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The latent heat of fusion of cis and trans decahydronaphthalene Pyle, Robert Gordon 1947

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L 15 3 6 ] P* L THE LATENT HEAT OF FUSION OF CIS AND TRANS DECAHYDRONAPHTHALENE Robert Gordon Pyle, 'B.A.Sc. A thesis submitted in partial fulfilment of the requirements for the degree of MASTER OF APPLIED SCIENCE in the Department of .CHEMICAL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA May, 1947 ACOOWLEDGrFOTWTS I wish to acknowledge the assistance and many-helpful suggestions of Dr. W. F. Seyer under whose direction this work was carried out. If. Gordon Pyle May, 1946. TABLE OF CONTENTS Page Introduction 1 Method of Determining Latent Heats 1 Apparatus and Experimental Procedure 8 Experimental Readings 11 Treatment of Results 12 Latent Heat of Cis Decalin IZ Latent Heat of Trans Decalin 13 Calculation of Latent Heats hy Ln Solvent ~ Temperature Curve 15 Refractive Indices 16 Discussion of Results * 17 Bibliography 21 LIST OF ILLUSTRATIONS Page Figure 1. Relationship between Vapour Pressure, Temperature and Mol Fraction ... 3 Figure 2. Freezing Point Curve 11 A Figure 3. Latent Heat vs Temperature 13 A Figure 4. Ln solvent vs Temperature Curve ....... 15 A Figure 5. Latent Heat vs Temperature • 15 B Figure 6. Refractive Indices Curve •• 16 A I N T R O D U C T I O N The object o f t h i s research was, i n g e n e r a l , to o b t a i n f u r t h e r s c i e n t i f i c data concerning the two isomers, c i s and t r a n s decahydronaphthalene. More s p e c i f i c a l l y , i t was to determine the Latent Heat of f u s i o n of the two Isomers over the range o f temperature from the r e s p e c t i v e f r e e z i n g p o i n t s o f the pure isomers to the e u t e c t i c p o i n t o f t h e i r s o l u t i o n s . I t , furthermore, produced an opportunity to study the mesomorphic s t a t e o r , as i t i s more commonly c a l l e d , the " l i q u i d c r y s t a l " behavior o f the isomers. METHOD OF DETERMINING THE LATENT HEATS The method used l n determining the l a t e n t heats was e s s e n t i a l l y t h a t o u t l i n e d by J , H. Hildebrand©, Ph. D. i n h i s t e x t , " S o l u b i l i t i e s o f Non - e l e c t r o l y t e s . 1 " This method depends upon the f a c t t h a t the two substanoes under c o n s i d e r -a t i o n , must obey R a o u l t T s law. Since i t i s the determination o f the l a t e n t heats o f two isomers which are mutually s o l u a b l e i n a l l p r o p o r t i o n s , i t can, w i t h i n reason, be assumed they w i l l be s u f f i c i e n t l y a l i k e to obey Raoult's law. Therefore, assuming the law does h o l d , the p a r t i a l vapor pressure o f (2) the solute may he defined by the equation as follows p « p° H where p s the partial pressure of the solute pOn the pressure of the solute In i t s pure li q u i d form which has been supercooled U - the mol fraotion of the solute Since the solid i s the more stable form below the melting point of a substance, p° must be greater than p s, the vapor pressure of the solid at the same temperature, and we can have equilibrium only when the partial pressure of the solute i n the li q u i d phase is reduced by the pressure of the solvent u n t i l i t i s numerically equal to that of the s o l i d , When this equilibrium has been reached, we may equate the partial pressure of the solute, p* to be equal to the vapor pressure of the so l i d , p s . These relationships may be shown by Figure 1* The vapor pressure curves of the pure liquid and so l i d forms are repress ented along the temperature axis and w i l l intersect at the melting point, T m, The pressure-composition relations are shown at the three temperatures, T, T' and T m. At T and T 1, since the vapor pressure of the solid^ ps t i s less than that of the pure liquid, p°, i t is required in order to have equil-ibruim that pObe