Correlating Vapor Pressure A simple relation giving highly accurate results has been shown to relate reduced pres-
Use of Critical Constants’
sures and “reduced latent heats” (i. e., latent heat/critieal temperature) of any given material to those of a reference substance, always taken at the same reduced temperature :
DONALD F. OTHMER Polytechnic Institute, Brooklyn, N. Y .
T
HE temperature-vapor pressure function of various materials has been shown t o be reducible readily to straight lines by the use of the vapor pressure function of a reference substance (9). On the x axis of logarithmic graph paper the temperatures are marked which correspond to the vapor pressures of a reference substance indicated by the calibrated ordinates, auxiliary ordinates are erected for these temperatures, and the corresponding vapor pressures of the substance in question are plotted on these temperature ordinates. I n effect, this is a logarithmic plot of the vapor pressures of the desired material us. the vapor pressures of the reference substance, always taken a t the same temperatures. These lines are substantially straight, and their slopes were shown to equal the ratios of the molar latent heat of the material in question t o that of the reference substance a t the same temperature. Vapor pressures of different materials are of interest over almost the entire conceivable temperature range. Therefore, no one liquid could always be used as the reference material, because it would either freeze or go above its critical point somewhere throughout such a wide range. Also, it was noted that the lines curved somewhat when near the critical point of either the reference or of the plotted substance. It was suggested, therefore, that various liquids be used as reference materials and that the one used should have properties similar t o those of the plotted material. Reference materials varying in vapor pressure properties between carbon dioxide and mercury were used in the examples of the previous paper, so that the vapor pressures of the plotted material would not betoo diverse from that of the reference material. As an example may be cited the case of ammonia, which when plotted against water gives a line having a slope of 0.5206 throughout most of the range. Near the critical point the curve bends slightly and the slope increases to a maximum of 0.5678. Probably the large difference between the critical temperatures of water and ammonia accounts for this change of angle and the corresponding calculated value of latent heat in this range. Chlorine is a compound which may be used as a reference and which has vapor pressures and a critical temperature more nearly in line with those of ammonia. When ammonia was plotted against chlorine in the previous article, the deviation of the slope was much less; i. e., a much straighter line was obtained to represent the vapor pressures and latent heats.
log PR/log P i = LR/Lk
This equation may be used directly (since there is no constant to evaluate from a plot); and accurate values throughout the entire range of the vapor pressures and latent heats may be calculated (or read from a readily prepared nomogram) for various
factory lines and results were obtained on the direct plot, which can be made on readily obtainable coordinates of temperature and pressures; such a direct plot cannot be made when reduced values are used. (b) The calculations t o and from reduced values are tedious. (c) Absolute values of temperatures and pressures which are used for reduced values further complicate the plot. (d) Critical values are known only for a relatively small number of compounds, although methods have been proposed for calculating them for others. ( e ) The only substantial advantage shown by the use of reduced values as a means of expressing vapor pressures and latent heats is near the critical point; and this region only occasionally finds use in practice. (f) I n many of the most valuable uses of the plot, the vapor pressure of the reference compound itself was considered under some other condition, such as water out of an aqueous solution; and if the critical conditions are assumed t o be the same, the reduced plot is the same as the simple plot. Reduced values, like t,he method of plotting described, are used in attempts to balance the properties of different materials against one another in such a way that irregularities will be neutralized. The reduced temperature for a given material is the ratio between the absolute temperature under consideration (in either degrees Rankine or Kelvin) and the critical temperature of the compound on the same scale. It is thus a dimensionless quantity for the particular material; obviously, a t the same temperature as ordinarily considered, there will be a different value of the reduced temperature for every compound. The reduced pressure likewise is the ratio of the absolute pressure exerted by the compound and its critical pressure. Thus, P R
Reduced Temperatures and Pressures The use of so-called reduced temperatures and reduced pressures, depending on critical constants, was considered as a means of straightening the lines of the previous article right up to the critical points. These reduced values were not used, however, in the prior discussion because: (a) Very satis1 The previous paper describing the basic and muoh simpler method appeared i n 1940 (93).
