1YOTES
May, 1958
637
b.p. 140-146' (10 mm.) (reportedlo 143-146' (10 mm.)); solvent yielded a yellow solid which on standing open to the n * 9 ~1.5250. The reaction of methyl iodide with acetyl- atmosphere for several hours became quite powdery and acetone in methanolic sodium methoxide afforded 3-methyl- insoluble in carbon tetrachloride. 2,4-pentanedione, b.p. 77-78' (28 mm.) (reported" 77-79' (30 mm.)); n a b 1.4405. The following chelates were prepared by treating an aqueVISCOSITIES AND DENSITIES OF ous solution of a metal salt with the ammonium salt of the METHANOL-TOLUENE SOLUTIONS UP appropriate 8-diketone: bis-(2,4-pentanediono)-copper(II), micro m.p. 230' dec. (reportedl2 230' dec.); bis-(3-methyli TO THEIR NORMAL BOILING POINTS 2,4-pentanediono)-copper(II), micro m.p. dec. above 230 (reportedla no sharp m.p. or dec.); tris-(3-methyl-2,4-penBY L. w. HAMMOND, KATHERINE s. HOWARDAND tanediono)-aluminum, micro m.p. 216" (Anal. Calcd. for R. A. MCALLISTER' C1&706Al: C, 59.01; H , 7.43; Al, 7.36. Found: C, Engineering North Carolina State College, 58.85; H , 7.52; Al, 7.11); bis-(3-benzyl-2,4-pentanediono)- Department of ChemicalRaleigh, North'Carolina copper(II), micro m 203.0-203.5' (reported14 176'; Received January 2 , 1968 Anal. Calcd. for c 2 4 # 2 6 O C u : C, 65.21; H, 5.93; Cu, 14.38. Found: C, 65.06; H, 5.71; Cu, 14.30); tris-(3In a study of the effect of physical properties on benzyl-2,4-pentanediono)-aluminum, micro m.p. 164.5165' (Anal. Calcd. for C&3906A1: C, 72.71; H, 6.61; the efficiency of distillation for the binary methAl, 4.54. Found: C, 72.43; H , 6.61; AI, 4.61); bis-(ethyl anol-toluene system, the density, viscosity, molecuacetoacetat0)-copper(II), micro m.p. 195-196' dec. (re- lar diffusivity and surface tension were needed at ported16 192-193'). the boiling temperatures. The viscosity and denTris-(2,4-pentanediono)-aluminum, micro m.p. 195' sity of methanol-toluene mixtures a t 20" have been (reportedlB 193-194') and tris-(ethyl acetoacetat0)-aluminum, micro m.p. 79-81' (reported" 76") were prepared reported previously,2J but it would not be possible from the appropriate 8-diketone and aluminum isopropoxide to predict the boiling point values from these by the general method of Weygand and Forkel.17 Tetrakis-(2,4-pentanediono)-zirconium(IV) was prepared limited data, and therefore the present investigaby the method of Hevesy and Logstrup,lS micro m.p. 189- tion was undertaken. 190' (reported 193-194' ) . Bis- [tris-(2,4-pentanediono)Experimental titanium( IV)] hexachlorotitanate( IV) was prepared by the Materials.-The methanol used was Baker Analyzed Remethod of Young and Weyden.lg agent Grade. It was dried by heating just below the boilBis-( 2,4-pentanediono)-diisopropoxytitaniurn(IV) ."-A ing point for 48 hr. over CaSOd which had been regenerated solution of 28.4 g. (0.1 mole) of titanium isopropoxide and by drying at 200" for 5 hr. The methanol was then slowly 20 g. (0.2 mole) of acetylacetone in 150 ml. of benzene was distilled into a dry distilling receiver which was vented heated under reflux for one hour. The isopropyl alcohol to the atmosphere through a CaSOa gas drying unit. The liberated in the reaction was removed by azeotropic dis- first and last fractions (each approximately l/10 of the origitillation with benzene. The yield of isopropyl alcohol as nal volume) of methanol were discarded and the middle indicated by the refractive index of the distillate was 9.8 g. cut of the distillate was retained. The methanol thus (81.5%). The remainder of the benzene was removed dried had a density a t 20' of 0.7913 g./ml., which was in under vacuum and the residue was fractionated to yield good agreement with accepted value^.^ 25.75 g. (71%) of an orange-red oil, b.p. 130' (0.15 mm.); The toluene used was Baker Analyzed Reagent Grade, n a 71.5437. ~ On standing for several hours the oil turned a Lot. No. 1361. This lot was selected after careful indeep shade of red. vestigation of the physical roperties of many samples from Anal. Calcd. for c~&&Ti: c, 52.75; H, 7.75; Ti, different manufacturers. Jeveral samples were purified by 13.15. Found: C, 52.67:. H,7.82: distillation and/or dried using a variety of desiccants, and . . Ti,. 