reduced to p» ps by dilution with a solvent to the mol fractions H and respectively. The variation of (3) s o l u b i l i t y with temperature is shown on the basal plane of the figure, having the values H, N1 and 1 at the temperatures T, T* and T m respectively. r ~ T Figure 1, Relationship between vapor pressure, temperature and mol fraction. The solubility, H, at any temperature can be calculated from the ratio p s / p° . (4) By the use of the Clapeyron-Clausius equation, the relationship between the vapor pressures, p s and po, may be found. Since the volume of the liquid i s small in comparison to the vapor, i t is neglected and the Clapeyron-Clausius equation becomes d p 0 L e ~ - ~ ( 1 ) d T T V v where L Q s latent heat of evaporation v"v = volume of the vapor Furthermore, i n regions well below the c r i t i c a l temper-ature, the vapor pressure i s relatively small and we may assume that the ideal gas laws may be applied. Since the volume of the vapor is s t i l l large in comparison to the volume of the liq u i d , the equation becomes d p° L e po d T " R T 2" ( 2 ) By simpllcation, the equation becomes * d l n p° L d T E I e I" ( 3 ) The vapor pressure of the solid may also be found by a similar method, The volume of the solid may be neglected and since the vapor pressure w i l l be less than that of the l i q u i d , ( 5 ) we may assume that the ideal gas laws w i l l be, i n this case, even more accurate. Therefore, for the vapor pressure of the soli d , we have the following equation d In p s d T where L g s the latent heat of sublimation. The latent heat of fusion, L f, i s related to the latent heats of vaporization and sublimation by the f i r s t law of thermodynamics* That is L s = L f + L Q ( 5 ) since the same amount of heat must be absorbed i n the conversion of a given quantity of solid directly to the vapor (L s) as i t would for the change in two stages, f i r s t from the solid to the liquid (Lf) and then from the liquid to vapour(L e). The latent heat of fusion can be found by subtracting equation (3) from equation (4), a l n p s d l n p° L s - L e d T d T R T2" d i n ( Ps/P Q) d T Since the relationship p s/p° i s equal to the mol fraction s R T 2 ( 4 ) R r ( 6 ) (6) i f Raoult^s law i s a p p i c a b l e , the equation then "becomes & I n x L . _ ( 7 ) d T R T Although I do not agree w i t h the f o l l o w i n g d e r i v a t i o n * i t i s entered here i n order that i t may he dis c u s s e d l a t e r w i t h regard to the experimental r e s u l t s . I f the d i f f e r e n c e i n the s p e c i f i c heats o f the s o l i d and l i q u i d at the f r e e z i n g p o i n t i s s m a l l , the l a t e n t heat of f u s i o n can he assumed independant o f the temperature and equation ( 7 ) i n t e g r a t e d , L f I n x «• «• ————-• •» •+• I R T The oonstant of i n t e g r a t i o n can he evaluated s i n c e at the m e l t i n g p o i n t , T s T m i and x becomes u n i t y . L f I = Theref o r e , In x s R T m Ii£ Il£ R T " R T m In x - ( T * T m ) R T T m (V) If , however, the more exact value of the latent heat i s required, the change of latent heat of fusion with temperature may he accounted for by using the differences between the molal specific heats of the l i q u i d and so l id forms, c ° and o s respect-lve ly . This influence of temperature on the latent heat of fusion can be expressed by Kirehhof^s equation as follows j .