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Vapor pressure of normal decane Scott, Walter Francis 1936

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VAPOR PRESSURE OF IORMAL DBGAPI  f a l t e r Francis Scott  A T h e s i s submitted f o r the.degree o f Master o f A p p l i e d Science in- the Department Ox  Chemical E n g i n e e r i n g  The U n i v e r s i t y o f B r i t i s h Columbia  P L A N A — T H E IMPORTANCE OF C R I T I C A L PRESSURES. B—PREPARATION OF THE•NORMAL DECANE SAMPLE. C—DESIGN OF APPARATUS AND ITS ARRANGEMENT. (1)  The A p p a r a t u s as  (2)  Detailed D e s c r i p t i o n of the E s s e n t i a l  D—EQUILIBRIUM (lj (2)  a Whole.  CONDITIONS AND THEIR CONTROL.  Cooling System." Room T e m p e r a t u r e .  E — C A L I B R A T I O N OF APPARATUS. (1) (2) (3J F—MEASURING (lj (2) (3;  M e a s u r i n g Temperature (Tg and T j ) . Cathetometer Readings of P r e s s u r e . Results. THE VAPOR PRESSURE OF NORMAL DECANE. F i l l i n g the Furnace B u l b . Experimental Proceedure. Results.  G—TREATMENT OF R E S U L T S . H—CONCLUSIONS.  Parts.  1  A.  TBS THEORY OF CRITICAL PRESSURE. The  c r i t i c a l temperature (C.T.) of a gas i s the highest  temperature at wlv di that gas can be l i q u e f i e d . The  c r i t i c a l pressure ( C P . ) i s the pressure of the substance  at the c r i t i c a l point ("c"~Fig. 1 ) . The  general form of the isothermal curve for a substance  existing as a l i q u i d , vapor, and gas, i s represented i n F i g . ( l ) t The  two lower isothermal l i n e s a l l e T h i b i t the discontinuity  which i s associated with the passage of a part of the gas-like into the l i q u i d state.  substance  In area d.a.p. of the diagram the substance  wholly i n the l i q u i d condition.  is  In the parabolically-shaped curve,  o.a.p. part of the l i q u i d has been converter] into the gas-like . condition.  Hence, i n t h i s part of the diagram, the substance exists  i n the state of a l i q u i d i n the presence of i t s saturated vapor. Under the area d.a.p* the substance i s i n the . state of unsaturated vapor. Sach of -i-he lines (1 t o 5) represents an isothermal curve for some specific temperature.  Curve number (4) i s the one for the  c r i t i c a l temperature of the substance i n question.  Curves numbers  (1), (2), and (3), are isothermal for temperatures higher than the c r i t i c a l temperature and?>l-ie ln.i#ifs:: regiira In -which t h e substance  is  a permanent gas. I f . a volume represented by (V a ) it\ Figure (1) i s occupied partly;-by-a liquid..-and partly by the saturated vapor of the l i q u i d , and  the temperature be raised while the volume Is kept constant, the  substance v a i l pass through the conditions represented by the v e r t i c a l l i n e V a to Aj providing the original volume present is not so great that It w i l l f i l l the entire vohime by thermal expansion before the  c r i t i c a l point (a)  is.reached.  In our case, about to be discusseg., the changes were s l i g h t l y more complicated than those just explained, since the volume, the pressure and the saturated vapor pressure were a l l varied at the time. In any case, the point (a)  is f i n a l l y attained*.  This c r i t i c a l pressure of hydrocarbons i s important i n the O i l Cracking Process, as i t is here desirable to know the physical state (i.e.  s o l i d , l i q u i d or gas)  of the hydrocarbon at the pressure of  the cracking process+ • Hence, by ascertaining the c r i t i c a l pressure of a hydrocarbon, we are in a position to say whether or not that particular hydrocarbon can possibly e^ist in th© gaseous state under the known cracking conditions.'  Since the hydrocarbons above octane  are the ones which are "cracked", i t i s very important to know t h e i r c r i t i c a l conditions.- An investigation of these c r i t i c a l conditions was the purpose of t h i s Thesis.  TEE PEEBARATIOK OF. THE IiTDROCARBOH DECAMS: The sample of Decans which was used for investigation, was obtained from the Eastman Kodak Company.- It was purified by r e c r y s t a l l i z a t i o n three times, and was f i n a l l y dried over sodium.  