APPARATUS THOMAS N. DODD, Jr. St.Peter's College, Jersey City, New Jersey
THIS article is a sequel to the previous one describing a simplified magnetic rotation apparatus,' and the former article should be consulted before the present paper is read. The simplified apparatus had some inconvenient features: The magnetizing current could warm the tube, striate the liquid, and make the polarimeter difficult to read. Furthermore two people were required to operate the setup; one person had to adjust the current while the other read bhe polarimeter. Fortunately these difficulties can be avoided: An interval timer can be used t,o shut off the tube before it overheats, and an automatic current regulator can eliminate the need for a second operator. These improvements are included in the new apparatus shown in Figure 1, and the complete setup can he built from standard parts provided a converter-amplifier control unit is available. The latter is present in most electronic recorders, and it consist^ of the recorder amplifier and the balancing motor. Of course a separate control unit can be obtained from various manufa~turers,~ or built from inexpensive parts as described by Thomas and N ~ o k However .~ the automatic control system is optional, and everything included in the dotted lines in Figure 1 can be omitted if a second person is available to operate Rz. The exact components used in the present setup are shown in the Parts List, but the circuit is noncritical, and any similar components will work just as well. Even the polarimeter coil R3 can vary 0 from the specifications given in the former article.' Contrary to the recommendations of the previous paper1 a filter (C,, L, Cz) should be used to snlooth the pulsating direct current. This filter is necessary, as will be shown later, whether or not the automatic control unit is employed. Inductor L must carry 600 ma., and it should have a low d.c. resistance. Suitable chokes are available at high cost, but it. is more practical to use an inexpensive one rated for less current (see Parts List) and cool it with blower B. The motor M also needs cooling, and it may be placed by the choke without receiving or giving off ohjectional pickup; then both can be cooled at once. Of course the choke can tolerate 600 ma. intermittently without a blower, but this practice is not recommended. The filter shown in Figure 1 reduces the ax. ripple to 0.1% of its original value, and further reduction is unnecessary. Resistors R4 and Ra protect rectifier GR and capacitor C1 from surge cur' DODD,T.N., JR., J. CHEM.EDUC.,34, 444 (1957). %Americanrecorder rnanufscturers are tabulated by EWIXG, 33, 424 (1956). G . W., J. CHEM.EDUC., 'THOMAS, E.B., AND R. J. NOOK,J. CHEW.EDUC., 27, 217 (1950).
VOLUME 35, NO. 9, SEPTEMBER, 1958
rents, and these resistors should be of high wattage because they carry large a.c. currents. The Pomerstat TI should always be turned to O-volts before the current is switched on (to the filter); t,heu the voltage may be increased to the desired value. This procedure will prolong the life of capacitor C, (and prevent Powerstat fuse F from blowing). The circuit in Figure 1 includes an interval timer S1, a relay RL, and a bypass resistor Rr with its trimmer Rs. This trimmer should be adjusted so that Rr plus Rb has the same resistance as the tube coil R3. Then the current may be regulated at one's leisure by sending it through Rr and Rs rather than through the coil. When the timer button is pressed relay RL will close, the current will flow through the coil for a limited time, and the tube will stay cool. Coil R8 is au inductive load, and the relay contacts will arc whenever the timer snaps off. Thus capacitor C8 and resistor Rlo have been included to suppress this arcing. Of course an ordinary switch is included on most timers, and the operator may use this switch to mork the relay manually if he so desires. The polarimeter coil can safely withstand a current of about 600 ma. This current is suitable for water and aqueous solutions, but 400 ma. (or less) is more practical for organic liquids which have low specific heats and thus striate easily. Therefore the maximum output of the apparatus should be adjusted to 650 ma. This can be done by restricting the output of Powerstat T I to 115 v. ax., then by setting resistor Rg a t the proper value. The Powerstat output is limited by changing the connections in the terminal box according t o the manufacturer's directions (see step (10) of the Preliminary Adjustments). This will protect tube R8 and also the isolation transformer TP whose input cannot exceed 115 v. a.cl Of course transformer Tp could be placed between TI and the line, but then its output mould exceed 100 v.a., and a larger one than specified in the Parts List would be required. If the tube coil R3 has a resistance of 161 ohms, then R6 will be set near its midpoint to restrict. the current to 650 ma. Of course any tube with ,a resistance of 150-175 ohms can be used with the present setup merely by adjusting the 25-ohm resistor Rs, and any tube wound according to the directions in the previous article1 will have a resistance in this range. THE AUTOMATIC CONTROL UNIT
Lingane4 has described several automatic current reaulators. and those with motor controls seem most LINGANE, J. J., "Electroitnalytical Chemistry," Intewrience Publishers, Ine., New York, 1953, pp. 214-44; 381-86.
