INDUSTRIAL AND ENGINEERING CHEMISTRY
2202
Rock, L., in R. Memler, “Science of Rubber,” Reinhold Puhlishing Corp., New York, p. 498,1943. (14) Hock, L.. and Schmidt, H., Rubber Chem. and Technol., 7 , 462 (13)
(1934).
(15) Naunton, W. J. S., and Waring, J . R.
S.,Trans. Inst. Rubber
Ind., 14, 340 (1939). (16) Parkinson, D., “Advances in Colloid Science,’’Vol. 11, p 406,
New York, Interscience Publishers, 1946. (17) Rehner, J., J . Applied Phys., 14, 638 (1943); Gehman, S. D.. IND. ENG.CHEY.,36,715 (1944). and Morrison, R. E., R u b b e r Age, 61, 59 (19471. (18) Rostler, F. S., (19) Scott, J. R., Trans.lnst. RubberInd., 5 , 95 (1929). (20) Shepard, K. A , , Street, J. N., and Park, C. R., in Davis and Blake’s “Cheniistr3- and Technology of Rubber.” A.C.S. >lonograph 7 4 , pp. 40S~-9,Reinhold Pub. Corp., 1937.
Critical Co 0sitv
e
Vol. 40, No. 11
Smallwood, H. M.,J . Applied Phys., 15, 758 (1944). Spear, E. B., Xational Symposium on Colloid Chcmistiy, Vol. I Colloid Symposium Monograph, p. 321, Madison, Wis.. University Co-operative Go., 1923. (23) Starnherger, P., Rubber Chem. and Technol., 5, 146 (1932). (24) Thornhill, F. S., and Smith, W. R., IND.E N G CHEN., . 3 4 , 218 (21) (22)
(1942). (25)
Tronson, J. L., and Carpenter, A. W., Am. Soc. Testing Materi-
aTs, Proc., 31,P a r t 11,908 (1931). (26) Twiss, D. F., J . Soc. Chem. Ind., 44, 107T (1925). (27) Witco Chemical Go., “Witcarb R-Rubber Reinforcing Pigment.
Bull. 44-2 and 45-2.
RECEIVED .J!ine 10, 1947. Presented before the Division of Rubber Chemistry of the ~ M E R I C A XC H E - ~ I I C YocImi-, AL Cleveland, Ohio, i l a y 1947.
ARNOLD BOAS1, b’nieersity
of Cinchnuit, Cirtcinrmti, Ohio
d
T h e law of corresponding states is applied to some equations relating various physical properties. Reduced equations are obtained and, thereby, a means of estimating critical constants. Viscosity and density are considered here, although many others hare been tried in this study. Values for the constants are presented and examples are given to show how this method may be applied.
HERE is a definite need for accurate estimates of the critical These values find practical uses in various plot,s, in which reduced variables are resorted to as a means of obtaining a correlation. I n order to avoid an experimental determination of the critical constants (which is impossible in some cases, such as the higher members of the paraffin aeries which exhibit appreciable decomposition in the critical region), this study has been undertaken. A t the present time there are some relations that, are linown to exist between critical constants and other physical properties. Guldherg (4)showed that the ratio of the critical temperature to the boiling point (both expressed as absolute temperatures) is fairly constant, with a value equal to approximately 1.5, The critical temperature can also be estimated by Watson’s ( 8 ) method with an accuracy of * 2%. However, this method requires a knowledge of the liquid density at the boiling point. In 1942, Meissner and Redding ( 5 ) presented a number of equations for the prediction of critical constants; for critical temperatures, a knowledge of bhe boiling point was required, the critical volume is given as a function of Sugden’sparachor, and the critical pressure is related to both critical temperature and critical volume. . constants.
DEKSITY
In 1915, Albertosi (1) introduced the following equation (for rionassociating liquids) relating density and temperature: (4513 = A - BT (1) where d is the density of the liquid, in grams per ml., T the temK.), and A and B are characteristic constants. If perature the folloiving substitutions are made in Equation 1, a reduced form of t,he Albertosi equation results: ( O
(d)6?3
=
(dc)6/3 (d,)6/3
T = TOT, where the subscripts c and r refer to critical and reduced values, respectively. The reduced equation is 1 Present address, Hydrocarbon Research, Inc., 115 Broadway, New York 6, N . Y.