13.41. Bis-(ethyl acetoacetato)-diisopropoxytitanium(IV).20- their properties were examined. No sample of higher puA solution of 28.4 g. (0.1 mole) of titanium isopropoxide and rity was obtained than this particular lot, which had a stated 26 g. (0.2 mole) of ethyl acetoacetate in 150 ml. of benzene boiling range of 0.lo, an average n Z 5of~1.49405, and a denwas heated under reflux for two hours. Azeotropic dis- sity a t 20' of 0.8669 g./ml.s The effect of trace water contillation afforded 11.1 g. (92.5%) of isopropyl alcohol. tamination of the toluene and methanol-toluene mixtures is The remainder of the benzene was removed by distillation described below. Apparatus and Procedure.-The apparatus and proceand the residue was fractionated under reduced pressure. The yield was 31.0 g. (74%) of a yellow oil, b.p. 133' (0.3 dure for the precision density measurements have been reported previously.0 For mixtures having a methanol conmm.): n a 71.5181. ~ Anal. Calcd. for C18H3208Ti:C, 50.94; H, 7.60; Ti, tent of 25 mole % or less, i t was extremely difficult to fill the pycnometer without having liquid droplets form on the 11.29. Found: C, 51.03; H, 7.76; Ti, 11.10. capillary arms above the main liquid body. Recleaning the Bis-(3-benzyl-2,4-pentanediono)-diisopropoxytitanium- pycnometer, redistilling the solvents, filtering the solutions, (IV).-A solution of 6.00 g. (0.0315 mole) of 3-benzylacetyl- and overnight soaking of the pycnometer in the solutions acetone and 4.48 g. (0.0158 mole) of titanium isopropoxide before the determination, all seemed to be of no avail in in 50 ml. of carbon tetrachloride was heated under reflux for combatting the problem. As many as a dozen separate three hours. Azeotropic distillation afforded 1.67 g. (88%) fillings of the pycnometer, on separate days, were often reof isopropyl alcohol. The residue was subjected to infrared quired before a successful determination could be made. analysis without further treatment. Evaporation of the No such trouble was encountered for pure methanol, for pure toluene, or for methanol compositions greater than 25 (10) J. M. Sprague, L. J. Beckham and H. Adkins, ibid., 56, 2665 mole %.
.
(1934). (11) J. T. Adams and C. R. Hauser, ibid., 67, 284 (1945). (12) L. Claisen and E. F. Ehrhardt, Bsr., 22, 1009 (1889). (13) C. R. Hauser and J. T. Adams, J . A m . Chem. Soc., 6 6 , 345 (1944). (14) G. T. Morgan and C. J. A. Taylor, J . Cham. Soc., 127, 797 (1925). (15) W. Wislicenus, E m . , 31, 3154 (1898'. (16) A. Combes, Compt. rend., 108, 406 (1889). (17) C. Weygand and H. Forkel, Ber., 59B,2243 (1926). (18) G. von Hevesy and M . Logstrup, ibid., 59B, 1890 (1926). (19) R. C. Young and A. J. V. Weyden, "Inorganic Syntheses," W. C. Fernelius, Editor, Vol. 11, McGraw-Hill Book Co., New York, N. Y.,1946, p. 119. (20) A. Yamamoto and S. Kambara, J . A m . Chem. SOC.,79, 4344 (1957).
(1) Department of Chemical Engineering, Lamar State College of Technology, Beaumont, Texas. (2) B. Ya. Teltel'baum, T . H . Gormaloua and S. G. Ganelina, Zhur. Obshchel Khim., 83,pt. 20, 1422 (1950). (3) N. Madscn, Science, 114, 300 (1951). (4) J. Timmermans, "Physico-Chemical Constanta of Pure Organic Compounds," Elsevier Publishing Co., Ino., New York, N. Y., 1950, p. 304. (5) (a) Timmcrmans (ref. 4, p. 152) gives ~ * O D of 1.49405 and a density a t 20' of 0.8669 g./ml. for toluene; (b) R. R. Dreisbach, "Physical Properties of Chemical Compounds," Am. Chem. Soc., Washington, D.C., 1955,p. 12, gives n * b of 1.49414 and a density a t 20' of 0.8669 g./ml. ( 6 ) K. T. Thomas and R. A. McAllister, A.I.Ch.E. Journal, 3, 161 (1957).
NOTES
638
Kinematic viscosities of the methanol-toluene solutions were measured in a Cannon-Ubbelohde viscometer. The technique of operation and the details of the calibrations have been reported p r e v i ~ u s l y . ~ Refractive index measurements were made using a Bausch and Lomb precision refractometer capable of giving results accurate to h0.00003 refractive index unit.