MANUALLY C O M O L L E D L P P I R A I U 8
4 2 100
Menvsl hpperatus w i t h Optional Avtornatic Current Control
Pa& List for Manual Apparatus A. Milhammeter (0-750 ma. d.c.) B. Blower to cool choke L (and motor M), see text C,, C?. 250 rr fd., 300 v. electrolytic capacitors (Mnllory type WD 425) 0.5 p fd., 200 v. moulded tubular oapapacitor C1. F. Powerstat fuse ( I amp., 250 v.) Galvanometer of moderate sensitivity, capable of deG. tecting a 0.1 mv. error (Weston model 375) GR. Germanium reotifier stack, single phase bridge; input 140 v. a s . maximum output (with capacitive load) 196 v., makimum current 0.7 amp. (General Electric No. 4JA211BBlACl) Filter choke; 0.8 Hys. with 375 ma. d.c. in the coil; 25 L. ohms d.c. resistance (Stancor No. C-2328). This choke can carry 600 ma. continuously if cooled by blower B, see text. P. Potentiometer plus all xcessories (batteries, standardizing resistors, switches, tapping keys, protective resistar, standard cell, and galvanometer G) PG.. . .PoW.cablble,.e~nqmtpr, qmle;(kmphenol No. -91-..
%.- - - Pb;lariaed chassis receptacle, female (Amphenol No:91PC3F) Precision resistor, 1 ohm, I watt, zt 0.15% (General Radio type 500 A) R?. High quality wire wound potentiometer, 10 ohms, 5 watts, 0.5% resolution (General Radio type 973 D, with pointer type knoh KNSP-6 to fit a/*-inch shaft) Polmimeter tube coil (161 ohms at 2Z°C., see previous R.. article).' Nole: Any tube with a resistance of 150175 ohms will fit the apparatus. 10 ohm, 20 watt, wire wound power resistor R,. 25 ohm, 50 watt, adjustable wire wound power re~istor Rs. (set to limit tube current to 650 me.) 25,000 ohm, 10 watt, wire wound bleed resistor Rs. 200 ohm, loo watt, adjustable wire wound power re& R,. tor; set a t 5 ohms less than the resistance of tube R3 (IRC type 61/nHA) RB,R9. 10 ohm, 5 watt, wire wound potentiometers (Centralah No. WW-100) 100 ohm, 1 watt, wire wound resistor (f 10%) R . RL. 60-cycle a.o. relay, 115 v. (contacts s.p.d.t., 5 amps.) St. Powerstat switch (d.p.s.t.) Automatic interval timer (General Electric type T-48, 8%. 120 sec.; available at photographic stores) SS. Blower switch (s.p.s.t.) Reversing switch (d.p.d.t. with interconnected jaws) Sd. T,. variable autotransformer; output 0-115 ,,. a.c., at least 150 v.a. (Pawerstat type 116 with terminals connected to limit output to 115 v. as., see text) T,. Straight isolation transformer, at least 100 v.s.; maximum input and output 115 v. a.c. (UTC type R-73) R,.