C. DESIGH AMD ARRAKGMEET OF APPARATUS* Figure ( 2 ) shows, diagramati calljr, the arrangement of the apparatus used i n the c r i t i c a l pressure determination. A b r i e f outline of the set-up-is as  follows;  B - a water bath, containing the pressure bomb... submerged i n water. P - the hydrogen pressure guage-  J- - the constant temperature jaclret for P, T]- a mercury thermometer immersed i n J , K - glass connecting arm, joining the hydrocarbon bulbs (situate in the furnace F) and the pressure bomb (situated i n B). Y7 -. a wooden box, seated on a brick base, to f a c i l i t a t e the adjusting of the furnace P.  .  E - The source of e l e c t r i c i t y ( 1 1 0 v o l t D. C.) A - ammeter. R - rheostats. D - a Bull-Dog pump, driven.by motor M^. H - water reservoir, lined with c o i l s " H " and fitted with •V s t i r r e r "S" and heaters nQ™. Tp''- a mercury thermometer. Tg - a resistance thermometer. . K]_ - a- small motor to drive the fan in the oven F, to get complete circulation of a i r in the furnace*  k detailed discussion of the various parts and their functions i s now possible. The Steel  Pressure-Apparatus  This part of the apparatus i s shown i n mechanical detail- in Figures ( 3 ) , ( 4 ) , and ( 5 ) . apparatus to a \  n  scale.  Figure ( 3 ) i s a drawing oT the pressure  This pressure-apparatus was machined from a  solid block of lovr-carbon steel and was designed to withstand pressures far exceeding any which- "would be met -vvitb i n our particular work. inside volume of the apparatus i s about 75 cubic inches. an-'1 the bottom rims are flanged. t o give s t a b i l i t y .  The  Both the top  The bottom flange i s merely designed  The top flange is machined on i t s upper surface and  is fitted with a machined packing ring of l / 8 " groove.  i/l Sca.Ce. N-T3.  4-  The l i d of the .pr.assu.re bomb (see Fig. (4)) i s machined on i t s lower face t o -lit the.'top surface, of the pressure bomb* The l i d i s held in position, against the machined surface of the bomb, by ei.^ht bolts, which pass through eight' standard 3/8" d r i l l holes, d r i l l e d symmetrically through the l i d and the upper flange. In Figure (4), (a) and (b) represent glands. A pressure tube (If), Figure (2), made of pyrex capillary tubing passes through, gland (a). A second glass pressure -tubing (P), (containing hydrogen gas i n i t s one, .sealed end - see Figure 6 for details) Figure (2) passes -through gland (b)« Both these glass pressure-tubes are held i n place by gland•screws and packing •fibre (illustrated i n Figure (5))« The packing and -the glands, mentioned above, are of the utmost • importance and merit some discussion'at this point. The packing must be such, that i t w i l l not yield too .much to pressure, and so cause large volume changes; but yet i t must be sufficiently eorapressable, i n order that i t w i l l contact the glass tubing at a l l points and so present a pressure-proof joint.  The d i f f i c u l t y arises from the irregularity i n  the outer diameter of the glass tubes of t h i s capillary size. Ground glass cannot be used as. i t would not stand the high pressure. The gland-screws-are also of.special design, as shown in Figure (5). (a) represents the steel gland-screw, (c) the gland-packing, and (b) a smooth steel ring separating the sere?: and the packing Y<M ch prevents the glass tubing from being subjected t o a torsional strainjotherwise present i f the screw (a) i s screwed down i n direct contact with (c).. ..After a great deal of experimentation we found the most. satisfactory . paoking to be laminated hard-rubber, fitted in the .gland several plies thick*  -.  '  F/  4-, :  The Glass Pressure Tube (Figure 6) This part of the apparatus consists of a piece of heavy-walled, pyrex-glass,, capillary tubing of a f a i r l y xmiform bore., The entire length of the rod was- measured and marked into centimeter- lengths in the following manner* The outside surface of th© tubing was coated with a fin©, uniform layer of wax.  