July, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
would yield 43.5% sodium pazobenzenesulfonate. The highest crude vanillin yield of 29.2% wa8 obtained under the conditions of experirhent 94. This crude vanillin consisted of over SO% of the pure compound. ACKNOWLEDGMENT
This paper represents a portion of the results obtained in the research program sponsored by the Sulphite pulp h!k~.~faCtUrers’ On Waste and conducted for the Committee by The Institute of Paper Chemistry. Acknowledgment is made
669
by the Institute for permission on the part of the Committee to publish these results. LITERATURE CITED
(1) Creighton, R. H. J., McCarthy, J. L., and Hibbert, H., J. Am. Chem. SOC.,63, 3049 (1941). (2) Freudenberg, K., Lautsch, W., and Engler, K., Ber., 73B, 167 (1940). (3) Opolonick, N.,IND.ENQ.CHEM.,27, 1045 (1935). (4) Schul~,L.,u. S. Patent 2,187,366(Jan. 16, 1940).
PRBSENTED before the Division of Cellulose Chemiatry at the 106th Meeting of the AMBRIOANCHEMICAL SOCIETY, Pittaburgh, Pa.
Correlating Vapor Pressure and Equilibrium Constant Data -
Data for equilibrium constant K, used in distillation and gas absorption design calculations, are correlated by a logarithmic plot against vapor pressure of a reference substance a t the same temperatures to give substantially straight lines. A nomogram has been prepared based on this correlation which gives K values for the hydrocarbons below nonane a t different pressures and temperatures in a form which is useful when constant K values are to be compared. A second nomogram is also Presented which is particularly useful for obtaining K values for hydrocarbons in this range a t the same temperature and pressure as would be necessary, for example, in plate-to-plate calculations of a distilling column handling hydrocarbons*
I
N PREVIOUS articles (1, 8 ) a logarithm plot of vapor or re-
DONALD F. OTHRSER Polytechnic Institute, Brooklyn, N. Y.
and Dalton’s law,
P =zp
‘(2)
which, when combined with Avogadro‘s law, give the equilibrium relation: p =
P,x = Py
(3)
where, a t a given temperature, p is the partial pressure of the hydrocarbon under discussion in the gas phase; P, is the vapor pressure of the pure component; P is the total pressure; x and y represent the mole fractions of the particular hydrocarbon in the liquid and the gas phase, respectively; and & repre-
lated pressures of a compound against the pressures exerted by a reference substance at the same temperature was used t o correlate data of vapor p r e s s u r e s , latent heats, Temperature O F heats of chemical reaction, g a s s o l u b i l i t i e s , heats of solution, adsorption equilibrium pressures, heats of adsorption, and other properties. It was also shown that the c o r r e s p o n d i n g logarithmic plot of reduced pressures a t the same reduced temperatures added somewhat t o the precision of the plot and the accuracy of data obtained therefrom. It appeared that the same plot might be a useful tool for correlating values of the so-called equilibrium constant, K , used in the design of distillation, absorption, and related systems involving particularly hydrocarbons, such as petroleum , fractions. This equilibrium constant Vopor P r e s s u r e W a t e r , mm.Hg is usually derived, as by Sherwood (4), from Raoult’s Figure 1. Equilibrium Constant K Values of Methane (Solid Lines) and of Propane (Dashed Lines) a t Constant Pressures, Plotted as Straight Lines against Vapor Pressures law p = P-x . (1) of Water and Corresponding Temperatures on Log Paper
INDUSTRIAL AND ENGINEERING CHEMISTRY
670
50fe
607
0
70
80: 100
90: 1007
w
3
E 210:
-I
1.0
2
%?+
220 230: 240250260: 270280: 290: 300:
?
310: 320:-
t?. 0.I
'
340:-
.02
360:3801 -
Vol. 36. No. 7
work; it follows that if straight lines are obtained when plotted against water, * straight lines would also be obtained if plotted against the same or a different hydrocarbon.) As an example, Figure 1 is a plot of the K values of methane and of propane against the vapor pressures of water, which is similar to the usual plot for pressures, and is made by the following steps:
3. A scale is laid off on the Y axis for the K va.lues. The unit used for this scale does not have to be the same as that used for the X scale; and a different unit would merely have the effect of moving the line up or down by a distance equal to the conversion factor, without changing it,s slope or form. 4. The tabu!ated K values for the lower six temperatures from Sherwood (6) and for 400" F. from Robinson and Gilliland ( 3 ) are plqtted on the temperature ordinates. a. Points representing the same pressure are connected by lines; and these isobars were constructed for 0.5, 1, 2, 5, 10, and 25 atmospheres. RELATION OF K TO P AND T
The lines plotted in Figure 1 would be ex-
July, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
pressure ranges where the log plot of pressures holds, fortunately these ranges cover most of the f i e l d of e n g i n e e r i n g practice. The lines of Figure 1 are drawn, using water a s a r e f e r e n c e substance; and its vapor pressure has a straight line relation with that of the individual hydrocarbons on this plot, as already indicated; hence adjustment of the values of a and b gives this equation based on the vapor pressure of the substance itself, if desired. Deviations from Equation 8 and a straight line are probably within range of precision of the values given for K for these lower hydrocarbons. I n extended ranges of temperature and pressure, the correlation may not be linear on the log plot; and the use of critical constants t o give red u c e d values of the temperatures and pressures might aid the, correlation. NOMOGRAM OF K AND TEMPERATURE
671 60 7 4
s 10-
20W
w 2 II
30'
10-
40: 10-
eo-
eo-
TO00-
uo-
30-
10040
-
80-
eoeoo-
70'
8090100-
3004001
. 000
0.5
Figure 3.