Moto~ Dvivr Details
Additional Parts for Automatic Current Control
~~,","~f,"~-,"$~~2r tLiel;2i$hhrup type R-820-1, used in Speodamss G electronic recorders, see text)
Ruhber stopper clutch (No. 24 long form, solid, see text) CL*. Rubber stopper clutch (No. 0, solid, see text) GT. Small gear train, 30: 1 reduction. (The one actually . . . used .was.taken from a surplus electricmotor.) . . M. Small induction motor; 115 v., 60-cycle, Ephase; oooledby blower B (balancing matar from L e e d ~& Northrup Speedomsx G recorder) 390-ohm, '/*-watt, wire wound resistor (&lo%) R11. 100-ohm, 2-n.att, wire wound potentiometer R,2, Ru,RX. 1-ohm, I/*-wat,t, wire wound resistors ( f 5 % ) R . 3300-ohm, 1-watt, wire wound resistor ( f 10%) 2-ohm, 2-watt, wre wound potentiometer Rrs. Toggle switch (s.p.s.t.) s6, Balancing motor switch, s.p.6.t. (located on recorder) S.. S;. Amplifier line switch, d.p.s.t. (located on recorder)
convenient. I n the present setup the balancing motor ,YaS removed from a speedomax type G electronic recorders and connected to the current control rheostat R2 as shown in Figure 2. Gear train GT is an inexpensive 30 :1 reduction train, and the slip clutches CL, and CLI are solid rubber stoppers drilled so the shafts will slip when R2is turned to its limit. The motor shaft gears need not be removed, and the outer one can press against the rubber stopper as illustrated in Figure 2. Of course the rheostat should not be allowed to reach its limit; otherwise the motor ill continue running (by slipping the clutches) and overheat. This situation can be avoided by using limit switches, but they are not essential. The operator can hear the motor running against the stops and can quickly adjust R u (or Powerstat TI) to recenter Leeds $ Northrup Company, 4907 Stentan Avenue, Philadelphia, Pa. JOURNAL OF CHEMICAL EDUCATION
the rheostat. A blower (Figure 1) should be used to keep motor M (and choke L) cool a t all times. The amplifier signal is taken from the potentiometer galvanometer G. If the tube current is incorrect, the galvanometer will deflect and send a signal to amplifier CA; then the motor will turn rheostat R2 and correct the current. Actually the signal was too large for the sensitive amplifier used (Leeds & Northrup R-820-I), and it had to be cut down by resistors R,, and Rlz. The sum of RI1 and Rlz is 490 ohms, and this matches the output of potentiometer P. Of course the amplifier signal must have the right polarity; otherwise the rheostat will be driven away from the correct setting instead of toward it. (see step (9) of the Operation Procedure). Many variations of this system are possible: Control units made by other manufacturers2 can be used, but R,,, R,,, and the gear train ratio may need changing to suit, the new conditions. The motor does not even have to be removed from the recorder because rheostat Rz can be attached directly to the shaft which operat,es the pen. However the motor may overheat., nnd n good blower should still be used t,o cool it. THE DAMPING CIRCUIT
The balancing motor and gear train have ronsiderable inertia. Thus rheostat Rz will overshoot the end point and oscillate hack and forth unless the system is adequately damped. The Speedomax type G recorder has an excellent damping circuit. A reverse current t o slow down the motor is produced indirectly by the recorder slidewire whenever the pen approaches the end point. This method is so efficient that some models can balance full scale in 0.4 of a second without overshoot. However, no reverse current is produced in the present setup because the pen and slidewire are not used. Thus the system must be damped by some other means, and it is done most effectively as follows: First the input filter of the amplifier is shorted out (or removed) because it tends to produce oscillations (see step (6) of the Preliminary Adjustments). Then capacitors of proper size (C, and Cz) are shunted across the load to dampen the motor. These capacitors also filter the rectifier output; thus they serve a dual purpose. The operation of the damping circuit is illustrated in Figure 3, and all components therein are the same as