By means of "a special apparatus.,, used for t h i s and  similar purposes, we scratched t h i s wax coating into divisions of centimeters along.the length of tubing, . The 'number of each of these • .calibration marks was scratched into the wax coat; A l l scratches were f i n a l l y f i l l e d with hydrofluoric acid. When the exposed glass surface was sufficiently etched, the acid- wa,3 washed off and the wax coat removed*  _  A small length (approximately the sains tube.  .1.3 cm.) of mercury was drawn up into  By moving this mercury bulb progressively along the tube  and measuring i t s length at different points by means of a cathstometer, the. volume of the tube was found^psing then-weight of the mercury drop and the density of mercury. (Corrections were made for th-j meniscus.) When t h i s was,fiiii.shed, one end o f-^he • tube was sealed off and the sealed, end f i l l e d with mercury. Again, by weighing the mercury used, v;e were able to determine the volume of the-sealed end. results were recorded arid plotted. (See Table  These volume  and Graph  )  This calibrated tube was then sealed on to a larger bulb of glass. This latter glass bulb i s not of the. same watt thickness as the capillary tubing as i t does not have to withstand internal pressure.  Figure (6)  shows the final glass tube.The next step was to f i l l the clean glass tube, Figure (6), with pure mercury.This was done by distilling, the mercury in under vacuum. When the entire pressure tube and 'connected glass bulb were f i l l e d  completely with mercury, they were disconnected from the d i s t i l l i n g apparatus and placed upright with the open end (a) Figure (6) submerge! in. a bath of clean mercury. Pure hydrogen (cleaned by passing through concentrated  H2SO4  and  concentrated .KaOil bottles and finally driert over PgOp) was obtained from a hydrogen cylinder and added., by means of a small rubber tube passing under the surface of the mercury bath and up into the big bulb by way of the open " t i t " (a) Figure ( 6 ) . When enough hydrogen, gas, was allowed to enter the glass bulb, the ;  " t i t " (a) Figure (6) was closed off under the mercxiry surface i n the bath,, and, the hydrogen shaken into the small.capillary tube. . . The steel pressure apparatus was partly f i l l e d with pure mercury and the glass bulb of the capillary pressure guage was submerged Injit. The side-arm glass tube,. (K) in Figure '(2), was fitted into gland (a) Figure (4).  The l i d was adjusted on so that the calibrated pressure  tube fitted through the gland (b). The gland (b) however, was not screwed tight at f i r s t and as the l i d was fitted on, the mercury was forced up through (b), thus removing a l l the a i r .  Both gland screws  (a) and (b) were finally fitted tightly, and the l i d was bolted down. This last step forced some mercury out of the bomb, into the side arm, to a height of several inche.s. Mercury was then distilled' into the remaining verticle length of side arm under vacuum (to prevent oxidation). Obviously, a vacuum can be used In this way., as the hydrogen volume i n the capillary tube i s so very' small that, on expanding into the large connecting bulb (when vacuum i s applied), the pressure i s so reduced that only a very short head of mercury i s required i n th® side ana to prevent the hydrogen from escaping out of the glass bulb altogether. On removing the vacuum the hydrogen i s again forced into the. capillcry tube as before.  The Furnace Bulb-Figure ( 7 ) When the v e r t i c l e length of side arm was f i l l e d with mercury, the glass "U" part of the side arm was sealed on..  The other end of the'  'D" glass was sealed t o bulb (a) of the furnace bulbs, Figure ( 7 ) .  T  The bulb (a) ( i . e . the "reservoir bulb?') was f i l l e d with sufficient mercury — arm. (6)  (calculated beforehand) -- t o f i l l the remainder of the side  The pressure bomb was then placed i n the vjater bath " B " , Figure and hot water was addon to f i l l " B " .  The increase- i n temperature  was sufficient t o expand the mercury column i n the v e r t i c l e side arm (K),  around the . " 0 " bend t o j o i n up with the mercury i n bulb (a)  Figure ( 7 ) . When the hot water was removed from " B " , Figure ( 2 ) and normal temperature  conditions once more restored* the mercury i n  reservoir bulb (a) Figure ( 7 ) was drawn bade into the " U " arm, thus f i l l i n g side arm ( K )  4  completely.  