P/PC
where PR = reduced pressure P = normal pressure Pc = critical pressure Reduced pressure is also individual for every different compound a t the same pressure. For example, the normal boiling point (1 atmosphere), when converted to reduced pressures is the reciprocal of PCmeasured in atmospheres. Thus, there is 1072
and Latent Heat Data compounds, by using a single point of reduced temperature and vapor pressure, and values of a reference compound. The equation also gives exact plots and entirely eliminates the slight curvaturesin the critical regions of the lines of the logarithmic plot, previously described, for expressing the vapor pressure function. The necessary computations for the interconversion of reduced and usual values of temperatures and pressures may be made graphically by nomograms which are presented. They also allow ready plotting and use when any one standard substance (such as water) is always used as a reference substance.
different reduced pressure for the atmospheric boiling point for every material. An advantage of the units per se is that they are dimensionless; and reduced temperatures and pressures calculated in a n y English or metric unit may be used interchangeably with any other values calculated from other units. When reduced temperatures and pressures are considered as a means of comparison in this method of plotting, the plot is of the log of the reduced pressure of one substance against the log of the reduced pressure of the other substance a t the same reduced temperature for each. I n the same manner as
the equation previously obtained, the following general relation may be developed: log P R = L R / L &log P;E
+C
where P and P’ are reduced pressures of the two materials a t the same value of the reduced temperature. L and L’ may be termed the “reduced molal latent heats” of the respective compounds, also at the same value of the reduced temperature. Thus,
L
LR = - and Tc or
LR LA = 3 L’Tc = m
LA =
L’ To
=-
slope of line
The pencil of lines of Figure 1 represent reduced vapor pressures of several compounds selected a t random, plotted against the reduced vapor pressures of water, always taken a t the same reduced temperature. The data for ammonia are plotted throughout the entire range between the atmospheric boiling point and the critical point, and by this method give a line which is straight right up t o the critical. T o prevent confusion in the plot, only the points corresponding to the boiling points of the other compounds are indicated, although their respective data also fall on the indicated lines. It \Fill be noted that there is no correlation between these boiling points-i. e., no line or area of constant pressure. As a further illustration of the apparent incongruit,y of this method of plotting, a single line (number 6) represents the vapor pressures of two different compounds having characteristics as widely differing as those of acetic acid and phenol. The lower dot on this line represents the atmospheric boiling point of phenol, the upper open circle represents the atmospheric boiling point of acetic acid, 64 O lower. Of even more interest is the fact that every one of these absolutely straight lines goes through the reduced pressure point 1,1, corresponding to the critical points of all of the plotted compounds and of water. This has an interesting and useful corollary. From the twopoint-slope form of R straight line, when m is slope,
there follows:
Since log 1 = 0, log PR/log P i = m
Reduced Pressure Equation FIQURE 1. LOGARITHMIC PLOTOF REDUCED VAPORPRESSURES OF SEVERAL COMPOUNDS AQAINST REDUCED VAPOR PRESSURES OF WATER, ALWAYS AT THE SAMEREDUCED TEMPERATURES 1013
The last equation, showing the ratio of the reduced pressures as equal to m, may
INDUSTRIAL AND ENGINEERING CHEMISTRY
1074
be equated to the ratio of the reduced latent heats, u-hich also equals m, the slope of the line. Thus, log PR/log P i = L R / L ~ ~ This may be stated: At any given value of reduced temperature, the ratio of the value of the reduced pressure of any material to that of another is equal to the slope of the line on logarithmic coordinates representing the reduced pressures, and is also equal to the ratio of the reduced molal latent heats of these compounds. One advantage of the above statement is that i t allows, by the use of only one point of vapor pressure, the immediate and exact calculation of the vapor pressure and of the latent heat a t any temperature up to the critical point of any substance for which the critical values are known or can be calculated. It is unnecessary t o make any plot, since there is no constant to be considered or evaluated. A problem illustrates this: Required for ammonia the vapor pressure and latent heat per pound at 120" F., knowing that the atmospheric boiling point is -28' F., the critical pressure is 111.5 atmospheres, and the critical temperature is 270.3' F: AMMONIA AT -28" F. AND 1 ATMOSPHERE
P(,-,,, = 0.178 X 11.5 = 19.8 atm. (Tabulated value = 286 lb./sq. in.) .: error = 1.8%
Vol. 34, No. 9 =
291 lb./sq. in.