developed across the 1-ohm resistor R,. If potentiometer P is set at only 0.50 v. the motor will rotate and increase R2 in order to reduce the current. If the voltage across the load stays at 86, the load must be increased to 172 ohms (Figure 36) t o produce a 0.5-amp. tube current. This may be done by increasing Rz from 2 to 5 ohms as shown in the figure. However the voltage will not stay at 86 because the output voltage of a rectifier (with capacitor-input filter) always varies with the load. When RZ is increased to produce a 0.5-amp. tube current, t,he voltage will increase to 87 as shown in Figure 3d, and R2 must eventually be changed from 2 to 7 ohms to correct the current. This voltage increase from 86 to 87 is not immediate, and the time required for the change to take place is proportional to the size of C2 (and C,). This time lag causes the necessnry damping, and some examples will be given to explain its action: Let us assume we have the 0.51-amp. tube current shown in Figure 3a but desire 0.5 amp. instead. The motor must increase Rz until the bn!anre conditions of Figure 3d are eventually met. If Ca is very small the voltage across the load will increase from 86 to 87 just as fast as R2 changes from 2 t.o 7 ohms. The balance point will be reached abruptly and overshot; then the motor will reverse and oscillate back and forth, and it may never come to rest. On the other hand if C2 is large the voltage will not increase from 86 to 87 as fast as R2 changes from 2 to 7 ohms. By the time R2has traveled 80% of its distance (from 2 t o 6 ohms) the voltage may havc traveled only 50% of its distance (from 86 to 865. as shown in Figure 3c). Now balance conditions are met ahead of time (anticipated) because 86.5 u. is the correct potential to pass 0.5 amp. through the 173-ohm load. Of course the motor will overshoot and make Rz larger than 6 ohms, but then the signal current will reverse and exert a braking torque to slow down the coasting motor. If Cz is exactly the right size the rheostat will decelerate to a stop at 7 ohms just as the voltage reaches 87 (Figure 3d). Equilibrium conditions will be met with the motor at rest, and there will be no oscillation. If C2 is too large the braking action will come too soon, and the motor will have to start up again. The control action will be sluggish, and Rz may stop at the wrong position. 4 C, and Cz are the size specified in the Parts List the damping will be excellent provided a Leeds 8: Northrup R-820-1 amplifier, and a 30: 1 reduction train are used. However, the capacitors are not too critical, and the same size will probably work mdl with other control units. THE ZERO-OFFSET CONTROL
in Figure 1. Let us assume that the Powerstat is adjusted to develop 86 v. across the 169-ohm load shown in Figure 3a. According to Ohm's law 0.51 amp. will flow through the load, and 0.51 v. will be VOLUME 35, NO. 9, SEPTEMBER, 1958
Theoretically Rz should stop turning when the galvanometer is centered. However, spurious a s . voltages (picked up by the signal leads) can drive the motor even though the legitimate signal is zero. Thus R2 may stop turning when the galvanometer reads some value other than zero, and the size of the error will depend on the size and phase of the spurious voltage. These error voltages can be minimized by proper wiring techniques (see step (5) of the Preliminary Adjustments), but it may be difficult to eliminate them completely. Even the legitimate signal ron-
tains some rectifier ripple, and this has 60-cycle component which can shift the null-balance of the amplifier. Recorder manufacturers supress ax. error voltages by placing a filter capacitor across the input terminals of the amplifier. However in the present setup this filter must be removed to prevent oscillations (as explained above), and some pickup will be inevitable. Thus a zero-offset bridge consisting of resistors Rls t o Rt6has been included to correct these pickup errors. Offset control Ra can be adjusted so the motor will center the galvanometer when the tube is energized. However the galvanometer may not stay centered when the current is switched back t o the bypass resistors R, and Rs. This is due to the fact that tube coil R8 is an inductive load which shifts the phase of the spurious voltages, hut Ri and Rs do not cause a phase shift. Thus the pickup error when the tube is energized will differ from the error produced when Ri and Rs are in the circuit, and it is practical t o correct only one of them (the tube error). SENSITIVITY O F THE CONTROL UNIT
The resistance in the d. c. circuit consists mainly of L Rt l/z (Rs F 4 RI '/a Rs R* (Figure I), and it adds up t o about 220 ohms. The motor will keep R2 within 2 rheostat windings (0.1 ohm) of the correct position, and this represents 1/2200 of the total resistance. Therefore the control unit will regulate the tube current to better than one part in a thousand which is a11 that is required.' If GT is a 30:l reduction train the motor can turn the 10-ohm rheostat Rzfrom one end to the other in about 2 seconds. Thus a 10-ohm error in the 220-ohm circuit can theoretically he corrected in 2 seconds, or a 1%error in0.5 seconds. In actual practice the correction rate is not quite this fast because small error signals will make the motor turn more slowly. However, the largest error that ever occurs takes place when relay RL switches the load, and even this is corrected in about half a second.