According to the law of corresponding states, the constants -4/(dc’5’ 3 and BT,/(d,)6/3 should be universal, for the variables involved are reduced and, hence, independent of the wbstance. Let us designate the constants by K’ and IC”, rcspectivelj. It nil1 be noted that although the individual constants are functions of the critical density, the ratio of the two-Le., K“/K‘is independent of doand is equal to BT,/A. Since critical density data are not too reliable, this iatio was considered and the constant evaluated for 25 liquids. Table I lists the data used and the values of the constant. The characteristic constants il and B n-ere determined by least squares. The constant was found to be 0.6979 + lVo error. Table I1 shows the data for the individual constants I(’ and K”. The most reliable data were used and 18 of thc liquidq were considered. The values for IC’ and IC” were found to be. K’ = 9.448 * 2.5% error K ” = 6.597 * 37, error Recently, an article concerned with the physical properties of fluorocarbons appeared in the literature ( 3 ) . The following values of density vs. temperature were given for perfluoro-n-heptane‘ TemDerature. 0.0
‘ c.
Density, Grams/2rL 1.7740 1.7019 1.6031
27.0 63.2
TABLE I. DATAUSEDA N D Substance Pentane Isopentane Hexane Heptane Octane Decane Methyl formate Ethyl formate Ethyl acetate Ethyl ropionate Ethyl {utyrate Benzene Cyclohexane Ethyl benzene Toluene Chlorobenzene Iodobenzene Rromobensene Dichloroethane Ethylene chloride Chluroforin
Carbon tetrachloride
L t h y l hromide Ethyl iodxde
Pentachloroethane
T H E VALCE O F THE C O S S T A N T
A
B
TO
K“IK’
0,80998 0.79321 0.82796 0.85103 0.86694 0,889R3 1,65621 1.47233 1.38931 1.33046 1,27598 1,27962 1.04409 1.18079 1.20080 1.75018 3,85263 2.81‘390 2.14986 2.27923 3.13191 3.46399 3.16691 4,71826 3.43072
0,001200 0.001167 0,001120 0.001093 0.001G64 0.001016 0.002383 0,002040 0.001874 0.001728 0.001600 0.001614 0.001314 0.001339 0.001407 0.001933 0.003796 0.002931 0.002866 0.002808 0.004058 0.004395 0.004387 0.005837 0.003599
470.4 400.9 208.0 540.0
0.69691 0.67809 0.68719 0.69354 0.69883 0.69218 0.70100 0.704~56 0.rO586 0.70927 0,70970 0.70848 0.29621 0.,0141 0.69577 0.69R46 0.71060 0.70136 0.69748 0.69189
569.4
603.6 487.2 508.5 523.3
546.1 566.0
561.7 553.2 019.0 508.8 232.4 (21.2 670.2 023.2 X1.6 636.2 536.3 209.2 554.2 646.2
0.69475 0.70582
0.70538 0,68559 0.6ii’OO
November 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLE 11. DATAFOR
THE
IXDIVIDUAL CONSTANTS K‘ dc 0,2323 0.2343 0.2344 0.2341 0.2327 0.3489 0.3232 0.3077 0,3045 0,2735 0.2862 0,3654 0.5814 0,4853 0.4190 0.4190 0.6070 0.5576
Substance Pentane Isopentane Hexane Heptane Octane Methyl formate Ethyl formate Ethyl acetate Benzene Cyclohexane Toluene Chlorobenzene Iodobenzene Bromobenzene Dicbloroethane Ethylene chloride Chloroform Carbon tetrachloride
AXD
TABLE111. COMPARISONBETWEEN CALCULATED AKD REPORTED CRITICALDENSITIES
K“
K‘
K”
9.2270 8.9078 9.2912 9.5707 9.8476 9.5779 9.6730 9.9067 9.2847 9.0601 9.6613 9.3713 9.5127 9.4091 9.1632 9.7146 9.7156 9.1701
6.4304 6.0403 6.3848 6.6377 6.8818 6.7141 6.8152 6.9927 6.5780 6.3077 6.7220 6.5455 6.7597 6,5992 6.3911 6.7214 6.7499 6.4724
,
The characteristic constants A and B were determined by least squares and were found t o be 4.3486 and 0.006402, respectively. The critical temperature can be estimated by using the relation
T,
K “A K ’B
(3)
I s K ” / K ’ was found t o be 0.6979, a direct substitution in Equation 3 leads t o
The reported value is 475.8 K. and this compares favorably with the calculated value. The relation K’ = A/(d,)6/3 was used t o calculate the critical density and this was found to be 0.629 gram per ml. Although no value was given for perfluoron-heptane, there was a value for perfluoro-n-butane. Since, in the paraffin hydrocarbon series, the critical densities are of the eame magnitude and do not differ very much, it will be assumed that the same generalization applies to the fluorocarbon series. The reported value for perfluoro-n-butane was given as 0.63 gram per ml. ( 2 ) . The Albertosi equation is valid within the range used, because the temperatures used here are well below the critical temperature. VISCOSITY