These minor discrepancies may be disregarded since they are probably within the limits of accuracy of the tabular data. Similarly, other values for other substances may be calculated. Nomograms (to be described later as Figures 3 and 4) allow the rapid solution of these and similar problems, I n many cases where critical temperatures and pressures are unknown, they may be approximated by any one of the several methods which have been suggested for this purpose. Fortunately, the critical temperature is more readily determined experimentally or approximated by other calculations ; and values are tabulated for many substances for which critical pressures are not available. The critical temperature is essential for use in this equation; and if it is known, as well as vapor pressures at two different temperatures, or if the vapor pressure at one temperature and the latent heat a t the same or a different temperature are known, the value of the critical pressure may be calculated immediately, as well as latent heats and vapor pressures at all temperatures. This will be referred to again later.
Application of Reduced Pressure Plot
THzo= 0.591 X (460
.:
+ 705.2) - 460 = 228.5'
F.
PHZO = 1.369 atm. (from tables)
P R ( H ~ O )=
' 369 217.72
~
=
The lines in Figure 1 of the reduced vapor pressures of the different compounds plotted against reduced vapor pressures of mater, always at the same reduced temperature, are sensibly straight up to the critical point. Thus they are a n improvement over the lines of the previous plot which may be slightly bowed in the critical range. These lines form a pencil through the common point 1,1,corresponding to the critical conditions, It is to be noted that the differential plot, as presented in the prior article (Z), also formed a pencil of lines, in that case through the point 0,O; but there also the value of 0,O represents the critical point for each of several compounds. The differential plot, however, is represented by a pencil of absolutely straight lines when reduced pressures and temperatures are used; here again the critical conditions are at the common point of the pencil.
0.00629
From equation:
AMMONIAAT 120' F.
Since T R ( ~= ~T R~( N)E ~ ) THIO 0.794 X (460
+ 705.2) - 460 = 466" F,
Latent heat of water at 466" F. B. t. u./mole
:.
=
=
755.2 B. t. u./lb. or 13,593.6/
0.919 X 11.66
=
10.72
10.72 X '730.3 = 17 461 B.t.u./lb. at 120' F. (calcd.) (Tabulated value = 455 B.t.u./lb. at 120" F.) :. error = +1.3% Also vapor pressure of water at 466" F. = 495 lb./sq. in. = 33.7 atm. or latent heat =
It is necessary only to know the temperature and pressure a t a single point in order to represent the complete range of vapor pressures, if the critical conditions are known. For example, the atmospheric boiling points of different compounds may be taken and converted to reduced conditions of temperature. The atmospheric boiling point is particularly convenient to use, since it is generally known accurately; and since it represents 1 atmosphere pressure, the reduced pressure t o be plotted is therefore the reciprocal of the critical pressure, expressed in atmospheres. A straight line from this point through point 1,l represents the vapor pressure function in its entirety. A convenient aid in these plots is the tables prepared by Osborne and Meyers (1) of the pressure of water vapor in atmospheres and various other units. Because the slope is equal to the ratio of the reduced latent heats and because this is always constant (as compared to slight variations in the previously described plot) the values of latent heats may be obtained more precisely whnn using this plot or formula, particularly at temperatures anywhere near the critical. It is possible to obtain lines of the same slope as obtained in this plot if normal pressures are plotted against normal pressures of the reference compound at the same reduced temperatures. The reason follows from a consideration of the properties of a logarithmic plot. E o convergence of all lines to a point results; and this type of plot appears to have no worthwhile advantages.
September, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 2 is a vapor pressure chart prepared on a reduced pressure background for the lower straight-chain hydrocarbons. Each hydrocarbon is represented by a straight line passing through the common point 1,l. All of the boiling points, which are indicated and nqmbered, fall on a straight line. (Methane is always an exception in the correlation of vapor pressure data for hydrocarbons; and in other correlations, as in this, it falls apart.) This straight line connecting the boiling points is therefore a line of constant pressure (1 atmosphere) on this plot for hydrocarbons. Lines have been drawn for constant pressures of 0.5, 1, 2, 3, 5, 10, and 20 atmospheres. Likewise the lines of constant temperature for these compounds have been determined; and a few lines, those for 50°, loo”, and 150” C., have been plotted. No attempt is made to work out a complete plot in this manner; but it is desired merely to show how such a vapor pressure plot for a homologous series of compounds might be prepared.
Nomograms for Plotting and Using Plots Obviously the simple plot previously described (a) which is close enough for most engineering purposes, would be used for most work of this type. Nevertheless, for some work (particularly operations in the critical range) the plot of reduced conditions described here has merit; and means of making it readily usable were attempted. A large plot was made of the reduced pressure of water us. reduced temperature, so that points could be picked off with a degree of precision, a t least as good as would be possible in plotting. Even by the use of this aid for part of the work, the plotting is tedious; and Figures 3 and 4 represent nomograms which have been constructed to facilitate both the plotting and the use of such a plot of reduced conditions. Figure 3 represents an ordinary parallel-line nomogram for multiplication or division, all of the scales of which are divided logarithmically for use in converting to or from reduced pressures. It is readily constructed in the usual manner for such a chart. We will consider first the scales labeled. respectively, “critical pressure”, “pressure”, and “redkced Dressure”. On either of the critical Diessure scales the critical pressure of the compound is foudd; and a line is drawn through this point and any given pressure on the pressure scale. The continuation of this line to the reduced pressure scale gives immediately the value of this rat,io, Pa. For convenience in use, the outer critical pressure scale, (number I) has a scale calibrated in atmospheres. It is for use with the scale for pressure in millimeters of mercury (number IV), and
1075
the conversion from atmospheres t o millimeters of mercury is taken care of in the calibration. Scale I1 is in pounds per square inch and is to be used with scale V, also in pounds per square inch. Scales I1 and V, as well as VI (which is used with either I and IV or I1 and V), are calibrated directly. Any desired pressure unit may be used with 11, V, and VI, and all values may be multiplied by any multiplier, such as a convenient power of 10, if necessary to secure a desired range. The corresponding plot for reduced temperature (Figure 4) is based on the other usual standard form of multiplication chart. I n this case a Z-chart is used in order to have straightline calibration of both critical temperatures and normal temperatures. On a 2-chart the diagonal scale must go through the zero points on the parallel scales; and since absolute units are necessary for the calculation of reduced temperatures, the zero points (falling off the chart) represent the absolute zero of temperature. These two scales are calibrated both in Fahrenheit and centigrade degrees; of course the same temperature system is used on each scale at any one time. By connecting the critical temperature of the compound on the left-hand scale with the boiling point desired on the right-hand scale, the reduced temperature is found by the intersection of the straight line with the right-hand calibration of the diagonal line, This value may be taken directly for a given use. However, in the usual case, with water as a reference substance, it is desired instead to know the value of the reduced pressure of water corresponding to its indicated reduced temperature; and the diagonal is therefore also calibrated for the reduced pressures corresponding to the reduced temperatures. To plot a point, therefore, on a graph such as Figures 1 or 2, by the use of these two charts a line is drawn through the value of the critical temperature of a given compound on the
FIGURE2. LOGARITHMIC PLOTOF REDUCED VAPOR PRESSURES OF LOWER HYDROCARBONS 1, ethane; 2, propane; 3, butane; 4, pentane; 5, hexane; 6 , heptane; 7. ootane. Cross linea are isobars (oonstant normal pressure) and are straight; dotted curves are isotherms (oonstant normal temperature).