The following should be done before the setup in Figure 1 is placed in operation: (If the automatic control unit is left out do steps (7) through (12) only.) (1) Adjust rheostat R to have a minimum torque; then adjust the shaft to extend through both ends of the case. (2) If s, recorder is used, remove the balancing motor and connect it (through gear train GT) to the bottom end of the rheostrtt shaft as shown in Figure 2; then attach a pointer type knob to the other end of the shaft. (3) Be sure clutches CL, and CL2can dip when Ik is turned to its limit. (4) If a recorder is used, remove the chart-motor fuse or disconnect the motor leads. Leave the chart and pen in place. (5) Make the low voltage leads as short a s possible, twist them together to reduce pickup, and keep them away from all lines and components containing a s . or fluctuating d.c. vole ages. (The low voltage leads include all wiring and parts from amplifier CA down through potentiometer P and up to resistor
(6) Connect the signal leads directly to the amplifier itself and short out (or disconnect) the input filter. Be sure the negetive lead is also connected to the amplifier chassis and to ground. (If a Leeds & Northrup R-820-1 amplifier is used get a separate male input plug (Cinch No. M-61)). Attach the positive signal lead to terminal 2 and the negative lead to 5. Connect terminals 4 and 5 together to short out the filter; then attach 5 to the chessis and ground the latter.
(7) Be sure the e.m.f. leads from potentiometer P are connected directly to the terminals of precision resistor R,. (8) Adjust relay RL so the contacts are as close together as possible without danger of malfunctioning. This will reduce the dead space and minimize galvanometer kick when the load is switched. (9) Adjust R, so that R, plus R, (aet s t midposition) has the same resistance as tuhe coil RJ. Use an ordinary ohmmeter for this measurement, and if necessary readjust Ra to get a good match. (10) Limit the output of Powemtat T, to 115 v. a.c. (If Powerstat type 116 is used remove the knob, outer case, and terminal hox cover; then change the wire on terminal 2 to position 4.) (11) Be sure a l-amp. fuse (F) is placed in the Powerstat. (12) Set R. s t maximum resistance, Q and R. at midposition, and Powerstat T I at O-volts. Connect the Powerstst to the a.c. line, switch on the current, and turn up the voltage to meximum. Now adjust Re to let 650 ma. flow through meter A; then turn the Powerstat back to O-volts and switch off the current.
OPERATION PROCEDURE (1) Be sure Powerstat TI is turned to O-volts and that timer switch S2and motor switch Sa are turned off. (2) Set controls &, Rs, Rn, and Ra a t their midpositions. (3) Plug in all a.c. lines including that of blower B. (4) Turn on switches B,Ss, Ss and Si (Ss may be in either position). (5) Turn up the Powerstat untii the desired current flows through meter A. (400 ma. is a good current to start with.) (6) Set the dials of potentiometer P so the voltage is numerically equal to the desired current (400 mv. in the above example). (7) Standardiee the potentiometer against a standard cell. (A precision of 0.1 mv. is satisfactory.) (8) Switch the potentiometer to e.m.f. and tap the galvanometer key. If the needle deflects center it by adjusting Powerstat T, and vernier control R.. 9) Lock down the ynlvarwnrtrr key thrtt bus rm protective r e A o r ; thru torn on motor *witch S.. (Tlw mutor h u l d kty) the gnlvmonrercr needle nt a runrt:ir>t vulur nrbr z e r o If tlnv needle is driven away from zero reverse the signal leads s t points X and Y (Figure I).) (10) Increase R,Qif the motor control is sluggish. Decrease RIzif the motor tends to oscillate or auiver. (11) Set intervzl timer S1 for 5 seeonds. (12) Push the timer button to energize the tuhe; then adjust R 9 to make the motor center rheostat Q. This adjustment should be done before the 5 seconds are up. (13) When the timer snaps off, rheostat & maymove to e. new position. Adjust Rs to recent,er it (thus making Ri plus Ra equal to the tuhe resistance). (14) Press the timer hutton again; then adjust R,. to make the galvanometer read zero when the tube is energized. (The gelvanometer may not read zero after the timer snaps dl.) (151 Now oush the timer button and eet the ~olarimeterreadvalues is 2a (see previous paper).' (16) Turn off motor switch Ss,unlock the galvanometer key, and restandardize the potentiometer. Then lock the key again and switch on the motor. ( l i ) Wait 30 seconds then repeat step (15) to get another set of values. Continue steps (16) and (15) to get additional readings. (18) If rheostat Q should drift toward one of its limit8 recenter it by turning vernier RQ(or Powerstat TI). If R, getn very hat reedjust Rs by repeating steps (12) and (13). (19) When finished turn off motor switch Sa, unlock the galvmometer key, turn the Powerstat back to O-volts, shut off all current (including switch Ss), and disconnect the patentiometer batteries and standard cell. (20) If a different tube current is desired start again at step (1) of the Operation Procedure.
