Representation of Equilibrium Constant Data EDWARD G. SCHEIBEL AND FRANK J. JENNY Hydrocarbon Research. Inc., New York,N . Y .
construct the scales over the complete range of temperatures and pressures usually encountered in design calculations. Recently Miller and Barley (4) presented a nomograph based on the principle that the liquid fugacity is a function of temperature alone and the vapor fugacity is a function of pressure alone. This latter effect does not hold a t high pressures since temperature then becomes an appreciable factor. Thus their nomograph was also somewhat limited in the range over which accurate results could be obtained. Also the construction of the nomograph was such that two separate operations were required to obtain the K value of any particular compound.
A nomograph is presented which gives the equilibrium constant data for hydrocarbon mixtures. It covers a wider range of temperatures and pressures with much greater accuracy than previous ones. The construction of the nomograph is completely empirical, with the calibration of the temperature scale based on the liquid fugacity of a reference substance and the pressure scale based on the vapor fugacity of the reference substance. The nomograph is useful in the calculation of bubble points, dew points, and equilibrium flashes on hydrocarbon mixtures in that a single setting gives the value of the equilibrium constants for all the components.
CONSTRUCTION OF NOMOGRAPH
N AN IDEAL multicomponent mixture the partial pressure of any component is proportional to its concentration. This ie known as Raoult’s law and, when combined with Dalton’s and Avogadro’s laws, can be expressed in the familiar form ( 6 , 8 ) :
Figure 1 is based on the principles used by Miller and Barley and applied to the type of nomograph presented by Othmer to combine both the convenience and the precision of application. The temperature scale is baaed on the logarithm of the fugacity of liquid pentane. The pressure scale is based on the logarithm of the fugacity of the vapor of pentane. For this calibration a curve passing approximately through the center of the range of fugacity variation waa chosen. If the vapor fugacity were independent of temperature, all the component scales in the nomograph would be straight lines parallel to the pressure and temperature scales and logarithmically calibrated. The major deviations are compensated by the curved lines which result from the empirical construction of various compound scales. All ot these scales were found by the intersection of lines connecting the various temperature and pressure conditions which give the particular K value to be located. The scales of methane through octane were based on the K values reported by Sherwood (8) and by Robinson and Gilliland (6). The scales of decane and tetradecane were based on values given by Brown (I), and the remaining scales were located by interpolation and extrapolation of the data of Brown (I). The gap between the scales of octane and nonane corresponds to the change in the source of the data. However, the values for heptane and lighter components given by Brown are for all practical purposes in sufficient agreement with those of Sherwood and Robinson and Gilliland.
y = KX
where y = mole fraction of component in vapor z = mole fraction of component in liquid K = equilibrium constant The value of K is a function of the temperature and pressure, and also varies with the different components. I n ideal solutions it can be readily shown to be equal to the ratio of the vapor pressure of the pure liquid to the total pressure on the system. A more general expression is the ratio of the fug%cityof the liquid to the fugacity of the vapor. This takes into account the deviations of the vapor and liquid from ideality. The K values are usually represented by a set of graphs showing either the effect of temperature and pressure on the equilibrium constant of a given compound or the effect of temperature on the equilibrium constants for the different compounds a t a given pressure, The first set requires the use of all the necessary charts to carry out the usual bubble point, dew point, and equilibrium flssh calculations. The second set is generally more convenient to use but is difficult t o interpolate a t pressures not given by the charts. Several attempts have been made to represent all the data on a single plot. Shiah ( 9 ) developed a chart baaed on the assumption that the relation, between the temperatures a t which any two compounds have the same K value is independent of pressure. This is not strictly true. However, Shiah was able to equalize the errors by choosing as the reference substance a compound occurring at the center of the series of compounds covered by thechart, namely, +pentane. A better chart was developed by Othmer ( 5 )who found that the logarithm of the K values of any compound a t a given pressure waa a linear function when plotted against the logarithm of the vapor pressure of water at the same temperature. A more convenient and precise chart was also developed by Othmer, based on the fact that a t a constant K value the logarithm of the pressure was a linear function of the logarithm of the vapor pressure of water a t the same temperature. The nomograph was limited by the fact that deviations occurred which made it inadvisable to
USE OF THE NOMOGRAPH
A line connecting the given temperature and pressure intersects all the component scales at the values of the respective equilibrium constants. Over the greatest range of conditions the nomograph gives values which agree with published data with an accuracy of about 2%. This is within the reliability of the basic data. However, a t pressures greater than 300 and less than 10 pounds per square inch, the deviation of the values given by the nomograph from the published data increases to about 10% or more at certain temperatures. At high pressures the K values for the different components have been found to vary with the composition of the mixture. This variation is greatest as the critical point of the mixture is approached. A t the critical point the K values of all components 80
January, 1945
INDUSTRIAL A N D ENGINEERING CHEMISTRY
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@oo : 90
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4 70 1
do
1
60 ‘j
IO
1
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Fbure 1. Nomograph for Equilibrium Constants of Hydrocarbon6
81
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INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
are unity. Considerable data on this subject have been presented by Sage and Lacey (7), and they found .that K varies with the molecular weight and chemical nature of the other components present. Brown and Souders (8) also observed an appreciable deviation of K values at low concentrations of the particular component in the liquid. The limitations of the calculated K values are fully discussed by Dodge (3). For temperatures below 300’ F. and for pressures between 10 and 300 pounds per square inch absolute, Figure 1 gives results which agree exceptionally well with the calculated K values. Outside this r d g e , the K values obtained from the nomograph should be checked against actual experimental data in line with the limitations discussed in the preceding paragraph. Thus Figure 1 can be used over the range of conditions usually encountered in engineering design to give results as reliable aa the equilibrium constant data upon which it is bmed.