The bulb (b) ( i n case of the experiment  to calibrate the apparatus)  contained pure water and was sealed on t o bulb (a) as i n Figure ( 7 ) » A vacuum was applied at the open tube (d) Figure ( 7 ) and part of the water i n bulb (b) was boiled o f f under redt^ced pressure. all  In t h i s way,  the a i r was removed from (a) and (b) bulbs Figure ( 7 ) and replaced  by water and mercury vapor. The function of bulb (a) Figure ( 7 ) i s to take up the volume of mercury drawn out of the pressure bomb when a vacuum i s applied and also to take care of the expansion of the mercury i n the furnace at high, temperatures. The tube (d) Figure ( 7 ) was collapsed under vacuum and so a closed system was set up.  8  The .Electric Furnace Figure (8). Consist.1? of a central pyrex glass tube (inside diameter sealed off at one end.  3j>"),  Since i t i s necessary to observe the c r i t i c a l  condition ( i . e . the point at which the meniscus of the hydrocarbon disappears) , the furnace was designed to have two windows (YJj and Wg Figure (6)).  The glass tube was wrapped above and below the window  area with asbestos and the heating wire was wrapped eo-axially, i n insulated layers, on top o £ . ± h i s »  Each side of the glass cylinder,  between the two windows, was covered with asbestos lugs about which the heating wire wo.s spiralled (see  (1) Figure (8)).  The furnace was housed  in a square metal box, packed well with 'asbestos* The heating current was obtained from a 110 v o l t , direct current,, source ( S Figure (2)).  The amperage was controlled by rheostats  (1 Figure ( 2)), D.  EQUILIBRIUM CONDITIONS AND THEIR CONTROL. .  The Water Cooling SystemjReferring to Figure (2),  (H) was a large water reservoir  fitted  with cooling c o i l s through which water from top(C) Figure (2) was circulated.  Two automatic heating c o i l s (G) Figure (2)  water bath (H).  dipped into the  Ylhon the temperature of the reservoir rose above 2 0 ° © . ,  the heaters automatically switched off and the cooling c o i l s (IT) removed heat u n t i l the temperature f e l l back to 2 0 ° C .  I f the temperature  f e l l b e l o w . 2 0 ° C . , the heaters (G) automatically switched.on and restored the temperature to 2 0 ° C . A s t i r r e r (S), driven by a small motor (Mg) > kept the reservoir at a uniform temperature of 20 ° C . throughout. The water was syphoned from (H), thgough a rubber tube, to the water jacket (J)  Figure (2) surrounding the hydrogen pressure tube (P).  In t h i s 7/ay the temperature of P was always kept near 20 °C«  From (J) , the water flowed t o bath (b) Figure ( 2 ) and was f i n a l l y pumped back to (H) , by, means of a small pump (D), to complete a continuous circuit.'' The water-from the'cooling c o i l (S) , circulated through t,he various e l e c t r i c a l resistances and was f i n a l l y returned t o the sink at (C). The entire apparatus shown i n Figure ( 2 ) i s housed i n a constant temperature room.  Calibration Of Apparatus. For calibration purposes, the bulb (b), Figure ( 7 ) was f i l l e d with water*  A mark was made on •the' hydrogen pressure tube (P) and the  apparatus set up as explained above i n Figure ( 2 ) . By adjusting the current flowing through the ammeter (a), a constant heating was obtained as desired.  effect  The s t i r r i n g fan in the furnace just under  the l i d kept the a i r circulating vigorously and so prevented the formation of "hot--spots", . •  .  Both the mercury and the water i n the furnace bulbs (a) and (b) Figure (7) "exerted a definite and known pressure for each temperature. By allowing the system to reach a state of eaui Librium for various current values and by measuring the furnace temperature at each of these established points., (using a platinum resistance thermometer and galvanometer)  and the height of the mercury column i n (P), above the  aforementioned mark (using a v e r t i c l e cathetometer), we were able to record the pressure of the hydrogen gas volume in terms of the height of mercury column i n (P).  