Nomogram for Determining Equilibrium Constant Kof Several Components in a Hydrocarbon Mixture
A straight line between poimtn reprenenting preaoure and temperature on outer scales given K values for each Because of the simple component on ita individual line; insert indioates m e t b d of constructing chart from plots such as Figure 1. relation between K and t e m p e r a t u r e a t constant pressure, a nomogram may be drawn to relate these 0.02 to approximately 1000 or a range of about 50,000 to 1. three guantities. An alignment chart (Figure 2) was conThus, the values for K may not be obtained with the precision if structed: the same chart is t o be used for all hydrocarbons, from methane to octane, as drawn. Several charts with lemer ranges would 1. The K scale was calibrated logarithmically on a vertical give greater precision in use. Although the intersections deterline throughout the entire range of values encountered with K increasing upwardly. mining the points on the grid showed slight variations, which 2. At a convenient distance to the right, a parallel line was were probably within the precision of the data, the nomogram drawn for the temperature scale, calibrated on a logarithmic scale may be used readily if it is desired to find all of the conditions of of pressures with temperatures corresponding to the vapor pressures of water. This was done as for the X axis of Figure 1, and compounds and pressures where K would have the same value values of temperature increased downward. a t the same temperature; a line through the K value and the 3. Several values of K for methane were taken from the tables temperature on the respective scale will cut the compound lines a t the same pressure and different temperatures. Lines were a t the appropriate pressures. drawn between the K values on the left-hand 'scale and the corresponding temperature values on the right-hand scale. These lines intersected in a common point between the two NOMOGRAM FOR MULTICOMPONENT SYSTEM scales. 4. Other values of K for methane and corresponding temperaIf it is desired to read all values of K for different components tures were taken a t another pressure, and an additional point was likewise found. a t the same temperature and pressure, another nomogram may be 5. These steps were repeated for each of the six pressures for made. Figure 3 was constructed graphically starting with the methane, and then a t all six pressures for each of the other hydrolinear relation shown in Figure 1 between log K and log P, a t carbons, whose values are tabulated by Sherwood (4). the same temperature and the additional relation; a t constant 6. Lines connected all of the points for each compound, and all of the points a t the same pressures were drawn, to give a grid temperatures there is a roughly proportional variation of tabuwork as shown. lated values of K with the absolute pressure (as indicated by Equation 5 or the gas laws). This representation gives a logical This nomogram has a disadvantage in that the calibration of presentation of the three variables, pressure, temperature, and K , the line for K runs through a very wide range-i.e., from about
672
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
since K is usually regarded as the dependent variable; in this chart i t falls on lines between those representing the other two. As a first step in constructing Figure 3, plots of K against the vapor pressure of water a t the same temperature were drawn as isobars, as indicated in Figure 1 for all of Sherwood’s data ( d ) , covering the hydrocarbons up to n-octane. (Because of the fact that in most cases the relation of K to pressure changes between 25 and 50 atmospheres, data a t 50 atmospheres were not used.) These plots were simply made as all of the data are tabulated at the samesix temperatures. The six ordinates, corresponding t o the vapor pressures of water a t the six temperatures, were drawn on identical sheets of logarithmic paper. The values of K were then plotted to give the isobars for each compound. Since values of K vary greatly, the scales on the vertical axis for the different hydrocarbons were varied to correspond. The construction of the nomogram for one hydrocarbon, such as methane, was then made as indicated in the insert sketch at the bottom of Figure 3. A vertical line, the pressure scale, was drawn at the left-hand margin of the sheet and calibrated logarithmically throughout the range of pressures from 0.5 to 25 atmospheres. These values increased upward. The temperature scale, a parallel line, was then drawn a convenient distance to the right and calibrated identically with the calibrations on the X axes qf the plots of log K us. log P, just mentioned. These temperatures increased downward. The original sheet of Figure 1 (for methane) was then superimposed on the sheet for the nomogram so that the X axis (the temperature axis) coincided with the temperature line of the nomogram. Any given value of K on Figure 1 was now a vertical line, since Figure 1 had been rotated 90” in superimposing its X axis on the temperature scale. This line of constant K intersected the isobars a t different points. Thus, in the insert sketch of Figure 3, the vertical line on the K plot intersects three isobars a t as many different temperatures. The points for the K scale for methane were then located mechanically by the following steps: 1. The intersections of the values of a constant K line with the isobars are projected to the left until they intersect the temperature scale: the resulting points indicate the temperatures corresponding, respectively, to the pressures where K has the given value. 