Adsorption Isotherms for Pure Hvdrocarbons d
ROBERT A. KOBLE AND THOMAS E. CORRIGA" D e p a r t m e n t of Chemical Engineering, W e s t Virginia University, M o r g a n t o w n , W . Va.
I
L'K'pn" K'pnn
N ONE of the early papers by Langmuir ( 4 ) in which he derived his famous adsorption isotherm
= 1
In this equation L' and K' are related to the more basic constants, L and K. The basis of the equation may be regarded as theoretical since the constants appear to be related to basic physical and chemical properties-K' to the thermodynamic equilibrium constant, and L' to the total number of active centers. Nevertheless, these constants must be evaluated from experimental adsorption data, because, at present, there are no means of calculating them from fundamental sources. This, however, does not appear to detract from their usefulness in expressing adsorption data. The fundamental adsorption data for hydrocarbons on activated charcoal, reported by Ray and Box ( 5 ) ,which cevered awide range of temperature and pressure, have been used to test the general isotherm. T o test this isotherm and determine the constants L',K', and n,Equation 8 may be inverted and rearranged to give
he also suggested conditions under which the pressure would take on some fractional power. I n the more recent literature, Sips (6) suggested the same type of equation as being of a more logical form than the Freundlich isotherm, but he indicated that he knew of no case where the isotherm had represented any actual experimental data. The propoged isotherm was
One method of derivation of this type of adsorption isotherm begins by assuming that adsorption takes place aa a chemical reaction between the "active centers" of the adsorbent and the gas being adsorbed. If the simplest adsorption reaction is assumednamely, combination of one molecule with one active center, the result will be the Langmuir isotherm. But, if some complicating factor such as dissociation upon adsorption is assumed, an equation similar to Equation 2 is obtained. The derivation assuming dissociation follows; this is adapted from the method of deriving rate equations for catalytic reactions presented by Hougen and Watson (3). Dissociative chemical adsorption may be represented by the equation
+ 21 = 2A1
(3)
+ 2i = RI + si
(4)
AI
(9)
which is the equation of a straight line on logarithmic coordinates. The data have been converted and plotted according to Equation 9. DATA AND CALCULATIONS
Original data were reported as a volume of gas adsorbed, in cubic centimeters a t standard conditions, determined a t a certain pressure recorded as either millimeters of mercury or pounds per square inch absolute. Corrections for compressibility deviations at high pressures were made. Details of the experimental method and original data are available in the original paper ( 5 ) . These data were converted to pound moles of gas adsorbed per 100 pound atoms of carbon, and to pressure in atmospheres. Reciprocals of the converted values were determined. First approximations of the constant L', for a given gas, were determined from the intercept of a rectangular plot of 1 / c A versus l / p (Figure ~ 1). The quantity ( 1 / c A - l/L')waa then plotted versus 1 / p A on logarithmic coordinates for a temperature of 100 OF. (Figures 2 t o 6). The value of L' was then corrected by trial until the plot gave the required straight line. The final value o f L' was used to plot the other isotherms for the particular hydrocarbon. The fact that L' is a constant and is independent of temperature is shown by the fact that once it is determined at one temperature, the same value may be used to plot the remaining isotherms for that hydrocarbon. Isotherms were plotted in this manner for the five gases, methane, ethane, propane, ethylene and propylene; these plots are shown in Figures 2 to 6.
or
A
where I is a symbol indicating an active center. Equation 3 presumes a symmetrical dissociation of a diatomic molecule, while Equation 4 is more general, indicating a split into unlike particles. Only the first case, in this example, will be considered. Writing the equilibrium constant, K , for Equation 3
(5) Also, if L is the total concentration of active centers
L
CZ
+
CAl
+
(6)
Eliminating C,from Equations 5 and 6, and remembering that C A= ~ '/a C A ~the , adsorption isotherm
(7) RESULTS AND ANALYSIS
is obtained. Equations of a form sfiilar to Equation 7 always result from this method of derivation. Hence, a general equation of this form may be written 1
It can be seen from Figures 2 to 6 that plots of the data according to Equation 9 are the straight lines postulated. While it is true that the value of L' was so chosen as to make the lines straight, this correction appears to be necessary only because of the inherent weaknesses in the graphical method of making the
Present address, Vulcan Copper and Supply Co., Cincinnati, Ohio,
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INDUSTRIAL AND ENGINEERING CHEMISTRY
first approximations, and not because of any discrepancy in the theory itself. The inaccuracy in L‘ is greatly magnified by the subtraction, 1 / c A - l/L’, Even so, the necessary corrections did not exceed 3 or 4%. The fact that L‘ is independent of temperature has been mentioned. The fact that the isotherms for each gas are parallel indicates that the exponent, n, of P A is a constant, also independent of temperature.