0.0I Reduced Pressure of W o t e r
,
INDUSTRIAL AND ENGINEERING CHEMISTRY
1076
I
m
II
m
n
Vol. 34, No. 9
m
32001 3000-$
200-
-w
r
0
2600
In
160
2400
-I
3
IO
2200j.3
2000
#' W
a 100
a
90-
80: 707
1200 I4O0!
FIGURE3. PRESSURE AND REDUCED PRESSURE NOMOGRAM A atraight line through a point on oritical pressure scale I (or 11) and pressure scale I V (or V) gives value of reduced pressure on scale VI. A straight line through value of reduced pressure of water on scale A and value of ratio L R / L on ~ diagonal scale gives value of reduced pressure on scale VI.
{I' :P 40-
a (I)
:(I)
W
:E
J
30;
2 P
:I
'O0!
600
left-hand parallel scale of Figure 4, through a temperature value at which the vapor pressure is known on the right-hand scale; and the reduced pressure of water is read at the intersection of this line with the left-hand scale of the diagonal. This indicated value of the reduced pressure is picked off on the horizontal axis of a logarithmic sheet of graph paper; and against it is plotted the reduced pressure of the compound obtained from Figure 3. I n the reverse case of using a graph such as Figure 2 to find actual pressures and corresponding temperatures, the corresponding points are found, put through the nomograms of Figures 3 and 4 by the use of the known critical values, and read from these nomograms as pressures and temperatures in usual units.
Nomogram for Using Plot and Equation from Reduced Pressures The simple type of plot for reduced pressures represented by Figure 1 allows the construction of a very simple nomogram for the ready representation of all vapor pressure data
under reduced conditions. This is diagrammed in the small insert in the upper center of Figure 3. A nomogram satisfying a family of lines such as those of Figure 1 consists of two vertical logarithmic scales, one calibrated upward (PR), the other downward ( P k ) . Through the two extremities indicating point 1,l of Figure 1, a line is drawn. This line is the loci of all intermediate focal points, each of which represents the reduced pressure line for a substance, as plotted in Figure 1. This constraint on the location of the focal points, all on the diagonal, follows directly because the lines form a pencil through point 1 , l . Since every line on Figure 1 (representing vapor pressures of individual compounds) must go through 1,1,every focal point on a nomogram (for a n individual line on the plot such as Figure 1) must be on a line connecting point 1 on the one reduced pressure scale with point 1 on the other reduced pressure scale. Thus, in the insert diagram of Figure 3 a value for PR for one substance and for Pk for a reference substance at the same reduced temperatures are connected by a straight edge (dotted line) to give an inter-
September, 1942
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
1077
pressures with a single operation, due to the common usage of the reduced pressure scale. The two scales, A and reduced pressure, with the diagonal thus allow the representation of vapor pressures of all compounds. While vapor pressure nomograms have been used heretofore with two scales and individual pivot points in between for each compound, these points have no simple relation to one another; and they have been located by the intersection of two or more lines representing as many different known points of vapor pressure. The present nomogram is thus simpler and may be readily constructed to any desired size merely by calibrating two identical parallel scales logarithmically (using a slider from a slide rule or otherwise). Furthermore, because of the dimensionless character of reduced pressures, it may be used equally well with any units. The graphical conversion to or from reduced pressures by the other scales of Figure 3, and to or from reduced temperatures by the scales of Figure 4,makes the method readily useful for any vapor pressure determination. The diagonal line of Figure 3 is calibrated also to indicate the LEILA ratio for any given line on a plot, such as Figure 1. Since all lines pass through point 1.1, and each point on the diagonal represents a definite line, the slopes of these lines (tangents of their angles with the horizontal) r. may be indicated by suitable calibration. If scales I11 and VI were spaced a distance apart equal to the distance from 1.0 to 0.01 on scale VI, and the diagonal was io0 therefore drawn a t 45”, the calibration 300 would be simple. A series of lines could then be drawn through point 0.01 on scale VI. Their angles with the line of scale VI would then be measured; and their intersections with the diagonal could be cali500 brated with the values of the tangents of 250 these angles. Since scales I11 and VI are closer than the distance between 1.0 and 0.01 on scale VI (in order to minimize space requirements), the values for the calibrations were calculated and made in an100 200 other manner. They give, however, the slopes of the lines (values of LR/Lk) which t pass through any point indicated by reP