DESORPTIOK OF ETHYL CHLORIDE FROM CARBON
27
VACUUM DESORPTION OF ETHYL CHLORIDE FROM ACTIVATED CARBON;',* EDWIN 0. WIIG
AZD
STAXTOK B. SMITH'
Department of Chemistry, University of Rochester, Rochester, New York Received August 10, 1950 I . INTRODUCTIOK
As a part of a major research program in defensive gas warfare conducted during World War 11, various activated carbons were evaluated by the Chemical Warfare Service for effectiveness against the irritant agents in current use in chemical warfare and against certain volatile compounds which were thought to be representative of hypothetical enemy gases incapable of conversion to harmless products by current gas-mask impregnites (11, 14). The ability of any adsorbent to retain such agents in relatively high concentrations during subsequent use in uncontaminated areas is a prerequisite for a satisfactory gas mask carbon. This property, called retentivity, was evaluated in many ways, using a variety of adsorbates. The tests used were more or less empirical in nature, and were dependent upon a number of variables which had to be precisely specified and held constant, if reproducible and comparable results were to be obtained. One such test (8) utilized ethyl chloride because of its low boiling point (12.2' C.) and its low order of toxicity. This test measured the rate of desorption of ethyl chloride from a thin saturated bed of carbon in an air stream of constant velocity and temperature. Though results from this test were correlated empirically, no attempt was made to determine the physical basis for the plow rate of mass transfer at low vapor concentration or to correlate such data in detail with pore structure or surface area data. The work described here was an attempt to investigate the rate process involved. A group of chars prepared from one batch of raw material and differing only in respect to the length of the activation period was employed. The rate of desorption of ethyl chloride in the absence of all inert gases was then measured in as nearly a perfect vacuum as could be maintained by mechanical means. This method eliminated the complications of a carrier gas, columnar behavior, and the necessity for a complex analytical system. In order that capacity values could be obtained from total equilibrium pressure readings, the pure ethyl chloride equilibrium isotherm of each char was evaluated. The isotherm and desorption data obtained on the charcoals were compared 1 Presented at the Tmenty-I?ourth Sational Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the American Chemical Society a t St. Louis, Missouri, June 15-17, 1550. The work reported herein was conducted under the Fellowship of the Chemical Warfare Service, Contract W-18-035-CWS 1301, at the University of Rochester. The material for this paper was taken from a thesis submitted by Stanton B. Smith t o the Graduate Schml of the University of Rochester in partial fulfillment of the requirements for t h e degree of Doctor of Philosophy, Xovember, 1948. ' Present address: Pittsburgh Coke & Chemical Company, Pittsburgh 25, Pennsylvania.
28
E D W I N 0. WIIG AND STANTON B. SMITH
with their other physical properties as evaluated by A. J. Juhola (5). These data consisted of B.E.T. surface areas determined by nitrogen isotherms, micropore size distributions, as calculated by the Kelvin equation from water isotherms, macropore distributions by mercury penetration, and density values computed from displacement measurements using helium, water, and mercury. 11. EXPERIMENTAL
A . Apparatus and material used The activated carbon samples were furnished by the Pittsburgh Coke & Chemical Company as experimental samples. They were prepared from finely ground bituminous coal, which had been successively briquetted, crushed, and sized, baked to destroy the coking tendency, and then steam activated in rotary TABLE 1 S u m m a r y of charcoal structure constants CHAPCOAL SAMQLX.
..........................
PN 208
PN94
PN 98 IPN 102 PN 110
,t;”w
30 0.721 1.18 2.08 0.134 0.133 0.207
90 0.672 1.10 2.12 0.143 0.153 0.296
300 0.487 0.80 2.29 0.146 0.252 0.398
--__-__ Activation time, min.. . . . . . . . . . . . . . . Apparent density, g./ml.. . . . . . . . . . . . Particle density, g./ml.. . . . . . . . . . . . . True density, g./ml.. . . . . . . . . . . . . . . . Macropore volume, ml./ml.. . . . . . . . . Micropore volume, ml./ml . . . . . . . . . Total pore volume, ml./ml.. . . . . . . . .
