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 t o 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. T h e 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 t o 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 t o 25 atmospheres. These values increased upward. The temperature scale, a parallel line, was then drawn a convenient distance t o 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 o n the line, while the other hand was moving the other end of the straight edge t o 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. T h e 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 t o 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 t o 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 a t 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 t o 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 t o E. G. Schiebel and R. R. Umdenstock for their help and particularly t o R. F. Benenati for drafting the figures. LITERATURE CITED (1) Othmer, D. F., IND. ENG.CHEX.,32, 841 (1940). (2) 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.
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 t o 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 t o 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.
July, 1944
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
673
