 650 1.4 (1.41) 620 1 . 4 (1.35) 610 1 . 2 (1.23) 540 1 . 2 (1.23) 520 1.3 (1.32) 520 450 128b
THE ENTROPY OF FUSION OF LONG CHAIN HYDROCARBONS BY R. H. ARANOW, L. WITTENAND RIAS, Inc., 7212 Bellona Avenue, Baltimore 12, Maryland
DONALD H. ANDREWS The Johns Hopkins University, Baltimore 18, Maryland Received January 33, 1968
An analysis is made of the high entropy of fusion of long chain paraffins attributing that entropy to the onset a t melting of freedom of the molecule to undergo hindered rotation about each carbon t o carbon bond. The theoretical results are compared with the ex erimental observations. The entropy of fusion of heavy paraffins yields information concerning the rotational energy leveys of the molecules. An empirical relationship is stated connecting the energy levels of the molecule with the melting temperature of the molecule.
I. Introduction The entropy of fusion of long chain paraffins increases by a factor very close to R In 3 for each additional CH2 group added to the chain. The high values for the entropy of fusion of long chain paraffins have long been known and have been attributedzaPbto the onset a t melting of freedom of the molecule to change from one molecular configuration t o another by rotations around carbon to carbon bonds. There are three potential minima for rotation about each carbon to carbon bond and this yields a factor R In 3 for the entropy increase per mole on addition of a carbon-carbon bond. In this paper we examine this proposal more carefully and make comparisons with experimental results. For paraffins with an even number of carbons the R In 3 factor checks rather well with experiment, although with deviations which will be discussed later. Many paraffins with an odd number of (1) Much of this work is based on a thesis submitted by R. H. Aranow in partial fulfillment of the requirements of a Ph.D. degree a t the Johns Hopkins University. This research was supported in part by the United States Air Force through the Air Force Offiae of Scientific Research of the Air Research and Development Command under contract number A F 18(600)-765. (2) (a) I. Langmuir, J . Am. Cham. Soc., 54, 2798 (1932); (b) 8. Misushima, "Structure of Molecules," Academic Press, New York, N. Y., 1954, p. 111.
'
carbons undergo a phase change in the solid state, a few degrees of temperature below the melting point. The entropy of fusion of these paraffins yields a factor less than 2R In 3 for an additional two CH2 groups. However, if the entropy change a t the pre-melting transition is added to the entropy change of fusion, the resulting total entropy change is indeed 2R In 3 for each additional pair of CHZ groups. Deviations from the R la 3 rule can be expected to yield information concerning the excited states of the molecule and indeed they do so as will be shown. In the next section we give a theoretical analysis of fusion for a simplified model of paraffins., I n section 111 we discuss theoretically the model and its correspondence with the real molecule making detailed comparisons between experiment and theory. 11. Fusion of a Simple Model of Paraffins In this section we shall not discuss the real molecular configurations of paraffin but instead a fictional model in which there is also a threefold barrier to rotation around bonds. Our fictional model consists of parallel symmetrical triangles which are stacked along a straight line through their centers to form a linear chain, which straight
c