0 0.668 1.13 1.55 0.114 0.048 0.162
17,200 m.’/ml.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Calculated surface area fr er isotherm, m?/ml.. . . . . . . . 138 Surface area from CIHsCl point B , m.~/ml... . . . . . . . . . . . . . . . . . . . . . . . . . 155 (desorption) 147 (adsorption)
{,
150 270 0.621.0.515 1.02 0 . 8 5 2.17 2.25 0.146 0.156 0.174 0.218 0.320 0.376
b
9 , W 21,ooO 19,800 18,700 19,100 291
397
468
544
538
376
414
461
511
524
192
294
336
462
482
retorts for varying lengths of time. The raw baked material, called P N 208, is the starting point of the activation series which runs from P N 94 to PN 112. The physical data on these samples, including surface area and structure data as determined by A. J. Juhola, are tabulated in table 1 and plotted in figure 1. The ethyl chloride used in these experiments (obtained from the Ohio Chemical Company) was rated at 99.5 per cent purity. Careful fractionation and infrared analysis of forerun, middle cut, and residue failed to show any impurity other than a possible trace of water. A conventional high-vacuum system (see figure 2), consisting of a mechanical fore pump, mercury diffusion pump, two mercury manometers (D and E), a McLeod gage (B), and a desorption cell (H) (see figure 3), was used. Standardtaper solid-plug Pyrex stopcocks were used throughout, except as shown in figure 2, and were lubricated with grease of low volatility (Apiezon N).
DESORPTION OF ETHYL CHLORIDE FROM CARBON
29
B. Adsorption measurements
A weighed sample of the carbon to be tested was placed in a vial (A) and sealed to a small stopcock and standard-taper male joint. Each sample w&s evacuated for several hours on a mercury diffusion pump at a temperature of 25G300"C. After evacuation the sample stopcock was closed and the tube weighed on an analytical balance after being carefully wiped in a standardized procedure deL
io4,
10'
D :
0
.I
.2 V
3
.4
FIG. Pore-size distribution curves. Time-activation series of PittL irgh Coke & Chemical carbons. Ti = accumulated pore volume, ml./ml. of char, in pores of less than a given diameter; D = pore diameter in Angstrom units. a , P N 208; b, P N 94; c, P N 98; d, P N 102; e, P N 110; f , P S 112W.
signed t o minimize errors due to a film of moisture. With the sample in place in the thermostated bath (F) a small amount of ethyl chloride was admitted from the reservoir (C) to the sample and the sample allowed to equilibrate until successive pressure readings taken on the manometer or McLeod gage were constant. The sample cock was then closed and the sample vial removed, wiped, and weighed to 0.1 mg. as before. Subsequent additions of ethyl chloride were made similarly until saturation was nearly reached. The desorption side waa then evaluated by letting small quantities of gas escape to the vacuum manifold
30
EDWIN 0. WIIG AND STANTON B. SMITH
between measurements and again allowing the sample to equilibrate at a new lower pressure. When no more material could be pumped off at the thermostat temperature within a reasonable time, the sample was heated slightly under vacuum and the weight of the sample checked against the original weight before adsorption. Agreement within less than 1 mg. was obtained in all cases except one, where a difference of 2.6 mg. was noted. I n this case the desorption branch was corrected accordingly. Two corrections were made in calculating the isotherms from the observed data. In the region above 5.0 mg./l. a weight correction was made for the weight
FIQ.2. Equilibrium isotherm and vacuum desorption apparatus
of vapor in the intergranular and empty space in the tube. Since this amount waa small, it was arbitrarily calculated from an estimate of the volume of the empty sample tube (2.7 ml.). In the low-pressure region (below 1 mg./l.) the vapor concentration values were corrected for the pressure of noncondensable gases. This was done by allowing the ethyl chloride trapped in the McLeod gage to condense in the liquid-ni trogen trap and again reading the pressure. From this pressure reading, if allowance w a s made for the expansion of the gas into the larger system containing the trrtp, the true pressure of the ethyl chloride could be calculated. Points were considered reliable only if this correction amounted to less than 25 per cent of the total equilibrium pressure. In general this correction amounted to less than 0.005 mg./l. or 0.0015 mm. of mercury.