spective values on scales I11 and VI. Thus it is possible to read off directly the value f of LR/Lk, and to calculate LR and then L. 150 300 Or if L is known and LR and L,/Lk are obtained and indicated, the line is immediately fixed; and all points of P R then may be read off the P R scale (number VI). The combination of Figures 3 and 4 allows various intercalculations, only two 100 200 more of which will be indicated. These may usually be made algebraically with more effort; and both the algebraic calculations and the use of the nomograms are dependent on the facts that (a) straight 50 lines are involved, and (b) these straight 100 lines all go through point 1,l. Thus, if there is known for a compound only the critical temperature and the latent heat a t one temperature and pressure, (e. g., the normal boiling point), there can be obtained all other values of vapor presAND REDUCED TEMPERATURE NOMOGRAM FIGURE 4. TEMPERATURE sure and the critical pressure; L, and also A straight line through a value of critical temperature on the left-hand scale and a value of L,/L; are determined from L, and the the normal temperature on the right-hand soale gives a value of reduced temperature, TR, latter is located on the diagonal of Figure 3. on the diagonal scale. This value of T R oorresponds with a value of the reduced pressure of Any line through this point, therefore, will water in the calibrations on the other side of the diagonal scale.
section with the diagonal a t 0. Every line representing another value of vapor pressure of this compound will also pass through 0 and intersect the P Rand PA scales a t corresponding pressures for these two materials-i. e., solve the equation or indicate all points on a line such as those of Figure 1. By use of the corresponding values of the reference substance, the vapor pressures a t every temperature may be obtained for the substance under consideration. The working nomogram is also constructed in Figure 3 for convenience in use with the nomogram for giving reduced pressures. The reduced pressure scale (number VI) corresponds to the P Rscale of the insert (i. e., the reduced pressures of the compounds in question); the A scale (number 111) corresponds to the Pk scale (i. e., the reduced pressures of the reference substance, water); and the diagonal is drawn as shown. By use of this nomogram, problems similar to the one solved algebraically for ammonia above may be immediately solved if only one value of vapor pressure is known. Also, the common reduced pressure scale on the right-hand margin when used with the other or “reducing” scales of this nomogram, makes it possible to convert to or from ordinary
E
1078
INDUSTRIAL A N D ENGINEERING CHEMISTRY
intersect PR and PL a t corresponding values for the same value of TR. TRcan be determined since Tc is known; and since the value of P a t one temperature is known, and the value of PR may be obtained immediately for that point, the value of the critical pressure may be determined from the equation Pc = P / P , either from the nomogram or arithmetically. If the vapor pressures are known a t two points of temperature and the critical temperature is also known, the critical pressure and any other value of temperature and pressure may be determined. This solution uses Figure 3 in a cut-and-try calculation, which is simpler in use than the following description: Two points are obtained on the A scale of Figure 3 corresponding to values for water a t the two given temperatures. It is then desired to find the focal point on the diagonal scale which is characteristic for this compound. This cannot be done directly; but consideration of another property of the chart allows it t o be done indirectly. The critical pressure which is also to be obtained will be represented by some unknown point on scale I or 11; and this point must be assumed as a start in the cut-and-try calculation. The known two values of vapor pressure of the compound are indicated on scale IV or V, and are connected by lines with the assumed critical pressure point on scale I or 11, which lines are continued to intersect scale VI in two points. Each of these
Vol. 34, No. 9
points has t o be connected by a line drawn through the corresponding one of the first mentioned two points on the A scale. These lines should intersect at a common point on the diagonal scale, which point represents the ratio of the reduced latent heat of the compound t o that of water. If these two lines do not intersect a t a common point on the diagonal, the value of the critical pressure which mas assumed is incorrect, a new value is assumed, and the geometric construction is repeated. Two or three trials will usually give the desired value of the critical pressure and the focal point on the diagonal. The focal point, of course, fixes all points of vapor pressure, which may then be determined as indicated above. Furthermore, it may be noted that the latent heat of the compound may also be obtained a t any temperature.