If the automatic control unit is left out, t,he setup may be operated manually as follows: (1) Do steps (7) through (12) of the Preliminary Adjustments.
JOURNAL OF CHEMICAL EDUCATION
(2) Do steps (1) through (8) of the Operation Procedure.
(3) Lock down the galvanometer key that has no protective resistor. (4) Set interval timer d for 5 seconds. (5) Push the timer button to energize the tuhe. If the gdvanorneter deflects adjust Rq to recenter it before the 5 seconds are up. (6) When the timer snaps off, the galvanometer may deflect again. Adjust R8 to reoenter it (thus making R,plus R, equal to the tube.resistance). (7) Do step (15) of the Operation Procedure and have a second person oontrol FL manually to keep the galvanometer centered. (8) Wait 30 seconds (during which time restmdardiee the potentiometer) then repeat the above step to get another set of values. Continue this repetition to get additional readings. . should drift toward one of its limits re(9) If rheostat R center it by turning vernier R. (or Powerstat TI).If R, gets very hot readjust R8 by repeating steps (5) and (6) of this section. (10) See steps (19) and (20) of the Operation Procedure.
ERRORS CAUSED BY A.C. IN THE TUBE COIL
Pulsating current in the tube coil can cause errors in the polarimeter readings. These are undergoing further investigation, and some preliminary findings are outlined below: (1) Pulsating current will cause the polarimeter fields to flicker, and this will make them difficult to match. The operator cannot see this 120-cycle fluctuation; nevertheless it will lower the precision of his readings. The polarimeter used with the present setup could be read reproducibly to the nearest 0.01". When filtered d.c. was sent through the coil the average deviation in a series of readings was zero. However the a.d. rose to 15 parts per thousand when unfiltered d.c. was used. (2) The actual readings (not just the precision) will vary with the amount of ax. in the coil when the ripple wave is unsymmetrical. A rectified sine wave is unsymmetrical, and it can produce errors as large as 5%. (3) The readings will vary with the shape of the wave. A pure sine wave (symmetrical) will produce no error whereas a distorted wave of the same amplitude can produce errors even greater than 5%. (4) The readings will vary with the half shade angle (Laurent) of the polarimeter when an unsymmetrical wave is in the coil, and the variation can amount to more than 2%. Obviously the above errors should be eliminated, and filter C1, L, Cz is included to remove them. It reduces the ax. ripple to 0.1% of its original value, and makes the errors negligible as far as the present setup is concerned. Of course the filter is necessary
VOLUME 35, NO. 9, SEPTEMBER, 1958
when automatic current control is used because it dampens the motor and reduces spurious a x . vokages. PERFORMANCE
Table 1 shows some typical results obtained with the present apparatus. They are not the same as the results in the previous article1 because the earlier setup had no filter to smooth the rectifier ripple. This should have made the former results 5% too high, but a constant voltage transformer was used,' and this distorted the wave and lowered the values again. Therefore the results from both setups are nearly the same, and the earlier results are correct only by accident. A different (and better) standard. resistor R, is used with the present apparatus, but the difference between the two resistors is less than 1%. An examination of Table 1 will show in each case that 2ry is proportional to the tube current to the nearest 0.01". TABLE 1 Magnetic Rotations of Water and CS? Carbon disulfide
2my in den.
i n amus.
i n deu.
i n amps.
The quick action of the control unit allows the readings to he taken before the liquids warm up and striate. Thus low-boiling liquids such as carbon disulfide can be measured accurately even with as much as 0.3 amp. in the tuhe coil. The Verdet constant V of carhon disulfide may be calculated as follows: (See equation (4) of the previous paper.)' Vcs, = 0.01307 X 3.80/1.183
0.0420 min./cm. oersted
where 0.01307 is the Verdet constant of water a t F C . , and 3.80 and 1.183 are the magnetic rotations of carbon disuliide and water with 0.2 amp. in the coil (averaged from the values in Table 1). The new setup is accurate to 1 part in 400 even with organic liquids, and only 1% accuracy was claimed for the old setup. The Verdet constant of CS2 ohtained with the new apparatus is 0.0420 min./cm. oersted whereas the old apparatus gave a result of 0.0424. The literature value is 0.04206.6
6 See the nrevious oaoer' for calculated value based on renort of W*RING,C., H. HPMAN, AND S. STEINGISER, J. Am. Chem. Soc., 63, 1985 (1941).