Conversion of Refractive Dispersions to Other Wave-Length Intervals iI.HF.K'I' 5 i N K I N , C:. C. . \ I 4 K T l V , A I L ) 11. I
70GI Total
9 17 36
-
- 0.718 (5.2615 - 2.8800)] = 7.5 0.718 (no n o ) x io4 f 7.5 (15)
(13)
+ Kn, + lO-'K'
(16)
Using Equation 16 i t is possible to calculate a desired refractive index for a liquid from two other refractive indexes, providing the F-C dispersion of the liquid is less than 250. Figure 3 is a plot of deviations from Equation 16 against F-C dispersion for the calculation of the sodium D refractive index from those of the F and C lines of hydrogen.
Table VII.
Type Paraffirm Cyclo arsffins Alk ylgenzenea
Conversion of Dispersions for API-NBS No. of Compounds 18 21 21 60
-
Calculated Minus Experimental (np - no) X 10' Deviation Max. of av. deviation +1.7 +2.2 +0.9 +1.1 -1.3 -2.3 +0.4 -2.3
Av. deviation 1.7 0.9 1.3 1.3
ANALYTICAL CHEMISTRY
648 The agreement of the data for Figures 1 to 3 as well as soine calculations for the ultraviolet range are summarized in Tables IV t o VI. The tables include data a t many different temperatures with no distinction made among them. Most of these data are in the range 10”to 40” C. and within this range temperature has no appreciable effect. The indications are that Equation 14 with the average value of C Pwill satisfactorily represent data up to 100” C., providing all measurements on the sample are made a t the same temperature. However, this has not been completely checked. The data are separated into groups of concordant and discorda n t data. The discordant data are for liquids which, for a particular conversion, show deviations greater than 3.33 times the average deviation for all liquids. Table IV shows that the average deviations are generally largest for those calculations involving the largest magnitudes of K‘. This indicates that the principal source of error in the correlation is the assumption of a constant value for CZin Equation 14. The ’average deviation from a particular calculation is in general less than 30% of the magnitude of K‘. For most calculations in the visible range this is less than 2.0, which approaches the experimental accuracy of most of the literature data. The dala for the g-D to F-C conversion show the most consistent agreement with the correlation. These dispersions are relatively easily measured and have been determined most recently. As a n illustration of the application of the g-D to F-C conversion to a group of accurate hydrocarbon data recently obtained in a single laboratory, we may consider the dispersions of 60 A.P.1.-S.B.S. hydrocarbons reported by Forziati of the National Bureau of Standards (8). Table VI1 summarizes these data. Table V shows that only 4% of the hydrocarbons are listed as discordant and that few of the discordant data are for the types of hydrocarbons that are most likely to be found in petroleum. Furthermore, the petroleum fractions,,% which constitute more than 80% of the “mixtures,” show excellent agreement with the correlation. A possible explanation of the large deviations of some olefins and conjugated aromatic olefins is the experimental difficulty caused by the tendency of these compounds to undergo polymerization and atmospheric oxidation. In the 180 to 250 F-C dispersion range some nonhydrocarbons have been found for which the F-C dispersions calculated from the G‘D and G’f dispersions are larger than the experimental values. This is the only definite evidence of serious systematic deviation that has as yet been found. Even with the inclusion of the discordant data, Table VI shows that half of the liquids have deviations of 1 or less and more than 70% of them have deviations of no more than 2. Most naphthalenes have F-C dispersions of almost 300 and are, therefore, beyond the range of this correlation, as are anthracenes and phenanthrenes. Most of the very few data in the high dispersion range are for nonhydrocarbons. I n fact, with t h e exception of the previously mentioned polynuclear aromatics, none of the liquids having F-C dispersions beyond the range of the correlation are likely t o be found in petroleum. This correlation should be satisfactory for liquid mixtures having F-C dispersions less than 250 even if they have some high dispersion components. DISCUSSION
A study of the calculations and of the figures indicates that Equation 12 can be extended, as follows, so that it applies to liquids which have F-C dispersions higher than 250: n = C1
+ CZV*+ C3v3 + Cw‘ + . .
I
(17)
It would be extremely difficult to evaluate empirically both the exponents and coefficients for all the significant terms in this equation. However, consideration of the data shows that all the coefficients in this series are probably positive.