DESORPTION OF ETHYL CBLORIDE
FROM CARBON
31
C . Vacuum desorption measurements A specially designed desorption cell (H) consisted of a U-shaped tube (see figure 3) of rather large diameter (5 cm.), one arm of which contained a “cold finger” condenser (J) cooled with liquid nitrogen. This arm waa connected to an immersion-type liquid-nitrogen trap (K) and thence through a 2-1. expansion bulb (L) to the mercury diffusion pump. The bottom of the U contained a large mercury pool, the level of which could be quickly raised or lowered to close and open the space between the two arms of the U-tube. The sample holder (I) waa removable and consisted of a closed Pyrex “finger” projecting downward into the right arm of the U-tube. Against the outer surface of this tube a single layer
1 CELL
IMMERSION HEATER
DEGASSING HEATER
FIG. 3. Vacuum desorption cell
of char waa retained by a fine-mesh braes screen and a braas retainer ring which closed the annular space between the tube and the screen. A small resistance heater and a thermocouple could be lowered into the sample holder for degassing of the sample. During desorption, the sample was held at constant temperature by water pumped from the thermostated bath through the sample holder. A rubber tube, through which cold tap water was running, was wound around the bottom of the U-tube, thus keeping the temperature of the mercury pool below that of the sample so as to minimize distillation of mercury onto the sample. After initial degassing of the sample for several hours at an elevated temperature ethyl chloride was adsorbed on the sample. An ethyl chloride reservoir immersed in a dry ice-acetone slush a t about -80°C. waa opened to the sample
32
E D W I N 0. WIIG A N D STANTON B . SMITH
and the char allowed to equilibrate for 1 to 3 hr. a t this vapor pressure (3.5 mm.). The reservoir was closed during the last half-hour of equilibration and a reading on the McLeod gage made while taking the proper precautions not to disturb the equilibrium. The initial equilibrium vapor pressure was allowed to vary only between 11.7 and 12.7 mg./l. This confined the variation in char capacity to about 1-2 per cent. For each point on the desorption curve the sample was equilibrated and the cold finger filled with liquid nitrogen. When the pressure in the pumping system was mm. or lower, the mercury level in the cut-off was suddenly dropped and the timing started at the break of contact of the mercury with the cut-off point between the arms of the U-tube. After the desired length of time, the mercury level was quickly raised, to stop the desorption. The sample arm was then opened to the evacuated McLeod gage and allowed to stand several hours to reach equilibrium. The pressure was read when constant. A correction was applied to account for the gas filling the gage and connecting tubing. From the pressure reading the capacity of the carbon could be calculated from the equilibrium isotherm. The initial capacity was knpwn from the starting pressure, so the fraction of adsorbed ethyl chloride remaining on the char (0) was computed as 0 = N,/No, where N Oand N , represent the ethyl chloride capacity in the initial and final states, respectively. For the runs a t higher temperatures the samples were equilibrated as before at 25'C., but the sample chamber was then closed and the temperature raised to 56.5"C. by refluxing acetone in the sample holder with a nichrome immersion heater. Thus the adsorbed capacity was held essentially the same a t the higher temperature, though the pressure was increased somewhat. A correction was made in N o to compensate for the amount desorbed to bring about the increase of pressure in the cell. The sample was held a t this temperature for half an hour for equilibration before starting desorption. Desorption was carried out as before but with the sample held a t 56.5"C. After the desorption period the sample was returned to 25°C. and the char allowed to equilibrate as before, the ethyl chloride remaining then being determined from the pressure. 111. EXPERIMENTAL RESULTS
The ethyl chloride isotherms for the series of samples are shown in figure 4. A pronounced difference is shown between samples, especially in the low-pressure region. In the samples of low activity hysteresis was noted. Where this occurred, the initial capacity of the char before desorption was computed from the adsorption branch of the isotherm. The isotherms were determined between relative pressure limits of 0.7 down to less than 2 X The results of the vacuum desorption experiments are recorded in the curves of figure 5, where the logarithm of the fraction of adsorbate remaining on the char after desorption (8)is plotted against the logarithm of the time. This type of plot gave the best straight lines and showed most clearly the relationship between the different samples. The initial capacities from which desorption was started varied from 30 to 50
DESORPTION OF ETHYL CHLORIDE FROM CARBON
33
FIG.4. Equilibrium isotherms for ethyl chloride determined with Pittsburgh Coke & Chemical Company activated carbons. C = ethyl chloride vapor concentration, mg./l.; N . = equilibrium ethyl chloride capacity, mg./ml. a , P N 208 desorption at 25°C.; a’, PN 208 adsorption a t 25°C.; b, P K 94 desorption a t 25°C.; c, P N 98 desorption a t 25°C.; c’, P N 98 adsorption a t 25°C.; d , P N 102 desorption at 25°C.; e, PN 112W desorption a t 25‘C.; e’, PN 112W desorption a t 50°C.
FIG.5 . Log-log plot of relative vacuum desorption rates. t = desorption time in minutes; 9 = fraction of initial ethyl chloride remaining.