The mechanism for ethane and ethylene does not appear to follow such a simple equation; however, an isotherm which expresses their adsorption can be derived from the symbolic equation 2A
+ 31 = 3A2/,1
(12)
which merely indicates that two molecules are associated with three active centers. *his follows logically in considering,that methane, the smallest molecule, occupies one site; ethane and ethylene, the next larger, occupy the equivalent of 1.5 sites per molecule, while propane and propylene occupy two sites per molecule. This scheme breaks down upon reaching n-butane, which once again corresponds to a single site per molecule. An advantage of the method of correlation illustrated by Figures 2 to 6 is that it does not involve the misleading plot of P u8.
c.4
REOIPROCAL O f PRESSURE I N ATMOSPHERES.
Figure 1. Reciprocal Plot of Isothermal Adsorption Data for 100’ F.
According t o the method of derivation of Equation 8, n should be either an integer or a fraction composed of small integers. While the values of n determined from the slopes of lines in Figures 2 to 6 (Table I ) roughly approximate simple fractions, it appears that they disagree far enough t o indicate that if the present theory is t o hold, then adsorption occurs not wholly as indicated. Rather, complications such as incomplete dissociation, for example, occur.
TABLE I. VALUESOF L’ Gas Methane Ethane Propene Ethylene Propylene
AND
Slope of lines (Decimal Value of n) 1.0 0.678 0.540 0.632 0.569
n
FROM
FIGURES 2 TO 6
Nearest Fraction, n 1 =/a
’/= =/a ‘/?
L’ 6.25 7.94 7.40 10.30 8.94
According to Sips’s treatment (67, the occurrence of fractional powers of p corresponds approximately to Gaussian distributions of adsorption energies; thus, from this viewpoint, it is possible that fractional powers of pressure could result even in physical adsorption, due merely to the heterogeneous nature of adsorbent surfaces. A decrease in the value of n occurs when passing from methane, through ethane and ethylene, to propylene and propane-this corresponds to an increase in the breadth of the adsorption energy distribution curve. This does not follow into butane as will be noted later. Sips’s treatment does not require that n be a simple fraction as is implied by the method of derivations given above. A further interesting fact, according to this treatment, is that the distribution of adsorption energies, a property of the surface, here appears to depend upon the identity of the adsorbed gas. The temperature independence of n, whether n denotes a type of adsorption or a distribution of adsorption energies, is worth special mention. This constancy of slope does not occur with the Freundlich isotherm. Only methane follows Langmuir’s isotherm; its adsorption reaction may be expressed symbolically A+l=Al
p , which can easily indicate an apparent correlation where none exists, especially where the variation of CAwith p is small, as ie the case in adsorption a t ordinary or high pressures. As an example, ethylene has been reported as following Langmuir’s isotherm when adsorbed on charcoal (2); this disagrees with the present findings. However, the conclusion was based on the attainment of a reasonably straight line for the data when plotted with p r e s sure appearing in both ordinate And abscissa, and with pressure varying only between 4 and 35 atmospheres. This misleading appearance is illustrated in Figure 1, where all of the curves could be considered as reasonably straight, suggesting that all of the gases follow Langmuir’s isotherm. Actually, methane is the only one which does.
(10)
Propane and propylene may be assumed to dissociate according to the equation
Figure 2.
Correlation of Methane Data According to Equation[9
The values of K‘ were determined from the intercepts of the isotherms with the ordinate, l/pa = 1,in Figures 2 to 6. The intercept gives the value of the quantity l/L’K’, so that K‘ can be readily calculated. These values are reported in Table 11. TABLE 11. VALVESOF K‘ Temp., loo 150 200 250 300 350 400
F.
