June, 1933
I S D U S T R I A L -4N D E S G I N E E R I N G C H E 111 1 S T R Y
9. It does not shrink on absorption of water, or otherwise develop channels through the absorption column. 10. I t is available in large quantities at lox cost.
.LITERATURE CITED Baxter, G. P., and Starkweather, H. W,, J . A m . Chem. Soc.. 38, 2038 (1916). Baxter, G. P., a n < iWarren, R. D . , Ibid., 33, 340 (1911). Chassevent, L., A n n . chim., 1101 6,244, 313 (1926) 7,43 (1927). Cloee, C., Bull. so(:. chim., [3] 29, 169 (1903). Davis, TV. A., J . Soc. Chem. Ind., 26,727 (1907). Dover, M . V.,and Marden. J. W., J . A m . Chem. SOC.,39, 1609 (1917). Foster, Wm., “Introduction t o General Chemistry,” rev. ed., p. 143, Princeton University Press, 1931. Glasenapp, hl., Tonind. Ztg., 32, 1148 (1908); .T. SOC.Chem. Ind., 27, 858 (1908). Hoff, H. van’t, and others, 2. physik. Chem., 45,257 (1903). Keane, L. A , J . I’hys. Chem., 20, 701 (1916). Lacroix, A . , Compt. rend., 26, 360 (1898). Lavoisier, A., “Oeuvres Completes,” Tome 111, pp. 106-44, 1765-6 (Imprimerie Imperiale, 1865.) ~
639
(13) Le Chatelier, H., “Recherches Experimentales sur la Constitution des Mortiers Hydrauliques, 2nd. ed., Viech Dunod, Paris, 1904. (14) McPherson, A. T., J . Am. Chem. Soc., 39, 1317 (1917). (15) Mellor, 3. W., “Modern Inorganic Chemistry,” p. 533, Longmane, 1926. A m . J . Sci.. 34, 199 (1687); J . A m . Chem. Soc., (16) Morley, E. W., 26, 1171 (1904). (17) Potilitain, A,, Be?., 27 (4), 613 (1694); Chem. Zentr., 1894,615, 604. (18) Shenstone, IT. A . , and Cundall, J. T., J . Chem. Soc., 53, 544 (1888). (19) Smith, G . F., Chemist-Analyst, 17, 21-3 (Oct.. 1928). (20) Wilder, F. A., Iowa Geol. Survey, Ann. Repts., 28,275 (191716). (21) \I-ilson, R.E., J. I S D . ESG. CHEN., 13,326 (1921). RECEIVED December 30, 1932. A preliminary paper on this subject was presented before the Division of Inorganic and Physical Chemistry at the 77th Meeting of the American Chemical Society, Columbus, Ohio, April 29 to May 3, 1929. W. A. Hammond is at preeent associate professor of chemistry, Antioch College, Yellow Springs, Ohio. C’,
The Estimation of Latent Heats of Vaporization J. HOWARD ARNOLD,L n i v e r s i t y of M i n n e s o t a , Minneapolis, hlinn. The empirical rule of Hildebrand, as expressed = A log 1000PIT S A COXSEQUESCE of (1) the modern t e n d e n c y by Lewis arid meber and improved by .VcAdams toward the u t i l i z a t i o n Utilizing data a t h i g h presand J4orre11, is shown to be a n incomplete f o r m SureS f r o m the literature, they of high pressures and temperatures in the process industries. O f a n accurate empirical equation due to Diealso extended the range of the lerici and tested by dFlills. Graphical representaH i l d e b r a n d function toward it has become i n c r e a s i n g l y tion of the al!ailable calorimetric data indicates t h e critical p o i n t . T h o u g h necessary for t h e chemical engineer to develop methods of that the Dieterici equation is reliable to 5 per cent their method of plotting reprepredicting the physical behavior sented a considerable advance, of m a t e r i a l s u n d e r e x t r e m e or better o2‘er the range f r o m room temperature it is not w e l l s u i t e d f o r t h e conditions. F o r Kiang subto the CritiCd point. e s t i m a t i o n of l a t e n t h e a t s stances the data necessary for near the critical point, for two engineering design purposes are meager, inaccurate, and often reasons: The data for various substances fall, not on a single entirely wanting. It is the purpose of this paper to present line, but on a family of lines of different slopes and intera method, valid under all conditions of temperature and cepts; furthermore, as the critical point is approached, the pressure, for the calculation of the latent heat of vaporization curvature increases markedly, the method evidently breakfor normal substances. ing down in the neighborhood of MX/T = 12. Both these factors tend to reduce the accuracy of data obtained by esHILDEBRAKD RULE trapolation. Numerous empirical rules have been proposed for latent DIETERICIRULE heat estimation. Trouton’s rule states that the molal entropy of vaporization, M X / T , is constant from substance to It recently occurred to the writer that the Hildebrand rule substance a t the normal boiling point. Kirejev ( 7 ) and later is a special case of a n equation advanced by Dieterici (3) in Watson (16) plotted .WAIT against the reduced temperature, 1908, which states t h a t the internal latent heat is a function TIT,, finding similar curves for