—-2 - ~ i — s c° - c s ( 9 ) d T d T .. Therefore, I© * L s « (L° «* L s) s (co - C S ) ( T i ) do} m m in where the subscripts, m, refer to the values at the melting point. Substituting the value of L f from equation (10) into equation (7) and integrating d l n x L f (L® • Lg ) - (o° «cB)(Tm^T) d T E I ^ E l 2 jTd i n x * (L° • L s y ^ 1 dT J" ( c ° « . o s ) ( T m - T ) dT T m R T 2 T m R T 2 l n x a - (L° - L^)(Tm «. T) ( c ° « c s ) ( T m - T) R T T m R T ~ ( c ° - c s ) l n T m (11) R T (8) Equation (8) and the more exact equation (11) vary o n l y y s l i g h t l y and are u s u a l l y w i t h i n two o r three percent of each other, w i t h equation (11) g i v i n g a lower value f o r the l a t e n t heat o f f u s i o n * However* the r e s u l t s of t h i s work i n d i c a t e t h a t the l a t e n t heat v a r i e s c o n s i d e r a b l y w i t h temperature, much more than be accounted f o r by the d i f f e r e n c e i n the m o l a l s p e c i f i c heats, and t h e r e f o r e , equation (7) which does not assume t h a t the l a t e n t heats should be constant, has been used f o r the c a l c u l a t i o n s , APPARATUS AND EXPERIMENTAL PROCEDURE The l a t e n t heats o f f u s i o n o f c i s and tr a n s deoahydro-naphthalene were determined by f i r s t a c c u r a t e l y measuring the depression of the f r e e z i n g p o i n t s o f various mixtures of the two isomers. The mixtures o f d e c a l i n were weighed i n a small bulb which was then s e a l e d o f f from the atmosphere and placed i n an acetone bath. The acetone had been p r e v i o u s l y d r i e d w i t h oalcium c h l o r i d e to remove any water which may be present and would tend to freeze out on the glass bulb and obscure the v i s i b l e signs of c r y s t a l growth. The acetone bath was cooled by s o l i d GOg u n t i l the d e s i r e d temperature was reached, w i t h a h o r i z o n t a l s t i r r e r m i x i n g the acetone to maintain the temperature constant throughout. The temperature was measured and c o n t r o l l e d by the use o f a platinum r e s i s t a n c e thermometer. The thermometer gave c o n t r o l o f the temperature i n t h a t i t was measuring the temperature at a l l times d u r i n g an experimental (9) run and the galvanometer, i n s e r i e s w i t h i t , recorded immed-i a t e l y any v a r i a t i o n o f temperature o f magnitude of •005° C and i t could he correct e d immediately. The procedure d u r i n g a run was as f o l l o w s ; the c i s and t r a n s d e c a l i n were weighed very a c c u r a t e l y and then run through a s m a l l funnel i n t o a glas s b u l l ) . The bulb was then sealed o f f from the atmosphere w i t h only a s m a l l p o r t i o n of the neck remaining. An i n c h a i r gap was allowed between the neck and a gl a s s handle to prevent the passage o f heat from the atmosphere to the d e c a l i n i n the bulb. The mixture was then shaken i n t e r m i t t e n t l y f o r s e v e r a l hours and the allowed to stand f o r 24 o r 48 hours to in s u r e complete m i x i n g . The mixture was then f r o z e n and placed i n the acetone bath and the temper-ature r a i s e d s l o w l y u n t i l o n l y one or two s m a l l c r y s t a l s remained. The temperature was then h e l d constant u n t i l the c r y s t a l s showed signs o f growing o r disappearing whereupon the temperature was v a r i e d a c c o r d i n g to the r e s u l t . During t h i s time, the bulb was shaken con t i n u o u s l y to prevent the formation of surface f i l m s and thus cause a temperature gradient from the acetone bath to the d e c a l i n i n the b u l b . The temperature was then h e l d constant f o r n i n e t y minutes a f t e r which time, i f there was no v i s i b l e s i g n s o f the c r y s t a l s growing o r disappearing* t h i s temperature was assumed to be the m e l t i n g or f r e e z i n g p o i n t * The mixture was then checked E4 hours l a t e r and each succeeding day u n t i l the r e s u l t s became constant. I t i s t h i s f i n a l temperature that has been recorded as the f r e e z i n g p o i n t of the s o l u t i o n . The mixture was then r a i s e d to 20° C and the r e f r a c t i v e index taken w i t h a P u l f r i c h refTactometer, T h i s was done i n order to d i s c o v e r i f , at low temperatures, the c i s or t r a n s d e c a l i n was un s t a b l e and converted to the other isomer. The r e s u l t