Tbi3 follovred from t h o fact that, at  equilibrium, the combined pressure of mercury and water vapor i n the -. furnace bulb was transmitted, undiminished,! •fehroogfc the mercury medium, in the arm (K) and the pressure bomb (located in B) to the ga3  10  volume i n (P). Hence, knowing the pressure of water and mercury at any temperature (this data was obtained from the International C r i t i c a l Tables), we knew the gas press of (P) for a l l values of the mercury column heipht when equilibrium was established. This pressure relation can be changed to a volume raercury column relation by using the gas laiir as given for hydrogen in the International C r i t i c a l Tables* These calculated relations were recorded and plotted. A mercury thermometer (T<>) was hung in the furnace to give us a rough idea of the temperature so that our equilibrium points could be established at regular temperature intervals* F.  HEASUEIEG TES "TEMPERATURE-PRESSURE" RELATIONSHIP OF BECAME5The proceedure followed lines similar to the experiment•using  water for calibration purposes except that the bulb (b) -was f i l l e d with normal Decane... Since we wished to prevent any loss of the hydrocarbon, another bulb (c) was scaled on to arm (e) of bulb (b). This latter bulb xvas immersed i n an ice bath and so condensed the Decane evaporated over from bulb (b). Again the system was sealed off at (e) under vacuum. When the apparatus was again set up the temperature of the furnace was raised as before and equilibrium points again established. The height of the mercury column in (P), at 20°C, enabled us to read the pressure directly from the calibration chart. This pressurey of course, represented the combined pressures of the mercury and the normal Decane. The pressure of the latter vras found by subtracting the  kno-Tiai  pressure of the mercury, for the temperature In .question, from the t o t a l pressure*  11  These results were tabulated and plotted on graph paper. G.  TREATMENT OF RESULTS j A complete record was made of a l l the results obtained. Due to  experimental conditions, the c r i t i c a l condition could not be observed. However, work done by Carswell on the c r i t i c a l temperature, showed i t to be about 329 ° 0 . A plot made of the known c r i t i c a l pressures and temperatures of hydrocarbons up to octane, shows the c r i t i c a l temperature to be much greater than t h i s when extrapolated, Our results are i n favour of the extrapolated value*  H-  COSCLUSIOIS;-  •  .  In every case, the column of mercury i n (P) was observed to rise rapidly as the temperature increased i n (F) and kept increasing to a maximum value, after the temperature of (F) became constant. After the maximum point was reached, the column of mercury f e l l back to a lower but constant, equilibrium value.• Under such circumstances, i t i s not advisable to declare an equilibrium point as being attained u n t i l the column of mercury i n (P) and the temperature i n (F) have remained constant for at least t h i r t y minutes*  •  Small secondary c o i l s may be placed inside the furnace and heated with  an independent current of about l/lO to l/2 amps*; but such  devices are  usable only as a means of elevating the temperature to  the desired ecu!librium point, and should not be used during the equilibrium period, as the results established -when the entire system has come to equilibrium are alone reliable. The temperature of ( j ) must be kept at 20°C.  Any deviations from  12  this temperature are observed on thermometer (T^) and corresponding corrections must be made i n the results.  CRITICAL DATA FOR HYDROCARBONS •  •Sam©  ( C r t . T a b l e s , V 2 , p248)  M o l . Weight  C r t . Temp. '• {  C)  C r t , Press. ' C r t . Press. (at  M)  . Ethane  30.046  B ;- Propane • 44.064  '  • • D i v . by Absol. Crt.  Temp.  *3J3 « 1  48.8  0.16  95.6  43.0  0.117  36.0  0.0845  11 - Butane  55.080  M - Pentane  72.09 6  19 ? » 2  33.0  0.0704  H - Hexane  86.112  234,8  29.5  0.0580  100.128  266.8  26.8  0.0495  296.0  24.6  0.0495  .(23.7)  0.0494  (22.7)  " 0.0359  N - Heptane LI - Oetano  114.144  1? - Honane (extrap.)  128.16  (327.5)  I - Decane (extrap.)  142.176  (360.)  H - Decane  ( p r e v i o u s work gave C r t . Temp. 329)  o.o378  "f  0  X," ft ^  ^ s <o i  <3 0  \ i ft  '•si  X  C k l  o 00  P  • •  _/.  > to  0  »0  o  si  •S-3J3  TABLE; OF".VOLUME OF PRESSURE TUBE  D i v i s i o n , • Volume . ' .'Between "-,''•• Divisio  ' Volume • ' .. T o t a l •. D i f f e r e n c e Volume From Average  32 -31 .  0.0465  -0.0036  31 -3:6 . - 0,0485  -0.0016  0.0487  -0.0014  0.2626  29 -28  0.0485  -0.0016  0.3111  28 -27  0.0490  -0.0011 "• . •  0.3601  27 -26  0.049,4  -0.0007  •0.409 5'  26 -25  0.-0494  -0.0007  •" 0.4589  25 -24  '0.0499  -0.0002  0.5088  24 -23  0.0506  +0.0005  0..5594  23 -22  0.049.5  -0.0006 •" '  . 0.6089  22 -21  0.0503  -fO.0002 .  !.0,6:59*2  21 •-20  0.047 5  -0.002:6  20 -19 '  0.0475  -0.0026.'•  0,7542  : 0.0539  f0.0038 .  0.8181  30 -29  19 -18 .  ;  .  ".  ,p'.i654  Total Vol.  0.2139  V o l . o f end cone . ,0.01189c.  ...0,706.7 :  18 -17  0.0557  *0.00.56'".  17 -16  0.0499  -0,0002  •0.9 237  16 -15  0.0502  +0.0001  ,0.9739  15 -14  0.0509  +0.0008  1.0248  14 -13, ."  0.0511  -f 0.0010  1.07 59  13 -12  .0.0518  +0.0017.  1.1277  12 -11  " 0.0515  +0.0014.  1.1792  11 -10  0.0510  +0.0009  10 -9  0.0505  +.0.0004':  -'' '  0.8738  .1.2202 1.2707  1.6768  Vol!.. o.f unetched end" .0.0465 '. r \ •' Hydrogen e q u a t i o n pv a bp. ;( a 1.33,. b 0.14)  Table o f Volume of P r e s s u r e Tube by Mercury Method c o n t i n u e d .  Division  Volume Between Divisions  Volume Difference .From Average  Total Volume  9-8  0.0502  +-0.0001  1.3209  8-7  0.0506  +0.0005  1.3715  7-6  0.0510  f'0.0009  1.4225  6-5  0.0510  f0.0009  1.4735  5-4  0.0509  +0.0008  1.5244  4-3  0.0506  -r 0.0005  1.5750  3-2  0.0509  * 0.0008  1.6259  2-1  0.0509  -rO.0008  1.6768  •  V  9 00  03  1  ^  CALIBRATION O-F APPARATUS  Temperature of Furnace (degrees C.)  Pressure of Water (at M)  P r e s s u r e of. Meroury ( a t M)  He i g h t o f Mercury Above Mark (cm)  Pinal , Pressu] ( a t M)  1  .263.943  49.338  0.143  20.99 5  49.271  2 ;  257.832  44.693  0.120  20.440  44.509  251.954  .. 40.545  0.105  23.345'  40.375  246.780  37.145  0.091  20.203  36.984  5 .  •241.054  33.642  0.078  20.090  33,491  6  235.777  30.645  0.068  19.955  30.505  7  226.730  25.987  0.051  19.792  25.862  8  213.905.  20.342  0.036  19.370  20.240  9  207.741  17.9 59  0.034  18,920  17.860  10  19 5.224  13.868  0.020  18.067  13.936.  11  186.281  11.409  0.015  17.510  11.479  12.  175.419  8.89 6  0.012  16.600  8,9 51  13  179.721  9.832  0.012  16.995  9.891  14 . 168.140  7.473  0.007  16.206  7.455  15  *5 • <5 2 3  0.005  15.416  5.508  3  4  . v  156.127  "Vertex o f cone p o i n t above mark ( 42.055.) Ba&e of Cone P o i n t above mark  635 cms.  .( 42.055) 21.285 cms. £bG cms. .  Bottom of b l a e k mark  42.055 (on cathetometer[  Length of C y l i n d e r  21.285 cms.  TEMPERATUHE-PRSSSURE RELATION FOR If -  Temperature of Furnace (degrees C)  Experimental -ressure ( a t M)  Pressure o f Mercury fat M ) '  9.20  0.168  285.906  11.90  2"95.800  13.93  306.752  15.88  317.639  17.75  328.925  19.38  340.267  21.39  271.285  BECAME  Height o f Mercury Above Mark  P r e s s u r e o. H-Decane f a t M)  16.765  8.964  0.236  17.605  11.584  0.295  18.075  13.541  0.380  18.528  15.383  0.475  18.910  17.123  0.588  19.230  18.600  0.738  19.495  20.341  19.125  18.172  19.165  18.413  320.798  18.800  0.503  321.279  19.050  0.509  322.991  19.260  0.517  325.208  19.215  19.680  18.615  0.550  328.469  19.280.  20.150  18.966  0.588  329.234  19.355  20.300  19.361  0.596  330.409  19.378  20.650  19.704  0.609  332,002  19.405  20.840  20.041  0.629  333.413  19.440  21.560  20.211  0.646  334.9 59  19.490  21,550  20.714  0.666  337.135  19.510  22.120  20.884  0.696  338.182  19.660  22.420  21.424  0.709  19.585  21.711  -  Readings f 8 to 19)  a r e s l i g h t l y above t h e g r a p h i c v a l u e s obtained  by p l o t t i n g r e a d i n g s {1 t o 7 ) , due t o the f a c t t h a t a t r u e e q u i l i b r i u m c o n d i t i o n was never e s t a b l i s h e d .  It  is  a p l e a s u r e t o acknowledge t h e h e l p  o f D r . "W. F . S e y e r , added g r e a t l y t o t h e  whose a s s i s t a n c e and a d v i c e success of t h i s  thesis.  


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