2 . These points on the temperature scale are connected to their corresponding pressures on the pressure scales. 3. The lines so formed converge a t a point which locaqes the given or constant value of K as the first point on the K line for methane. 4. All other points on this K line for methane are similarly located’ and a line is drawn to connect them. (In locating and calibraiing the K line for each hydrocarbon, a total of only six points of pressure are used. As a mechanical aid in construction, pins are driven into the drawing board through each of these points on the pressure scale. The straight edge is always pressed against one of them in drawing the line to locate the K points. This could be done automatically with one hand to locate the one point on the line, while the other hand was moving the other end of the straight edge to the temperature point on its scale.) 5 . Similarly,the K points for each of the other hydrocarbons are found; the lines are constructed by using other plots of log K against log P, which were superimposed on the nomogram sheet with the X or temperature axis coinciding with the temperature scale of the nomogram, as done with the plot for methane. The same projections were made to give the points which defined the respective lines. 6. I n the calibration of the lines for each hydrocarbon, the intersections of the lines defining the K points tended to scatter a t the higher temperatures and pressures. These calibrations were not considered; and the lines were discontinued at values of K where the original data could not be represented on the nomogram. 7. It is possible to construct a grid work of these intermediate scales by connecting points of constant K on each of the scales with curved lines. Because of the wide range of K values, these curves are steep and make acute intersections with the individual scale, so that they add little to the usefulness of the chart.
Vol. 36, No. T
CONSTANT TEMPERATURE AND PRESSURE
As indicated above, the nomogram in the form of Figure 3 is particularly useful where the K values are desired for several components in a mixture at a given temperature and pressure. For example, in the design of a distilling column handling petroleum fractions (by plate-to-plate calculations), it is desired to know the K values for each of the several components at the particulas pressure of the distillation and a t the temperature on each particular plate. By connecting the points corresponding t o the operating conditions on the pressure and temperature scales with a straight line, the intersections of this line with the intermediate scales representing each individual component may be read by this one setting to give the respective values of K for each of the components at the conditions of temperature and pressure existing on the plate. Here, again, as in Figure 2, t h e representation of the unsaturated hydrocarbons is someq-hat different from that for the saturated compounds. ACKNOWLEDGRlENT
Thanks are due to E. G. Schiebel and R. R. Umdenstock for their help and particularly to R. F. Benenati for drafting the figures. LITERATURE CITED
Othmer, D. F., IND. ENG.CHEX.,32, 841 (1940). Othmer, D.F., et al., Ibid., 34, 962, 1072 (1942) : 35, 1269 (1943). (3) Robinson, C. S., and Gilliland, E. R., “Elements of Fractional Distillation”, New York, McGraw-Hill Book Co., 1939. (4) Sherwood, T. K., “Absorption and Extraction”, New York, McGraw-Hill Book Co., 1937.
(1) (2)
Mollier Diagrams for Theoretical Alcohol-Air and Octane-WaterAir Mixtures-Correction Figure 2 of the above article is incorrect, and the chart on the facing page must be substituted for the one previously given [IND. ENG. CHEM., 34, 577 (1942)l. This change, however, does not affect any of the calculations or data presented. For convenience the initial conditions for the compression charts are again enumerated: SENSIBLEINTERNAL ENERQY.E, = 0 at base temperature 520’ R. or 60’ F. Since “ideal gas” conditions have been assumed and no chemical reactions occur, E, is not a function of pressure. H , = E, PV since E, = 0 at 520’ R. H,= PV ENTHALPY. a t this temperature. Here too H , is not a function of pressure, nnrl PV . = RT ENmtoPY.--The entropy, 8, of any component is zero at the base temperature and 14.7 pounds per square inch: at any other temperature and pressure:
+
-
I---
S = nJT$dT-nRln520
P 14 7
where P = partial pressure n = moles of any constituent For alcohol the entropy of vaporization is to be added.
The 520’ R. isotherm, representing the vapor-liquid equilibrium at the base temperature, is omitted to avoid any possible error in interpretation. This isotherm follows closely the one for 540’ R. which is shown. We should like to axpress pur. than&. to.Glenp ,C. Williams, of Massachusetts Institute of Technology, for calling our attention to this oversight and also to A. P. Oleson for assistance in preparing the new chart. RICHARD WIEBE NORTHERN REQIONAL R~SEARO LABORATORY X PEORIA, ILL.