various substances. One of of the ratio of vapor volume to liquid volume: the most widely used methods of estimation has been a rariaTotal latent heat = External work + Internal latent heat tion of the rule discovered by Hildebrand ( 5 ) in 1915. This MA = P ( V z - V , ) CRT In V2/Til (2) states that MX/T is a function only of the molal concentration of the vapor evolved. As originally advanced by Hilde- Though no exact theoretical basis for this equation has yet brand, the rule was not in a form convenient for engineering been found, it has attracted considerable attention because of use, and accordingly was modified by Lewis and Weber (9) in its remarkable accuracy a t temperatures above the boiling 1923. I n the range of validity of the gas laws, the molal point. Dieterici claimed an accuracy better than 2 per cent; vapor concentration is P I R T ; hence, Lewis and Weber in 1909 Mills (IS), using as a basis the experimental data of plotted MX/T against 1000 P / T , and showed that a definite Young ( I O ) , substantiated this claim in a detailed investigarelationship existed. I n 1924 McAdams and Morrell (12), tion. The Dieterici rule may be written: noting that extrapolation at the ends of the Lewis-Weber MA/RT = ( P V 2 / R T )(1 - V l / V z ) CIn V z / V 1 (3) lines was hampered by the large curvature, used a logarithmic scale for 1000 P I T and obtained lines which were nearly As XX/RT is dimensionless, X may be expressed in any units straight, having an equation of the form: desired, with the units of R taken accordingly.
A
+
+
INDUSTRIAL AND ESGINEERING CHEMISTRY
660
At the boiling point, the vapor volume L'? is about 230 times the liquid volume V I , and V1/Vz may be neglected in comparison with unity. Since the deviation from the gas laws is only a few per cent (18), VI may be replaced by R T I P , and Equation 3 reduces to: MX/RT
=
(1
+ C In RIV,) - C In P I T
(4
which is of the same form as Equation 1. Therefore, a t low temperatures, substances having nearly equal values of V1 should give a single straight line on the McAdams-Morrell
Vol. 25, No. 6
boiling point and the critical temperature, both the external work and the internal latent heat decrease uniformly toward zero. Errors in the evaluation of the external work term will not, therefore, seriously affect the value of the total latent heat; we may assume to a sufficient approximation that M A / RT is proportional to In Vz/Vl. This results in a line slightly curved between the critical temperature and the boiling point, while below the boiling point the line is straight, projecting to an intercept of MX/RT = 1,as shown by the dotted line (Figure 1).
SOURCES OF PLOTTED DATA For the range from the normal boiling point t o the critical temperature, the data plotted have been taken from the International Critical Tables (6); the latent heats are all calorimetrically determined values. Three substances of different types are represented: ethyl ether, benzene. and carbon tetrachloride. Below the boiling point the calorimetric data of Griffiths and Marshall (4) are shown. Dana, Jenkins, Burdick, and Timm ( 2 ) have determined the latent heats of propane, butane, and isobutane; their data, omitted for clarity, show the same agreement as those plotted. For ether, Taylor and Smith (15) have given data calculated from the Clausius-Clapeyron e q u a t i o n , d o w n t o - 65 C.; they also supply the necessary specific volume data. The similarly calculated values of Mills (IS) for twenty-three normal substances have been included; these are a t 0" C., and the theoretical volumes calculated from the gas laws have been used for V Z . There is also shown a number of points representing the recent accurate calorimetric data of Mathews (11) at the normal boiling point. The liquid volumes \vere taken from LeBas' compilation ( 8 ) ,while the gas volumes were found from the gas laws, assuming a deviation of 3.5 per cent (18). O
FIGURE1