Methane 0.228 0.134 0.077
... ... . . I
...
Ethane 1.26 0.674 0.40 0.263 0.171 0,119 0.075
Propane 3.3 1.8 0:742
...
... ...
Ethylene 0.525 0.367 0.206 0,145
...
... ...
Propylene 2.54 1.4 0 ; 533
... ... ...
INDUSTRIAL A N D ENGINEERING CHEMISTRY
February 1952
As previously mentioned, K' is related t o the true thermodynamic equilibrium constant. This relation may be expressed by the equation K ' = aK"
(13)
where m is a power which may, but not necessarily, be equal to the slope of t h e logarithmic plot of ( 1 / c A - l / L ' ) us. I/pA, and a is a constant. Hence, like the equilibrium constant, a plot of log K' against the reciprocal of the absolute temperature should be a reasonably straight line. Such a plot is shown in Figure 7. The lines are not only straight, they are also parallel. This does not mean t h a t the heat of adsorption of all the gases studied is the same, for Figure 7 is not a plot of the true thermodynamic K. Actually, since the slopes of the lines are equal, the constant K' seems t o be a more fundamental and more useful number than the actual equilibrium constant. The constancy of slope furnishes a useful empirical constant which may be used to predict K' for temperatures other than t h a t measured, perhaps even for other substances of a given homologous series. 1 The slope of the log K' vs. F plots is actually a function of the heat of adsorption and t h e exponent, n. However, the constancy of the slope is of uncertain significance. The following equations show the relationship among K, K', a, and m: The basic relation lnK=-
ASa
-AHa
+R
RT
may be transformed t o common logarithms 10gK =
-AHa -+-
2.3 RT
Asa 2.3R
Taking logarithms in Equation 13
log K' = log aK" = log a f m log K
(16)
or rearranging, log K =
log K'
- log a
(17)
Hence, logK' =
-AHom Asam +2.3RT 2.3R -I- log
a
(18)
VP,
Figure 3 . Correlation of Ethane Data According to Equation 9
385
Thus, the slope of the lines in Figure 7 is given by
-AHam 2.3 R
For the special case of methane, since n = m = 1 , the plot of the true thermodynamic K would be parallel with the plot of K'. The intercept of t h e plot is related to the standard entropy change; however, since the value of a is unknown, the intercept of the log K us. 1 / T plot is useful only as a n empirical constant. According t o Polanyi's theory (1 ), the free energy of adsorption, which he termed the "adsorption potential," is independent of temperature, but depends Upon the volume of gas adsorbed. For the' free energy t o be independent of temperature, A S a must be negligible, so t h a t InK=-
-AGO
RT
If this be so, a plot of In K us. 1/T would pass through the origin 1 -AGO. (K = 1 , - = 0 )and the slope would be equal to T R The curves in Figure 7 should not be expected to go through the origin for reasons already given. Thus, although Figure 7 shows a relationship similar to t h a t suggested by Polanyi, i t can be used neither t o support nor refute that theory. It should be noted t h a t the slopes of the lines of Figure 7 ara independent of the mass of gas adsorbed, whereas Polanyi specifies constant adsorbed volume. However, at varying temperature and pressure, constant volume does involve a change in the mass of adsorbed phase. The possibility of a linear relation between the intercepts of the curves of Figure 7 and the number of carbon atoms in the gas is evident; however, data are too meager to support such a plot. Such a relation would not be surprising, however, since this a/ intercept is related t o an entropy change. It is possible to predict isotherms for these gases on carbon adsorbents, over a fairly wide range, through the use of the plots of K' against 1/T (Figure 7 ) . Experimental d a t a at one temperature are also needed to determine the constants L' and n, which may be considered invariant with temperature. The value of K' for any temperature may be read from ti plot of log K' us. 1 / T . Such lines may readily be plotted from the one
'/pn
Figure 4. Correlation of Propane Data According to Equation 9
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I /T,
I
I
I
400
350
300
250
Vol. 44, No. 2
OR
-' ZOO
I 150
L 100
TEMPERATURE, O F .
