tirr ( : o s s v t i r x uniformly with a n induction heatcr. The technique of rnoviIlga tempirnture gradient down a colunin shoiild also improve separations by liquid-adsorption and liquid-partition chromatography. The advantageous effect of thr, gradient would be
t o that described for gasliquid chromathrrinography.
LITERATURE CITED
(1) Keulemans, A. 1. hf., "Gas Chroma-
tography," pp. 96-129, Reinhold, New York, 1957. (2) Turkel'taub, N.ht., el a ~ , ~, ~ Khoz. 32, 72 (1954)~ Trudy Komissii. Anal. Khzm., Akad. h'auk S.S.S.R., Inst. Geokhim. i Anal. Khi?n. 6, 146 (1955); Zhur. Anal. Khim. 11, 159 (1956); Zhur. Fiz. Khzm 27, 1827 (1953); 30,334 (1956 j.
(3) ZhukovitskiI, A. A., et al., Doklady Akad. Nauk S.S.S.R. 77, 435 (1951); 88, 859 (l953); l Z 3 t 1037 (lQ58).
f
A. ~ GLENN ~NERIiEIM~
t
Research and Develo ment Department Standard oil co.(InZiana) Whiting, Ind. RECEIVEDfor review October 23, 1959. Accepted December 7, 1959.
Application of Optical Polarimetry and Density Measurements to the Analysis of a Ternary Mixture SIR: Ar. effectii.e and relativeiy rapid niethod has been developed for determining tlie cor:iposit,ion of a ternary mixt'ure which n'as produced during the thermai isomerization of B-pinene. Only measurenimts of the density and the optkni r.3t:ition are necessary for the nnalyr--is. 'i'lic :rpproirinte equations iieecied fLJ! t11(, (':iiuii9Tion of the com2osition require t h e d u e s . Application of t h k mc,t!iod t o other systems is also inriirated A fen >. 3
xeight C'oapoun,! hlyrene p-Pinene Limonene Myrcene 8-Pinene Limonene Nyrcene 8-Pinene Limonene
FractiorJ 1L' &f We EL 2L'M WB
U'L ZL'M WB
WL
deviation from linearity in the relation between composition and such properties as density and refractive index (1. S;, only a small deviation In the additivity of the molar volumes in such mixtures would be expected. If these volumes are replaced by the corresponding ratios of the weight, G, in grams, of each substance to their densities. d there results the relatioi?
- :;nd as a result a
oo (of analysis was tiesirea nnc CII-'T The reactant. $-pinene. and the tw., niain protlucts, limonene and myrcenq have tile same molecular weight,q :in3 i:mali dipole moments
(4:
This equation does not hold rigorously in this case and hence a correction factor which is a function of the composition was introduced and is included in the equation
Comparison of True and Calculated Composition Values for Three-Component Mixtures
Sample SO.
where the w's are the weight fractions of the components and the l/d's are the specific volumes of the mixture and the compounds present. For the binary mixture of @-pinene and myrcene the equation becomes
Dividinp this equation by GP produces the following:
Weight Fraction Value Known Calcd. 0,388 0.383 0.513 0.516 0.099 0.101 0.334 0.337 0.598 0.599 0.068 0.064 0.78': 0.788 0,092
0.120
0,094
0.119
Difference +0.005 -0.003
-0.002 -0.003
-0.001 +0.004 -0.001 -0.002 -0.00:
which when rearranged gives
k was evaluated by determining the density of known mixtures of @-pinene and myrcene. The average of four such vaiues between 0.0041 and 0.004; was 0.0044. A similar calculation Twis made for mixtures of linionenc and myrcene. k \\-a$ about 0.0004 or abour one tenth as large as for the previous cas*. This, plus the fact, thar VO,.
32, NO. 3, MARCH 1960
8
437
~
tlic weight fraction of limoneiie was about 0.1 or less, in all cases, made it unnecessary to apply a correction factor for the presence of limonene as a third component. Hence, the equation for the product mixture was used in the form
If the original assumption that the volumes are additive is correct, it is appropriate to express the optical rotation of the mixture as a function of the volume fraction of each component. This may be represented by the equation
where the a's are the observed rotations per decimeter of liquid. If the V's are replaced by the corresponding G/d ratios, and the resulting relation divided through by d p and GP, there results the relation,
The specific rotation of a liquid,
nhere a' is the observed rotation in a tube 1 dcm. long. Hence, the ratios a/d in Equation 9 may be replaced by specific rotations t o give
constants for the reaction\ ca11 be calculated. The data in Table I cont,rin a romparison of anal! ses calculated by the
inactive, [CY]# = 0 and the last term in Equation 11 drops out in this particular case.
of the pure compounds nhich were obtained in this reaction nere:
-
Boiling Point,
dZ5
Compound p:Pinene Limonene LIyrcene
G./& 0 8669 0 8385 0 7921
.
IffI'd - 21 35" -107 91°
I n addition to Equations 7 and 11, there is the relation that the sum of the weight fractions equals unity, or
0"
C./20 l f m ,
59 5 71 5
1 1768 1 1710
65 5
1 4682
LITERATURE CITED
(1) Fuguitt, R. E., ~ ~ ~ l IT, l ~ D,, ~ ~ ~ , , Hawkins, J. E., J . A n i . C h e m Soc. 64, 2978 (1942) ( 2 ) Ha