For samples of very low dispersion, such as gases and saturated liquid hydrocarbons, i t is known that the simplified Cauchy equation (Equation 4) adequately represents the data with C, increasing proportionally to the dispersion. At about the lower limit of liquid dispersions Ccbecomes appreciable and CPincreases less rapidly than before, perhaps approaching a maximum. An increase in CI compensates for a continued increase in CZ,and makes it possible to use an average value for Cz in Equation 14. This average value of C2 is too large for saturated hydrocarbons, causing them to, have an appreciable deviation of average (see Table V). Fortunately, these compounds usually deviate less than two units of dispersion from the correlation. The calculated values for the exponent t of 2.7 and 2.8 shown in Table I are low, probably because saturated hydrocarbon data predominate in the two groups involved. The fact that water also has a very low dispersion caused the low value oft calculated from the data for water and toluene. At relatively high dispersions Cd is so large that its effect is no longer minimized by the opposing effect of C2 and Equation 14 is no longer valid. The high dispersion data will always deviate from Equation 14 in a direction away from the simplified Cauchy equation. This is to be expected, because data agreeing with Equation 17 (four or more terms) should be more nearly represented by Equation 14 (three terms) than by the simplified Cauchy (two terms). If refractive indexes are available a t three wave lengths and the index at a fourth is desired to *0.0001 or better, i t is recommended that the three available indexes be substituted in Equation 16 and K’ be calculated. After C2 has been calculated from K‘ at the three available wave lengths, this value may be used in Equation 16 for the calculation of the refractive index a t the fourth wave length. For liquids of very low dispersion, the simplified Cauchy equation (Equation 5) may give results as reliable as Equation 14 using the average value of CP. The procedure outlined in the previous paragraph, however, will give better results than the simplified Cauchy in any case. This procedure can also be used for liquids of F-C dispersion slightly larger than 250 or for samples a t temperatures over 100” C. However, for liquids of F-C dispersion over 320 i t would be better to have four experimental indexes and use Equation 17. It is not known as yet what the maximum d i 5 persion is at which a four-term equation is valid. On the basis of the work described, the following conclusions have been reached: Refractive index may be represented within experimental error in the visible and near ultraviolet ranges a t any temperature by a power series with positive coefficients, the first term of which involves Y O , and the third, v3. Because of the V S term this series cannot be simply derived from Equation 1 and therefore seems to disagree with present theory. LITERATURE CITED (1) Auwers, K. V., and Eisenlohr. F., Ber., 43, 806 (1910). (2) Auwers, K. V,., and Westermann. H., Ibid., 54, 2993 (1921). (3) Campbell, K. N., and Eby, L. T.,J . Am. Chem. SOC.,63, 2683 (1941). (4) Dixmier, G., Chirnie & Industrie, Special No., 338 (1926). (5) Drude, P . , Ann. Physik. 14, 677 (1904). (6) Egloff, G., “Physical Properties of Hydrocarbons,” New York, Reinhold Publishing Corp., Vol. I (1939), I1 (1940), I11 (1946). IV (1947). (7) Farmer, E . H., and Warren, F. L., J . Chem. SOC.,134, 3221 (1931). (8) Forziati, A. F., to be published inJ. ResearchNatZ. Bur. Standarde. (9) Garrett, A. B., Am. Petroleum Inst., Research Project 45 at Ohio State University, Serial No. 43, “Refractive Indices and Densities of some A.P.I. Hydrocarbons,’’ 1944. (10) Geldof, H., and Wibaut, J. P . , Rec. tras. chim., 67, 105 (1948). (11) Gladstone, J. H.. J. Chem. Soc.. 45, 241 (1884). (12) Ibid., 59, 290 (1891). (13) Gooding, R. M . , Adams, N. G., and Rall, H. T., IND. ENO. CHEM.,ANAL.ED., 18, 2 (1946).
V O L U M E 2 2 , NO. 5, M A Y 1 9 5 0 ( 1 4 ) H a r d y , -4, C . , arid I'rrrin. I'. € I . , "I'rinciplrs of Optics," S e w Y o r k , 1IcC;ra\v-Hiil I30ok C'u,, 1832. (15) " I n t e r n a t i o n a l Critical Tatrlw," S e w l - n r k . RIcGraw-IIill Hook
649 I,nrentz, H. .L, W i e d : l r o ~ . , 9, 641 (1850). Loreiia, I,. V., I b i d . , 11, i o (1880). S o t i o n a l Bureau of Standards, Certificate for S t a n d a r d h n i l j l e s 21 l a , 217, and 218. I'erkin, IV. H., .J. ('hem. S o c . , 69, 1 0 2 5 (18!46). Sellmcier. \V., Pogg. A n n . , 143, 272 ( 1 8 i l ) ; 145, 399, ,520 ( 1 6 7 2 ) : 147, 356, 5 2 5 (1872). S u n Oil u n ~ u l i l i s h e dd a t a . T h o r n c , H. k , , * l l u r p h y ,IY., a n d Ball, J. S., I s n . I k c . . C ' i i E i r , , \ T . \ L . En., 17, 481 (1945). T i l t o n , I,. I V , , a n d T a y l o r , J. Ti.,J . Rcscarch .Vatl. Bur. Sforidu r d , , 20, 418 (1938). T\.:ircI, .4. L., a n d l.'ulaeiler, IY.H . , I s n . Eso. CHEM!.. . \ x A I . .l , : i i , , 6, 396 (1834). \\.aid, ;\. L., and K u r t z . S . S . , J r . , I h i d . , 10, 559 (1035). \ \ . a d , A. I, , I i u r t a , S.8.. J r . , a n d Fulweiler, IV. If.. "Science of P e t r o l e u m , " et1 by D u n s t a u , A . E., S a s h , A . IY.,T3t.ooks, I3. T..a n d T i z a r d , H . , \.nl. 11. p. 1137, L o n d o n . Oxford I-niversity l'rese, 1935. Zeiss, C'nrl. I n r . , d a t a supplied w i t h Pulfrich refractometer.
co..
(19) K u r t z , S. S.. Jr.. IIills, I. W., M a r t i n . C. C., H a r v e y , \Y.T., and Tipkin. A I . R., A N \ I . . C R E M . 19, , 175 (1947). (20) K u r t z , S. S,,