Figure 7. Effect of Temperature on the Constant K f
t o Equation 9 for the particular hydrocarbon. The constant K' was determined from Figure 7. In the case of n-butane, a parallel line of K' us. 1/T was constructed using the value of K' determined from a plot according t o Equation 9. The value of n chosen for use in the calculations for propane and propylene was ' / z rather than the decimal values of the slopes of the lines in Figures 4 and 6. Spot checks revealed that this was responsible for most of the disagreement evident between calculated and experimental results. Apparently, better predictions could be obtained by using the true (decimal) value of n. While calculating the isotherm for n-butane, i t was noted that this compound also follows Langmuir's isotherm-that is, n = 1. CONCLUSIONS
1
, I
I
l
l
I
I
l
l
I
I
l
l
Equation 8 appears t o have advantages over both the Langmuir and Freundlich equations in that it expresses adsorption data over very wide ranges of pressures and temperatures, and may be more universally applicable than either. The following significant facts concerning the data in the range studied have been noted. 1. All isotherms plotted according to Equation 9 are straight and parallel for a given gas, indicating that the constants L' and n are independent of temperature. This is a specific advantage over the Freundlich equation, where the constants are dependent upon temperature. 2. The values of K' calculated from plots according t o Equation 9 form straight parallel lines when plotted against 1/T, and this fact is useful in the prediction of isotherms a t temperatures other than the ones studied.
value of K' from the experimental isotherm, as the lines of Figure 7 are parallel. An alternate method would be available if the relationship of g intercept and number of carbon atoms just mentioned were valid. Such a plot, cmnbined with an independent means of determining L' and n, would obviate the experimental determination of the initial isotherm. As a demonstration of the use of this method, the adsorption of n-butane on carbon a t 200' F., of propane a t 300" F., and of propyfene a t 200 F., have been TABLE 111. COMPARISON OF CALCULATED ADSORPTION WITH EXPERIMENTAL DATA calculated. Experimental data n-Butane a t 200' F . C Propylene at 200' F . b Propane at 300' F." not used previously have been ~ ~ , l b . / CA, CA, DeviaPA, CA, CA, DeviaPA, CA, CA, Deviacompared with the calculated sq. 1n. oalcd. exptl. tion, % mm. calcd. exptl. tion, 7% mm. calcd. exptl. tion, 7, 1.372 26.2 24 1.012 0.925 3.5 8.06 36 0.893 values. These are shown in 14.5 2.68 2.48 3.2 143 3.04 3.14 8 55 154 2.41 2.22 0.27 3.65 45.5 3.66 Table 111. The agreement is 71.5 4.8 550 4.34 4.14 4.11 4,12 3.7 396 3.37 3.25 0.24 4.2 680 4.46 4.28 3.91 1.28 11.6 699 3.96 5.00 fair. These isotherms were 100.5 4.42 a L ' = 7 4 n = 1/2, K f ,== 0.565. calculated according to Equab L' = 8:9'4. n = 1/2, K = 0.83. tion 8 with L'and n determined L' = 6.1,n = l, K' = 7.8. from a plot of data according C
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1952
3. The logarithm of the value of K‘ obtained by extrapolation of the plots of K‘ vs. 1/T to 1/T = 0 may be a linear function of the number of carbon atoms in the compounds for a homologous series. 4. From the above, K’ may be determined as a function of the temperature for a given compound, and the constants, L’and n, may be determined from one experimental isotherm, so that isothe+msat other temperatures may be predicted. At the present time, it is not possible t o calculate isotherms of a substance without a t least one experimental isotherm of that substance on the particular adsorbent; however, i t appears t h a t with further development of the behavior of the constants, L’ and n, such a calculation may become a possibility. NOMENCLATURE
A = a molecule of gas being adsorbed a, b = constants CA = concentration of adsorbed gas, moles per 100 moles carbon AG” = standard free energy change of adsorption A H “ = standard heat of adsorption K = thermodynamic equilibrium constant K’ = empirical adsorption constant related t o equilibrium constant
387
L = total concentration of active centers, moles per 100
L’
moles of adsorbent
= empirical adsorption constant related t o total number
of active centers available on adsorbent 1 = an active center m = aconstant n = aconstant p , P A = equilibrium pressure of adsorbed gas R = the gas constant R1, SI = a fra ment of a dissociated adsorbed molecule A S ” = stancfard entropy change of adsorption T = absolute tem erature B = fraction of afsorbent surface wvered LITERATURE CITED
(1)Brunauer, S.,“Adsorption of Gases and Vapors,” Vol. I, “Physical Adsorption,” p. 95,Princeton, N. J., Princeton University Press, 1945. (2) Glasstone, S., “Textbook of Physical Chemistry,” 2nd ed., p. 1199,New York, D.Van Nostrand Co., 1946. (3) Hougen, 0. A., and Watson, K. M., “Chemical Process Principles,” Vol. 111, “Kinetics and Catalysis,” p. 912,New York, John Wiley & Sons, 1947. (4) Langmuir, I., J . .Am. Chem. Soc., 40, 1361 (1918). IND.ENQ.CHEM.,42,1315 (1950). (6) Ray, G. C., and Box, E. 0.. (6) Sips, R.,J. Chem. Phys., 16, 490 (1948). RDCEIVED March 7, 1951.