Acknowledgment The painstaking assistance of Frederick G. SaTYyer and of Robert F. Morley in the calculations and preparation of graphs is gratefully acknowledged.
Literature Cited (1) Osboine, N. S.,and Meyera, C. H., J . Research .VatZ. Bur. Standards, 13, 1-20 (1934) (Research Paper 1391). ( 2 ) Othmer, D. F., IXD. EXG.CHEM..32, 841 (1940).
Absorption of Liquids by Coal Application of Radiographic Methods to the Problem GEORGE W. LAND Battelle Memorial Institute, Columbus, Ohio
T
HE reduction of the dust from coal by the application of liquids such as water, calcium chloride solutions, or oil depends on the maintenance of a film of the liquid on the coal that will stick the smaller t o the larger pieces or will agglomerate the small particles into larger pieces which will not be carried in air currents. Various investigators (1, 4, 6) have found that even such liquids as petroleum oils, which do not evaporate a t ordinary temperatures, disappear rapidly from the surfaces of some coals and leave the coal as dusty as before treatment. This disappearance has been attributed to absorption of the liquid into the cracks and pores of the coal substance. Of the various coals of the United States studied by Pilcher and Sherman (I),the lower rank coals of Indiana and Illinois were found to be the most absorptive for oil. I n further research on this problem for Bituminous Coal Research, Inc., aimed a t finding the most suitable and economical materials and methods for the treatment of such coals, use has been made of radiographic methods to determine the relative rate of absorption of coals of various ranks and of the banded constituents of the coals. The method used was similar to that employed by Beeching (2) who made radiographs of English and Scottish coals before and after immersion in solutions of lead acetate and lead nitrate in water. Because the lead salts are more absorbent to x-rays
than the coal material, their presence when absorbed in the coal is plainly shown on the film. Beeching’s pictures shon-ed that the lead solutions penetrated not only the cracks of the coal, but also the general body of the coal where no cracks were evident. He concluded that this second type of penetration niust be into the pore space of the coal. Using a formula in which he related viscosity, surface tension, and specific gravity of the solutions to the height of capillary rise of the liquid into a partially submerged piece of coal in a given time, he calculated that the mean diameter of pores was of the order of 50 X 10-7 cm. This value is of the same order as that determined for bituminous coals by the moisture equilibration method and Anderson’s formula, used by Rees, Land, and Reed ( 5 ) .
Experimental Procedure Because of the desire to relate absorption directly to the use of oil, a 20 per cent by volume solution of tetraethyllead in 200-viscosity oil was first tried. Radiographs of Illinois No. 6 and Pocahontas coals before and after immersion in this solution showed some evidence of penetration of the oil and lead solution, but the x-ray absorption of tetraethyllead was not great enough t o cause as high a degree of darkening of the