s are p l o t t e d w i t h the r e f r a c t i v e index a g a i n s t the percentage volume o f t r a n s d e c a l i n . The platinum r e s i s t a n c e thermometer was checked at v a r i o u s times and at no time v a r i e d from the Ice p o i n t "by more than ,004° C , I t was necessary t o balance the Iheatstone bridge d a l l y as a s l i g h t change i n atmospheric c o n d i t i o n s made i t vary c o n s i d e r a b l y . (11) EXPERIMENTAL READINGS RUN MOL FRACTION TEMPEHATURJ Trans Solvent °C 1 0.00000 1.00000 - 43.275 2 0.02428 0.97572 - 44.226 3 0.05361 0.94639 - 45.560 4 0.08558 0.91442 - 47.044 5 0*17520 0.82480 - 51.255 6 0.25250 0.74750 - 55.128 7 0.34786 0.65236 - 59.369 8 0.40008 0.40008* - 57.714 9 0.50236 0,50236 - 54.346 10 0.56614 0.56614 - 50.075 11 0.61998 0.61998 - 47.494 12 0.67905 0.67905 - 45.291 13 0.80000 0.80000 - 39.001 14 0.89970 0.89970 - 34.050 15 0.96880 0.96880 - 31.820 16 1.00000 1.00000 - 30.659 * According to the curve of the freezing points, this point is on the trans decalin side of the eutectic point. However, since these two isomers are mutually soluahle in each other| i t is only convention which states that the substance in the larger proportion is called the solvent. Furthermore, (12) Hildebrand, i n his text, calls the substance that freezes out of solution as the solute but i n this thesis, i t is more convenient to look upon the substance freezing out of the solution as the solvent, TREATMENT OF THE RESULTS The following tables have been calculated by the normal method of determining molal latent heats of fusion. Equation 7 that is R T T m In x T - T m has been used since the molal specific heats of the liquid and s o l i d forms are not available for the use of the more exact equation. Also, i n the following tables, the corrected temper™ ature has been taken from the freezing point curve and i t i s this value that has been used to calculate the latent heat. Latent Heat of Fusion of Cis Decalin Run Mol Fraction T emperature In Cis Reading Corrected Solvent cal, 1 1.00000 - 43.275 - 43.275 0.00000 2235 2 0.97572 44.226 - 44.412 -.02458 2249 3 0.94639 mm 45,560 - 45.786 -.05511 2275 4 0.91442 - 47.044 - 47.283 -.08945 2300 5 0.82480 - 51.255 - 51.480 -.19264 2376 6 0.74750 - 55.128 - 55.100 -.29115 2452 7 0.65214 59.369 - 59.566 -.42749 2559 r i s ) The value of the pure cis decalin has been taken from the graph on page 13 A. Latent Heat of Fusion of Trans Decalin Run Mol Fraction Ln Trans Solvent Temperature Latent Heat Reading Corrected Cal/mol 8 0,40008 -0.91610 -57.714 -57.602 3512 9 0.50236 -0.68848 -53.346 -53.007 3314 10 0.56614 -0*56895 -50.075 -50.143 3189 11 0.61998 -0.47793 -47.494 -47.725 3099 12 0.67905 -0.38702 -45.291 -45.073 3018 13 0.80000 -0.22301 -39.001 -39.631 2779 14 0.89970 -0*10543 -34.550 -35.163 2683 15 0*96880 -0.03170 -31.8E0 -32.060 2622 16 1.00000 00.00000 -30.659 -30.659 2605 The molal latent heat of trans decalin was interpolated from the graph of the latent heats plotted with temperature on page 13 A. Sample Calculation E l l , f " T ••m Lm In x where R = 1.9868 Sm= -43.275°C Z 229.910°A T a -45.7860C = 227.394°A In x = ln .94639 a -0.05511 /S A, 3.S\ 3.0 2o Z/o 240 (14) 1.9868 (229.910)(227*394)(-.05511) I = .-— ™ -- r -2.516 s £275 cal/mol at -45.786° C From the preceding two tables of latent heats, i t appears rather obvious that the latent heats of fusion is not a constant value but varies considerably with temperature. One Of the i n i t i a l assumptions in the derivation of this formula was that the molal specific heats of the l i q u i d and the solid at the freezing point w i l l be almost equal. Therefore, from inspection of the more exact equation (11), i t does not appear that the differences i n the molal specific heats could possibly bring about a constant for the value of the latent heat* Thus, i f the equation i s used where there was no restriction placed upon the latent heat, a more