chart. The observed deviations are traceable to the variation of V I with the temperature and the nature of the substance; between the boiling point and the critical temperature, the error caused by the omission of VI from the Hildebrand function becomes progressively larger, while the deviations from the gas laws similarly increase. As is to be expected, therefore, the Hildebrand rule breaks down long before the critical point is reached; the latent heat predicted by extrapolation to that point is not the theoretical zero, but a much higher value. The Dieterici equation behaves differently; as the critical point is approached, both the internal latent heat and the external work approach zero, since the vapor and liquid volumes tend toward equality. Hence, the Dieterici equation is inherently capable of representing the data Over a much wider range than the Hildebrand rule, and is particularly valuable between the boiling point and the critical temperature. GRAPHIC.4L APPLICATION Although the validity of Equation 2 has been well established by Dieterici and Mills, it is of interest to present the data in graphical form, to illustrate the relationship to the McAdams-Morrell chart. This might be done by plotting [MA - P(V2 - V I ) ] / R Tagainst the logarithm of V?/V1. I n practice, however, it is preferable to plot MA/RT, with V2/V1 replacing the 1000P/T of McAdams and Morrell, thereby securing a direct-reading chart. As shown by Equation 3, when the gas laws apply, the external work term is constant and equal to unity. At the boiling point this term amounts to about 10 per cent of M A / R T , the ratio assuming a limiting value of 14.6 per cent (from a plot of Mills' data) as the critical temperature is approached. Between the
VARI-4TIOk OF
c
?Ililla found that Equation 2 held within 2 per cent between the critical and boiling points for each Of twenty-seven normal compounds (though not for abnormal substances such as a h h o b acids, amines) Provided the Proper values of c %'ere chosen. The requisite values of C varied from 1.66 to 1.86, increasing with molecular Weight, and being very nearly for ten esters is equal to RTc/PcVc - 2. The average 1.80; for nine hydrocarbons and ether, 1 7 5 ; for Seven halides, 1.70. Figure 1 indicates that the available calorimetric data may he represented by the solid line, corresponding to a C value of 1.70. The broken line has been drawn through the points representing Mills' data for octane (C = 1.86) to serve as B guide. It is evident that by judicious choice of the value of C the latent heat may be estimated with an accuracy of 5 per cent or better.
c
LOW-TEMPERATURE LATENTHEATS In view of the frequent necessity for predicting latent heats a t low temperatures, for processes of drying and evaporation, it is desirable to test the Dieterici rule at temperatures below the boiling point. Using isolated values of the latent heat a t 0" C., which were admittedly somewhat inaccurate because of the low vapor pressures and consequent error in dP/dT, Mills concluded that the rule no longer held a t low temperatures. However, this conclusion is not borne out by the graphical representation of Mills' calculated data; in fact,
June, 1933
ISDUSTRIAL A S D ESGINEERING CHEIIISTRY
aside from a few erratic deviations, the agreement is excellent, and the constancy of C from substance to substance is better than a t high temperatures. Most of RIills’ data fall on the same line (C = 1.50) as the high-temperature calorimetric data, with the benzene halides forming a second group about 5 per cent below the line. However, a comparison of Mathews’ data ( 1 1 ) a t the boiling point with hlills‘ values (10) shows that the latter are too low, by 4.7 per cent for chlorobenzene and 3.5 for bromobenzene. If the error a t 0 ” C. is of the same nature, most of the discrepancy will disappear, and all Mills’ data fall on a single line. B ~ l o wthe boiling point the value of C apparently tends t o approach 1.70 for all substances, as shown by Mills’ data, or possibly to fall below 1.70, as indicated by the trend of the data of Smith and Taylor for ether. At about room temperature, however, a C value of 1.70 appears to reproduce hlills’ values with considerable accuracy, and is ther(,fore recommended for the estimation of latent heats in the range from 0 ” to 30” C. ES’rIxiTIox OF T‘OLCMES
i
The principal shortcoming of the present method is the necessity for knowing the value of T 7 g / V l ; hon-ever, as this ratio occurs as the logarithm, it need not be kn0n.n n i t h great accuracy. The method is therefore usable with vapor-pressure data of only fair accuracy, which could not be employed in the Clausius-Clapeyron equation with confidence. Kilson and Bahlke (17) have reviewed the liquid and vapor density data for the paraffin hydrocarbons. Cope, Lewis, and Weber ( I ) recently presented methods of estimating the vapor volumes of the higher hydrocarbons. For the estimation of liquid \rolumes the empirical equation of Saslavsky (14) is useful: V c / V = (1
+ 2.73 dl - O.95T/TC)
(5)
661
Though this obviously cannot hold a t the critical point, i t is valid u p to a reduced temperature of T/T,= 0.98 without serious error.