In 1938, Souders (6) presented the following equation, relating viscosity and density: log log (a) = md
- 2.9
(4)
with q in millipoises and d in grams per ml. Furthermore, it was shown t h a t the constant m was directly related t o t h e structure of the liquid in question. Denoting I as a viscosity-constitutional constant and M as the molecular weight, Souders found that m = I / M . The reduced form of the Souders’ equation appears as: log q, = (emdod7)(e-2.@) - log vc
(6)
Since this equation involves reduced variables and the term “log v i ’ is substantially constant for the nonpolar liquids studied ( 7 ) , the value of md, should be a universal constant. The value of m varies very slightly with temperature and a temperature of 20 C. was chosen arbitrarily. The values of m were taken from Souders’ (6) original article and the constant md, was determined. Table I11 shows the comparison between calculated and reported critical densities. The constant md, was found to be 0.9280 * 1.5% error. If viscosity versus density data were not on hand, the value of m could be calculated from the molecular weight and structure of
2203
Substance Pentane Hexane Heptane Octane Isopentane Benzene Toluene o-Xylene m-Xylene Methyl alcohol Methyl formate Ethyl formate Methyl acetate Ethyl acetate Nonane Decane Undecane Dodecane Iodobeneene Bromobenzene Chlorobenzene Ethyl ether Propyl formate Propyl acetate Methyl propionate Ethyl propionate
dc Reported
dc Calculated 0.2358 0.2360 0.2360 0.2357 0.2364 0.2903 0.2884 0,2840 0.2866 0,2635 0.3433 0.3192 0.3252 0.3078 0,2355 0,2353 0,2349 0,2347 0.8683 0.4744 0,3596 0.2680 0.3053 0.2965 0.3124 0.2991
the liquid. However, certain disadvantages will then become apparent. I n the case of isomers, this method would fail since the viscosity-constitutional constants and molecular weights are identical; therefore, the calculated critical density would be t h e same for both liquids. No provision is made to differentiate between ortho and para derivatives in determining the viscosityconstitutional constant and since the molecular weights are the same, it would seem t h a t their critical densities should be t h e same. Therefore, the observed values of m are recommended for the estimation of the critical density rather than the value calculated from m = I / M . Let us now consider a specific example of estimating the critical density of methyl formate. Assume t h a t the structure and molecular weight are known, but t h a t there are no other physical properties available. I can be calculated as follows (6): CHz 2H COO HOCR
55.6 5.4 90
loa
161.0 Souders in a personal communication stated t h a t the printed value of 16 for the “structural constant” for HOCR in aldehydes and formates is a typographical error and should have been 10.
Since the molecular weight of methyl formate is 60.05, the value of m = I / M = 161.0/60.05 = 2.681. The constant md, (0.9280) will now be used to evaluate d,; the critical density is found t o be 0.3461. The observed value is 0.3489. Other physical properties such as refractive index, vapor pressure, dielectric constant, etc., were tried but the correlation was not so good as the examples cited here. Therefore, viscosity and density are recommended as a means of estimating critical densities and temperatures. LITERATURE CITED
(1) Albertosi, Alfred, J . chim. phys., 13,390 (1915). (2) Fowler, R. D., Hamilton, J. M., Kasper, J. S., Weber, C. E., Burford, W. B., 111,and Anderson, H. C., IND.EXG.CHEM.,39, 375 (1947).
Grosse, A. V., and Cady, G. H., Ibid., 39, 367 (1947). (4) Guldberg, C. hf., 2.physiic. Chem., 5 , 374 (1890). ( 5 ) Meissner, H. P., and Redding, E. M., IND. ENG.CHEM.,34, 521 (3)
(1942).
(6) Souders, M., J r . , J. Am. Chem. SOC.,60, 154 (1938) (7) Trautz, M., Ann.Physik., 11, 190 (1931).
ENG.CHEM., 23, 361 (1931). (8) Watson, K. M., IND.
RECEIVBD August 16, 1947. Bbstracted from a thesis presented in July 1947 t o the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of master of science. The work was performed under the supervision of E. F. Farnau of the chemical engineering faculty.