exact value for the latent heat should be obtained. In the following table , the equation d In x mm mm _•<—>_-«— mm mm mm mm ** •—•»•»—»—»*_——••-» a i R T 2 0 has been used and the slope of the In solvent against the temperature found at the required temperatures £5?om the graph on page 15 A. Calculations of Latent Heat from Ln Solvent « Temperature Curve Hun Temperature Slope Latent Heat 3ST° T T 2 Cis 1 229.910 52,858 0.02100 2204 2 228.768 52,335 0.02135 2229 3 227.394 51,708 0.02212 2272 4 225.897 51*029 0.02294 2325 5 221.700 49,151 0,02542 2492 6 218.080 47,559 0.02842 2685 7 213.614 45,631 0.03200 2900 L a t e n t H e a t o f T r a n s 8 215.180 46,302 0.04770 4386 9 220.173 48,476 0.04100 3949 10 223.037 49,745 0.03765 3725 11 225.455 50,830 0.03436 3469 12 228.107 52,033 0.03125 3229 13 233.549 54,545 0.02725 2955 14 238.017 56,652 0.02400 2706 15 241.180 58,168 0.02252 2600 16 242.526 58,812 0.02187 2552 The values of these latent heats are plotted on the following graph on page 15 B. (16) REFRACTIYS INDICES The following are the refractive indices of the various mixtures of cis and trans decalin. Run Mol Fraction Percent Trans Refract i 1 N° Trans by volume at 20° 1 0.00000 0.000 1.48116 2 0.02428 2.359 1,48090 3.: 0.05361 5.209 1.48054 4 0.08558 8.340 1.48021 5 0.17520 17.115 1.47917 6 0.25250 24.700 1.47826 7 0.34786 34.120" 1.47727 8 0.40008 39.280 1.47662 9 0.50236 ' 49.500 1,47542 10 0.56614 55.880 1.47487 11 0.61998 61,350, 1*47401 12 0.67905 67.250 1,47347 13 0.80000 79.600 1.47202 14 0.89970 89.720 1.47090 15 0.96880 96.840 1*47017 16 1.00000 100.000 1.46968 The above values are plotted on the following graph on page 16, A. * •. ' < Densities at 20° C *'. ' Trans - 0.8700 gm/cc Cis - 0.8967 gm/cc (17) DISCUSSION OF THE RESULTS The results for the latent heats of fusion, found over the range from the melting points of cis and trans decalin to their eutectic temperature, appear to he reasonable although not 'in agreement with papers which have been published on the subject. These papers give no indication that the latent heat should vary with a change i n temperature, Hildebrand, who appears more interested i n the s o l u b i l i t i e s of the compounds than their latent heats, assumes the latent heat to be constant and interprets the variations in s o l u b i l i t i e s to be due to the change in the molal specific heats of the li q u i d and solid phases. This may be done for small temperature ranges of two or three degrees where the latent heat of fusion does not vary consider-ably but the variation for trans decalin from 2552 cal/mol at -30° C to^4386 cal/mol at - 58° C can scarcely be accounted for by the difference in specific heats since in most texts, i t is assumed that these values are very close at the melting points, F, A, Lindemann, in 1910, published a paper on the kinetics of fusion which was capable of quantitative treatment and, although It cannot be used in that sense in this paper, i t is possible to show that the heat of fusion should vary considerably with temperature. He assumed that as the heat i s applied, the amplitude of vibration of the atoms or molecules in a crystal l a t t i c e increased u n t i l i t became equal to the (18) average distance "between the atoms and collisions occurred. Thus the energy was shared and the destruction of the crystal, or melting, occurred. Lindemann assumed the particles to be classical oscillators and the motion of the vibrating particles to be simple harmonic. The mean vibrational energy i s then given by TJ a I f x dx vib J o where r Q e the vibrational amplitude when melting occurs f - the restoring force per cm displacement and is determined by the equation t i t V » •( f / m )* where \J » the frequency m = the mass of the particle. Although Lindemann goes further with his theory of the kinetics of fusion, i t is not of interest at this point. I f , the energy required to cause the destruction of the