L4, B , C d
= =
1’
= = = = =
M P R T
X =
SOTATIOS empirical constants differential operator molecular weight vapor (saturation) pressure gas law constant, in PV = RT abs. temp.; T , = critical temp. molal volume; V I , of liquid; Vz, of vapor; at critical point total latent heat
ITe,
LITERATURE CITED (1) Cope, Lewis, and V e b e r , ISD.ESG.CHEX.,23, 887 (1931).
(2) Dana, Jenkins, Burdick, and Timm, Refrigerating Eng., 12, 387 (1926). (3) Dieterici, A n n . Physik, 2 5 , 569 (1908). (4) Griffiths and Marshall, Phil. -\lag., 41, 1 (1896). (5) Hildebrand, J . A m . Chem. Soc., 37, 970 (1916). (6) International Critical Tables, T’ol. 111. p. 245, and Vol. T’, p. 138, McGraw-Hill, 1926. ( 7 ) Kirejev, 2. ccn.org. allgem. C‘hem., 182, 177 (1929). (6) LeBas, “Molecular T-olumes of Liquid Chemical Compounds,” Longmans, 1915. (9) Lewis and Weber, J. ISD.ESG.CHEX, 14,485 (1922). (10) Marie, Tables Annuelles de Constantes et Donn6es Kumbriques T’ol. I, p. 68, Gauthier-T’illare, Paris, 1910. (11) Mathew, J. H., J . Am. C‘hem. SOC.,48, 562 (1926). (12) McAdams and blorrell, ISD.ESG. CHEY.,16, 375 (1921). (13) Mills, J. E., J . A m . Chem. SOC.,31, 1099 (1909). (14) Saslavsky, Z . physik. Chem., 109, 111 (1924). (15) Taylor and Smith, J . A m . C‘hem. Soc., 44, 2460 (1922). (16) TTatson, IXD. ESG.CHEJI.,23, 360 (1931). (17) Wilson and Bahlke, I b i d . , 16, 115 (1924). ( l b ) Toung, Sydney, Phil. M a g . , 33, 153 (1892). RECEIVED Sovember 4 , 1932.
VitarYlins A and D in Tuna Meal ROGERM‘. TRUESDAIL AND LEE S I I A H I N I A S , Truesdail Laboratories, Inc., Los iingeles, Calif.
C
OSSIDERABLE data have been published upon the pended on fish meal or other related marine products, suitable the of ~man and beast,~ as has been completed on nutritive of fish meals as pointed out by ~ ~ for ~ dietary l of the science of nutrition would cod liver oil,i our knowledge
and McCollum ( I ) . Little of this concerns the vitamin be much It is only to be hoped that the future contents of such meals. Malcohi (4, 6)found a destruction n-ill Drovide such data. of v i t a m i n A when fresh fish and oysters were dried. Several A representatire sample of meal prepared The w o r k of K’elson a n d i n v e s t i g a t o r s (7, 8, 10) rehlannillg (’) and Of this laborschiefly from the dark meat of the tuna has been port varying vitamin D values tory (12) has indicated tuna oil for different fish meals. It is tested for its Titamin A and content. The to be an excellent source of vitaapparent that q u a n t i t a t i v e tuna meal prored to be a good source Of ritamin min D but inferior in its vitamin v i t a m i n studies of fish meals A , containing more than 14 Sherman units per A content. The canned white have been fern. l l a n n i n g (6) gram. It is an excellent Source of vitamin D, meat of the tuna has assumed a has stated this position a s assaying more than 62 units (A. D. AI. A.) of definite place in the American follows: dietary, and substantial quantifhisfactor per gram. ties of tuna meal, produced priU n f o r t u n a t e l y n e possess If is suggested that canned funa, which is the marily from the dark tunameat, f a r too meager a Of knou-lwhite luna meat, may protide these two factors are used in animal and poultry edge c o n c e r n i n g the v i t a m i n potency of fish meal and related f o r the human dietary. The citamin confent rations, although it has been reof canned tuna should be inziestigafed. ported as a source of food for marine p r o d u c t s , except in the case of cod liver oil where concertain groups of people. This siderable scientific i n f o r m a t i o n sideration should be given tuna meal as a source investigation undertaken to is a v a i l a b l e . Needless to say, of vitamins A and D f o r animal and poultry ,jetermine the tuna meal content If a c o r r e s p o n d i n g amount of scientific r e s e a r c h had been exrations. of vitamins A and D.
con-