Vapor Pressure of Benzene above 100”c. PAUL BENDER, GEORGE T. FURUKAWAl, AND JOHN R. HYNDMAN2 University of Wisconsin, Madison, Wis.
T
HE number of compounds for which there have been reported accurate vapor pressure data for the high temperature range is quite limited. To assist in supplying such information for materials of both industrial and academic interest there has been undertaken a t this laboratory a research program, the first results of which are reported in this paper. The vapor of benzene in the pressure range from slightly below 2 atmospheres to the critical point has been measured, with an estimated error of approximately 0.1 yo. The critical constants have been evaluated by means of compressibility measurements in the critical region. EXPERIMENTAL DETAILS
Apparatus. The apparatus constructed for this work was similar in design to that employed in studies of the compressibilities of gases by Beattie (Z), whose comprehensive description may be consulted for details. The sample under investigation was confined by mercury in a borosilicate glass liner in a stainless steel bomb. Initially liners of the design specified by Beattie and shown in Figure l a were used. The type shown in Figure l b was subsequently adopted because i t provided greater convenience and reliability in loading the bomb; loss of a purified sample through shattering of the liner on loading was almost completely eliminated. The thickness of the glass septum is not critical; diaphragms from 0.002 to 0.006 inch thick have been used successfully. The high temperature thermostat was essentially of the type described by Beattie ( 8 ) ; the bath fluid employed was the Socony-Vacuum Company’s Valrex oil A. Forced Ventilation was necessary with this medium a t temperatures above 250” C. Present address, National Bureau of Standards, Washington, D. C Arsenal Research Division, Rohm & Haas Co., Huntsville, Ala. 1
* Present address, Redetone
The control element in the thermostat was a resistance thermometer, of low thermal lag, which formed one arm of Mueller type direct current-operated Wheatstone bridge. The bridge output voltage a t unbalance was amplified by conventional means and applied as the control voltage in the phase-shifting thyratron circuit described by Reich (11)to regulate the current flowing through the control heaters in the thermostat. The temperature regulation obtained was f0.001”up to 200” C., &0.002” up to 250” C., and &0.003” up to 300” C. Temperature measurements made in rapid succession on each of several platinum thermometers in different positions in the bath verified the uniformity of temperature throughout the thermostat. All temperature measurements here reported are referred t o the International Centigrade Scale, and were made with research type platinum resistance thermometers obtained from the Leeds and Northrup Co. Several such thermometers, calibrated a t the National Bureau of Standards, were used interchangeably in the work. The resistance measurements were made with a thermostatted Rubicon Mueller bridge which was calibrated by means of an N.B.S. type standard resistor supplied by the University of Wisconsin Electrical Standards Laboratory. A thermometer current of 1.25 ma. gave a thermometric sensitivity of approximately 5 mm. per millidegree with the galvanometer scale a t two meters. A dead-weight gage of the type described by Keyes (7)was used in the pressure measurements. The piston-cylinder combination, of nominal effective diameter of 0.5 inch, was supplied by the gage division of the Pratt and Whitney Co. All weights of 100 grams and over were machined from stainless steel and calibrated against laboratory standards using a Paul Bunge balance of 5-kg. capacity and a sensitivity of the order of 5 mg. In the smaller sizes analytical weighb were used.