crystal must come from the heat supplied, then the amount of heat w i l l vary upon the restoring force on the particles, low when a substance i s at a temperature close to i t s melting point, i t is soft and pliable since the attraction between the molecules i s small and the restoring force i s almost negligable. However, as the temperature of the substance is lowered from i t s melting (19) point, the attraction or the restoring force on the molecules "becomes greater. Now since the restoring force w i l l vary .considerably the further the substance is away from i t s freezing vary considerably also. The latent heat of fusion which i s a measurement of the energy, w i l l therefore vary with the larger values as the temperature i s lowered. Thus the results which have been obtained, appear to be reasonable. When the natural log. of the solvent is plotted against the temperature, the slope of this curve i s , in the beginning, almost a straight line and i t is possibly this fact that i n previous papers, they assume the latent heat to be a constant value. However, i f the range of the freezing points i s increased, i t can be seen that this curve i s not straight but varies greatly as the temperature i s lowered. It i s for this reason also that, although they do not agree with the other papers, the results of these experiments seem to be reasonable* were measured as accurately as possible, i t was necessary to correct them as shown on page 12. This correction was caused by the formation of the mesomorphic state of the cis decalin which hindered the observation of the crystals. Although cis and trans decahydronaphthalene are not long chain hydrocarbons that are usually associated with liquid crystals, the decrease in the transparency of the cis decalin near i t s melting point could well be attributed to the arrange-point, the energy required w i l l Although the temperatures of the freezing points (20) -ment of the molecules into "swarms" as they were called "by E Bose to indicate a non-permenant grouping. Pure trans decalin does not, however, show any signs of the formation of "liquid crystal" hut cis w i l l be found ln a variable range. The "liquid crystal" w i l l be found over a variable range of 4 - 4.5° C at the freezing point of pure cis (-43,275°C) while at the eutectic point, the swarms w i l l be found over a range of 27°C and possibly even a larger range. The range was measured because of the d i f f i c u l t y in freezing the eutectic mixture and, by allowing i t to stand in an acetone bath at - 87°C for 24 hours, the mixture was f i n a l l y frozen. At this temperature, the swarms appeared readily and remained until the solution froze completely. If a lower temperature could have been used, the range may have been s t i l l larger. From the measurements of the refractive indices and the straight line graph of the plotted results, there is no i n d i -cation of the isomers changing at the lower temperatures. This however, i s not actually proven as the decalin was measured at 20°C In which case the isomers, i f changed at a l l due to stresses set up at the low temperature, could convert back to thevorlginal as the temperature is raised. (21) BIBLIOGRAPHY Hildebrand, J.H., Ph.D. textbook, "Solubilities of Non-electrolytes," second edition, 1936. Glasstone, Samuel, Ph.D. "Text-book of Physical Chemistry" Fischl, F.B. and Naylor, B.F., paper, " The Heat Capacity, Heat of Fusion and Entropy of ll-n-Decylheneicosane," Penn. State College, Journal of American Chemical Society, Vol. 67 p 2075, 1945. Schumann, S.C. and Aston, J.G. paper, "The Heat Capacity and Entropy, Heats of Transition, fusion and Vaporization and Vapor Pressure of Cyclopentane," J. of Am. Chem. Soc, Vol 65 p 341, 1943. Negishi, S.R., " The Heat of fusion and Vapor Pressure of Stannic Iodide," U of California, J. of Am. Chem. Soc, Vol 58 p 2180, 1936. 

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