Results The refractive index-composition values are in Table I. From these data a curve was drawn, from which was read the concentrations of samples drawn from the efflux bulb of the Cannon-Ubbelohde viscometer. Such analyses had an accuracy of h O . 1 mole yo methanol over the whole concentration range. The results in the high concentration range (>50 mole % methanol) are even more precise since the refractive index-composition curve has a greater slope in this range. TABLE I REFRACTIVE INDEX OF METHANOL-TOLUENE SOLUTIONS Methanol, inole %
n2hD
0.00 4.57 10.10 21.91 30.39 40.47 47.06 60.22 60.86 81.73 90.08 95.20 100.00
1.49405 1.49097 1.48710 1.47776 1.47002 1.45941 1.45116 1.43250 1.41523 1.38827 1.36397 1.34602 off scale
Table I1 gives the kinematic-viscosity values for methanol-toluene solutions. The results show that the viscosity a t a given temperature has first a minimum and then a maximum when plotted against mole fraction of methanol. The density of methanol-toluene mixtures is given in Table 111. T o investigate the error introduced by trace water contamination, samples were handled as if they were being loaded into a pycnometer, but instead they were analyzed by a KarlFischer titration.8 Addition of 0.01 wt. % water changed the density not more than $0.00003 g./ml. In no case was there more than 0.03 wt. % water in the samples reported here. The effect on the reported density values was less than 0.0001 g./ml. A few runs indicated that the trace amounts of water present did not change the viscosity, within the reported accuracy. The density, kinematic viscosity and absolute viscosity of methanol-toluene solutions a t their normal boiling points were extrapolated, and these data are presented in Table IV. The procedure for measuring the density6 is capable of giving density values accurate to *0.00002 g./ml. and every effort was made to uphold this precision. The data of Table 111, however, are listed to only four significant figures for two reasons. (1) The difficulty in obtaining a good measurement (7) Katherine S. Howard and R. A. MoAllister, ibid., in ~ x e s s . (8)J. Mitchell, Jr., and D. M. Smith, "Application of the Karl Fischer Reagent to Quantitative Analyses Involving water," Interscience Publ., Inc., New York, N. Y.,1948.
Vol. 62
below 25 mole % methanol made these data questionable in the fifth decimal place, and (2) different bottles of the same lot (Baker Analyzed Lot No. 1361) of toluene showed differences in the fifth decimal place for both density and refractive index. It is assumed that these differences resulted from unknown amounts of dissolved water and possibly dissolved gases. TABLE I1 KINEMATIC VISCOSITY OF LIQUIDMETHANOL-TOLUENE SOLUTIONS Methanol, mole %
(Centistoke) Y
20.00' 0.0 7.1 14.0 20.9 20.1 35.4 47.9 50.6 60.95 73.6 77.8 83.7 90.1 93.8 100.0 37 80' 0.0 3.1 9.1 13.6 19.2 29.1 46.3 60.6 68.8 71.15 77.8, 84.0 90.45 100.0
0.6786 .6672 .6683 .6738 .6849 .6914 .7134 .7176 .7338 .7486 ,7528 ,7542 .7524 .7471 .7373
I
60.11' 0.0 2.6 8.8 19.6 26.3 33.3 41.4 52.9 59.9 68.4 76.6 80.9 89.75 100.0
'
0.5621 ,5533 .5480 .5482 .5487 ,5542 ,5700 .5829 .5904 .5931 .5959 ,5982 .5977 .5908 0.4502 .4530 .4454 .4410 ,4404 ,4426 ,4455 .4499 ,4537 .4575 ,4601 ,4610 ,4621 .4590
Methanol, mole %
(centistoke)
25.00' 0.0 1.9 8.2 11.0 18.9 28.7 38.7 49.8 61.1 73.4 82.2 83.3 90.1 95.0 100.0
0.6414 ,6348 .6284 .6275 .6314 .6410 .6543 .6703 ,6852 ,7009 .7040 ,7049 .7025 ,6991 ,6914
50.05' 0.0 2.8 8.9 15.0 19.8 25.8 34.0 42.5 60.3 68.7 79.4 89.8 100.0
0.5009 .4938 .4876 .4852 .4845 .4865 ,4887 ,4938 .5056 .5103 .5152 .5163 .5138
70.20' 0.0 4.65 0.75
0.4238 ,4125 ,4086
Y
t
80.35' 0.0 4.92
0.3922 ,3839
The procedure for measuring the viscosity resulted in viscosity data accurate to k0.2yo0. The viscosity values given in Table I V are reported to three significant figures only bWause the boiling temperatures are no more accurate than 0.1".
b
NOTES
May, 1958 TABLE I11 DENSITYOF LIQUIDMETHANOL-TOLUENE SOLUTIONS Methanol, mole Yo
20.00" 0.00 24.82 49.55 76.13 100.00
(dml.)
Methanol, mole %
(?All.)
