Thermodynamic Equilibria among Benzene and the Methylbenzenes from Spectroscopic Data S. H. HASTINGS and D. E. NICHOLSON Manufacturing Department, Research and Development Division, Humble Oil 8 Refining Co., Baytown, Tex.
PERIODIC interest in the isomerization-disproportionation reactions existing among benzene and the 12 methylbenzenes provided an impetus for calculation of the thermodynamic equilibria involved. The requisite free energy of formation data were calculated previously from infrared and Raman spectroscopic data (2, 4 ) and calorimetric information. The actual computation of equilibria in complex mixtures can become involved, unless proper choice of equations is made. The method outlined by Kandiner and Brinkley (3) is particularly valuable in this regard. In any methylbenzene disproportionation reaction the possibility exists that all of the following components may be present a t equilibrium: NJ Benzene Methylbenzene N, 1 ,e-Dimethylbenzene 1,3-Dimethylbenzene Ni 1 ,4-Dimethylbenzene 1,2,3-TrimethyIbenzene 1,2,&Trimethylbenzene N I
1,3,5-Trimethylbenzene 1,2,3,4-Tetramethylbnzene 1,2,3,5-Tetramethylbenzene N S 1,2,4,5-Tetramethylbnzene Pentamethylbenzene N6 Hexamethylbenzene NT
This simplification reduces the number of components from 13 to seven for most calculations. To calculate the seven unknown concentrations, seven independent equations are required. It has not been found possible to write down seven equations explicit in the unknowns. Instead, successive approximations are required, until two criteria are fulfilled-namely, material balances on moles of benzene nuclei and methyl groups. Availability of these two criteria permits selection of two independent components: These are taken to be 1,3-dimethylbenzene and 1,2,4-trimethylbenzene. The important Kandiner and Brinkley contribution is the choice that is now made for the remaining five equations. Their criterion for this selection is that each equation contain only one of the unknown components in terms of the independent components. Using this criterion, the following equations can be written: 3 (1 ,d-Dimethylbenzene) Ks benzene + 2 (1,2,4-trimethylbenzene) c +
2(1,3-Dimethylbenzene)
K, methylbenzene + 1,2,4-trimethylbenzene c -+
2(1,2,4-Trimethylbenzene) Ks 2
1,2,3,5-tetramethylbenzene+ 1,3-dimethylbenzene
N , represents the mole fraction of the component present at equilibrium. The total dimethylbenzenes, trimethylbenzenes, and tetramethylbenzenes can be related to the concentration of a single isomer as follows: 1,3-Dimethylbenzene K+. 1,2-Dimethylbenzene c
1,3-Dimethylbenzene K , 1,4-Dimethylbenzene c
-3
(1.2-Dimethylbenzene) = K,(1,3-Dimethylbenzene) (1,4-Dimethylbenzene) = KY(1,3-DimethyIbenzene) (1,3-Dimethylbenzene)= (1,3-Dimethylbenzene) (Total dimethylbenzenes) = (1 VOL. 6, No. 1, JANUARY 1961
+
K , + KY)(1,3-dimethylbenzene)
3(1,2,4-Trimethylbenzene) Xs + -+
pentamethylbenzene+ 2(1,3-dimethylbenzene) 4(1,2,4-Trimethylbenzene)KT 4 Nz c hexamethylbenzene+ 3(1,3-&methylbenzene) NT NI
Accordingly , (NI) K,= N (Nd' Since K scan be computed from the data reported previously (2) and N,and N 2are assumed, one can obtain a value for
N,= KdNd' (Nl)'
or
(Continued on Page 4 )
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JOURNAL OF CHEMICAL AND ENGINEERING DATA
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Figure 2. Disproportionation of dimethylbenzenes
VOL 6, N o . 1, J A N U A R Y 1961
3
TEMPERATURE.
TEMPERATURE, QF. 621 801
OF.
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PENTAMETHYLBENZENE
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TETRAMETHYLBENZENES
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1
0 1000
300
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1000
Figure 5. Disproportionation of pentamethylbenzenes
I
I
f l -
I
should be equal to unity. The mole fraction of each component is further multiplied by the number of methyl groups in its structure. For methylbenzene disproportionation C C H 3 should be 1; dimethylbenzenes, 2; etc. N I and N 2 are systematically changed until the two criteria are fulfilled. A graphical method for rapid convergence is described by Smith ( 5 ) . The procedure outlined above was programmed on a Burroughs E-101 to permit convenient application of the successive approximation method. The resulting theoretical equilibrium concentrations derived from disproportionation of mono-, di-, tri-, tetra-, and pentamethylbenzenes a t 100" K. increments from 300" to 1000" K. are given in Table I on mole, weight, and liquid volume per cent bases. The liquid volume per cent data are plotted in Figures 1through 5 . An independent series of calculations of the equilibria presented in this article has been published ( 1 ) . The results of the former investigation are given in a considerably different form from those of the current study; a binomial distribution function was employed to show that statistical distribution of the methyl groups is approached as temperature increases.
HEXAMETHYLBENZENE I
90.
N7directly. Likewise, one can determine the other constituents of the equilibrium mixture. The Z N is found and
LITERATURE CITED
I
I
I
I
MMETHYLBENZENES\ I
0 300
400
500
600 700 TEMPERATURE, OK
\
I 800
TOLUENE1 900
Figure 4. Disproportionation of tetramethylbenzenes
4
1000
(1) Egan, C.J., J. CHEM.ENC.DATA 5 , 298 (1960). (2) Hastings, S.H., Nicholson, D.E., J . Phys. Chem. 61, 730 (1957). (3) Kandiner, H.J., Brinkley, S.R., Jr., Ind. E%. Chem. 42, 850 (1950). 6 5 , 803 (1943). (4) Pitzer, K.S., Scott, D.W., J . A m . Chern. SOC. (5) Smith, B.D., A.1.Ch.E.Journal5, 26 (1959).
RECEIVED for review April 11, 1960. Accepted October 6, 1960. JOURNAL OF CHEMICAL AND ENGINEERING DATA