Vd. 37, No. 1
ACKNOWLEDGM ENT
The authors wish to thank Hydrocarbon Research, Inc., for permiaeion to publish this work. LITERATURE CITED
Brown, G. G., Vaporisation Equilibrium Constant Charts ( a h reproduced in following reference). Brown, G. G., and Souders, M.,, in “Science of Petroleum”, New York, Oxford Univ. Press,1938. Dodge, B. F., “Chemical Engineering Thermodynamics”, New York, McGraw-Hill Book Co., 194.4. Miller, C. O., and Barley, R. C., IND.ENQ.CHIM., 36, io18 (1944).
Othmer, D. F., Zbid., 36,669 (1944). Robinson, C. S., and Qilliland, E. R., “Elements of Fractional Distillation”, 3rd ed., New York, McGraw-Hill Book Co., 1939. Sage,B. H., and Lacey, W. H., IND.ENQ.Cnm., 1934-44.
Sherwood, T. K., “Absorption and Extraction”, New York. McGraw-Hill Book Co., 1937. Shiah, C. D., Refiner Natural Gasoline Mfr., 21, 132 (1942).
NITROCELLULOSE LACQUERS Factors Affecting Amount of Nonvolatiles at Sprayable Viscosity’ William Koch, N. C. Phillips, and Rufus Wint HERCULES POWDER COMPANY, WILMXNGTON, DEL.
N
ITROCELLULOSE lacquers of increased nonvolatile content at spraying viscosity have an economic appeal because they offer real promise as a means of reducing finishing costs, through a saving in solvent, and a reduction in the number of finishing coats required. Several factors have been recognized as having an influence on the nonvolatile content of nitrocellulose lacquers: ( a ) Since the n i t r o c e l l u l o s e , b e c a u s e of i t s highly polymeric nature, is the principal viscosity-contributing ingredient in a lacquer, the use of lower-viscosity types makes possible higher solids at a n y selected viscosity level without otherwise altering the composition. (b) It is well known that the lower-molecularweight esters and ketones, such as ethyl acetate, acetone, and methyl ethyl ketone, have a greater capacity to disperse nitrocellulose than highermolecular-weight esters and ketones, such as butyl acetate and methyl isobutyl ketone. This is reflected in lacquers of higher nonvolatile content a t the same viscosity level (.$, 6). It is also well known that 1 The first article in this series appeared in August, 1944 (6).
Viscpsity-concentration dat? were obtained on nitrocellulose lacquers to determine how nitrocellulose viscosity, richness or activity of solvent, high-temperature application, and ratio of nitrocellulose to resin affect the percentage of nonvolatiles. Plotted data illustrate the influence of each of these factors and the relation between them. The nonvolatile content of lacquers at maximum spraying viscosity (80 centipoises) was taken from the plotted graphs. These data show that the gain in nonvolatile content contributed b y each factor is cumulative when two or more methods of increasing nonvolatiIe content are utilized at the same time. In this way high solids, compared to past practice, are possible. Recognized limitations of these methods for increasing nonvolatile content are discussed to show how each of the factors can contribute to higher nonvolatile content, without sacrificing the inherent high-quality performance of nitrocellulose lacquers. Thus it is considered safe to use nitrocellulose as low in viscosity as 30 to 35 centipoises, in a ratio of 1 :2 nitrocellulose to nonoxidizing alkyd resin with a high-solvency type solvent toobtain appro~imately29.5~~ non’volatile, or at elevated temperaturesashigh as70’Ctoobtain approximately 36.570nonvolatile in clear compositions. Pigmentation will increase these gains somewhat, depending upon the pigment employed.
the addition of a diluent, Buch 88 toluene or an aliphatic petroleum distillate, will’ increase the viscosity of a lacquer considerably as the limit of dilution is approached @, 7‘). Thus, by making me of greater proportions of the more active lowmolecular-weight nitrocellulose solvents and less diluent, and p r o p erly balancing the solvent mixture for good spraying performance, i t is possible to effect greater nonvolatile concentration at spraying viscosity. This principle will be referred to as the high-solvency type of formulation. (c) It is possible to increase the nonvolatile content of a lacquer and yet maintain a desired viscosity by raising its temperature of application (3). This technique has been termed “hot-spray” application. ( d ) Finally, i t is possible to increase nonvolatile content by increasing the proportion of resin to nitrocellulose in the lacquer composition. The purpose of this article is to illustrate how each of these factors affect nonvolatile content, and to point out how the benefits of each can be realized without eacrificing in any way the recognized high-quality performance of nitrocellulose lacquers.