0.8669 .8589 .8470 .8267 .7913
50.05" 0.00 24.22 49.37 76.38 100.00
0.8389 .8302 ,8181 * 7972 .7630
25.00" 0.00 23.16 50.29 76.07 100.00
0.8622 ,8548 .8420 ,8220 .7865
37.80" 0.00 10.62 24.64 37.53 49.84 65.53 76.13 87.34 95.47 100.00
0.8503 .8469 .8422 ,8364 ,8299 .8193 .8096 ,7962 .7834 .7746
60.11" 0.00 25.03 50.69 75.73 100.00
0.8291 .8205 .8077 ,7878 ,7531
70.20' 0.00 10.04
0.8193 .8163
80.35" 0.00 5.95
0.8097 .8078
90.54" 0.00
0. 7995
National Science Foundation, and the support of this organization is also gratefully acknowledged. '
THE KINETIC SYSTEM CONSISTING OF TWO PAIRS OF COMPETITIVE CONSECUTIVE SECOND-ORDER REACTIONS BY CHAO-TUNG CHEN Department of Chemistry, Northwestern Universzty, Evanston, I l l , Received March 6 , 1968
The kinetic system consisting of two competitive and consecutive irreversible second-order reactions has been studied by several authors since 1931. The results of these studies have been summarized by Frost and Pearson.' Recently McMillan2 has developed a method of obtaining the rate constant ratio as an implicit function of any two simultaneous concentrations. Despite the rather simple appearance of the system, its complexity may be appreciated from the references cited. The present report deals with a more complicated system consisting of two pairs of competitive and consecutive second-order reactions. This has not been studied before. kl
B+B+C+F k2
TABLE IV DENSITY A N D VISCOSITY OF LIQUIDMETHANOL-TOLUENE SOLUTIONS AT THEIRNORMAL BOILINGPOINTS Methanol, mole %
B.p.5
("C.)
639
A+C+D+G A+B+E+G ka A + E + D + F
Y
(P./pml.)
(05.1
( O b
0 110.7 0.7801 0.329 0.257 5 83.5 ,8041 .376 .302 10 74.0 ,8155 ,396 ,323 .409 69.2 ,8149 15 .333 .413 20 67.6 ,8147 .336 .415 66.7 ,8140 25 ,338 30 66.2 .8126 .417 ,339 35 ,419 65.8 .8109 ,340 40 ,421 65.5 .8088 ,341 45 .424 65.2 ,8061 .342 50 .427 65.0 .8035 ,343 55 ,431 64.7 ,8001 ,345 60 G4.5 .7966 .435 ,347 65 64.3 ,7928 .438 .347 70 64.1 ,7891 .440 .347 .442 75 C3.9 .7853 .347 .444 80 63.8 .7799 .346 .445 85 63.7 .7734 .344 90 63.5 .7681 ,446 .343 .444 95 63.7 .7595 .337 100 ,438 64.5 .7488 .328 a Boiling points of the solutiona from the data of M. Benedict, C. L. Johnson, E. Solomon and L. C. Rubin, Trans. Am. Inst. Chem. Engrs., 41, 3171 (1945). Boiling points of the pure components from Timmermans (ref. 4) and Dreisbach (ref. 5).
Acknowledgments.-This work was initiated by the American Institute of Chemical Engineers, Research Project No. 1, "Tray Efficiencies in Distillation Columns." The authors acknowledpe the support and encouragement of the A. I.°Ch.E. Research Committee during this investigation* The work was completed with funds granted by the
(1)
k3
The scheme 1 represents many systems where two similar but different groups in the same molecule undergo reactions. The successive and competitive saponification of unsymmetrical diesters is an example. The technique for solving the present problem involves the use of a parameter in terms of which the concentrations A , B, C , etc., are expressed, and a graphical method to obtain the rate constant ratios. It should be pointed out that the treatment does not employ any approximation and that the initial conditions are only that A = A,, B = BO,and C, etc. = 0. However, it requires the concentrations of products and reactants, for instance, B, C and E. Fortunately, it is now often possible to determine the various conceatrations simultaneously by the current advanced analytical methods. With 5 = A dt as in the French method3 for the one-pair system, the rate equations are dA/dx dB/dx dC/dx dD/dx dE/& dF/dx dG/dx
where k = ICl
+ ICg.
-kB -k,C -krE -kB klB -kzC k2C +&E = kaB -kaE = klB f k 4 E = kzC ksB = = = =
(2)
+
Equation 2-2 is readily inte-
A. A. Frost and R. G. Pearson. "Kinetics and Mechanism." John Wilev and Sons. New York. N. Y . . 1953. DD. 165-171. ( 2 ) W. G. McMillan, J . A m . Chem. Soc., 79,4838 (1957). (3) D. French, tbzd., 72, 4806 (1950). (1)