34
EDWIN 0. WIIG AND STANTON B . SMITH
per cent of the saturation capacity, depending upon the isotherm of the char. Desorption tests were run as far as the accuracy of pressure readings would permit. Some points were recorded beyond the limits shown in the figures, but these were taken into consideration in drawing the curves shown. IV. DISCUSSION O F EXPERIMENTAL RESULTS
A . Equilibrium isotherms All the ethyl chloride isotherms determined were of the same general character; that is, of the Freundlich (4)type in the low-concentration region but approaching a saturation point a t high concentrations as shown in figure 4. A
-
5-
0
. I
1
1 1 1 1
1 1
I
I
1 1 1
variety of tests were applied to the PN 112W isotherm in an attempt to obtain an equation which would fit the observed capacities over a wide range of vapor concentration, but no equation gave agreement over extended ranges, except the modification of the Freundlich expression described below. It has been pointed out that the Freundlich equation, though empirical in its origin, may be given a theoretical basis (15) if it is assumed that the adsorbent surface is heterogeneous in regard to heat of adsorption. An equilibrium isotherm was determined for PN 112W at 50°C. as well as a t 25'C. From these isotherms isosteric heats of adsorption were calculated by the standard method (l),and a graph of the data is shown in figure 6. The values are far from constant, varying smoothly from 14.7 kcal. to 7.8 kcal. (the heat of liquefaction) over the capacity range investigated (1-200 mg./ml.). If all sites of equal energies act in accordance
35
DESORPTION OF ETHYL CHLORIDE FROM CARBON
/ - _ - _ ---1
CEAPCOAL SAMPLE
. . . . . . . . . . .'
PN 208
. . . Sips' constant n . Freundlich constant K , nig./ml. a t 1 mg./l.. . . . . . . . . . . . . . Monolayer capacity (point B ) ,mg./rnl./ 63 Sips' constant A . . . . . . . 5.38 Site energy of maximum frequency (q,) less Po, kcal. /mole . . . . . . 2.76 Site energy of maximum frequency (q,), kcal./mole (pa = 7.32). . . . . . 10.1 Pore diameter of maximum area ( d d , Angstrom units: Calculated.. . . . . . . . 17.5 Observed. . . . . . . . . . . . . No maximum
!
PN 98
PN 102
0.447
0.442
PN 1lZW
0.490
~
120 15.24 3.62 11.0 Matched at 16
1
1
43 137 10.2 3.13
20 196 4.86 1.92
10.5
9.24
16.8 16.8
Matched a t 19
is approached in most cases. He therefore suggests the following equation as a closer approximation to actual cases:
where 8 has the same meaning as in the Langmuir (6) equation (Le., fraction of a monolayer adsorbed a t the pressure p , in atmospheres) ; n is a number less than 1, which is the slope of the straight-line portion of the isotherm (log 0 us. log p ) ; and A is the intercept of the extrapolated straight portion with the log p = 0 axis ( p = 1). This treatment assumes that a t saturation only a monolayer has been established. In the light of the B.E.T. theory (3) this is not likely to be the case with chars such as these, since some of the adsorption in the second and higher, layers will occur. This being the case, an increasing discrepancy will be noted between the observed capacities and those calculated from Sips' equation if the capacity for a monolayer (Nm)as determined by the point B method (3) from the isotherm is used in the calculation of 0. In table 3 are given the N,,
36
E D W I N 0 . WIIG AND STANTON B . SMITH
A , and n values for the various chars as determined from the ethyl chloride equilibrium isotherm (desorption branch in the case of PN 98 and PN 208). The experimental and calculated isotherms are shown in figure 7 and the values
c
I
102
IO
IC?
FIG.7. Comparison of equilibrium isotherms with Sips’ isotherm equation. C = vapor concentration of ethyl chloride, m g . / l . ; N e = ethyl chloride equilibrium capacity of chsrcoal, mg./ml.
TABLE 3 Comparison of equilibrium isotherms with calculated values from Sips’ isotherm equation (Based on Point B values for N,, 8 = 1) ETHYL CEWPIDE CAPACITIES Or c&uCU*Ls IN MO./KL. ETHYL CRLOPIDE VAPOR CONCENTPATION
PN 98 Calculated
)brewed
1 .o
5.0 10.0 50.0 100
lo00
)eviatioo
--
Ibrerved
per ccnl
mg. /1.
0.01 0.1
PN 102 Calculated
6.5 16.7 37 58 67 87 94 109
-
6.9 18.0 41 64 74 93 100 120
6 7 10 9 9 5 6 9
PN l l 2 W )eviation
Calculated
per cenf
5.4 14 33 53 64 88 97 119
5.6 15 38 63 75 102 111 126
3 9 13 15 16 14 13 6
Ibserved Deviation
-
per c e d
2.1 6.3 18 36 47 79 97 147
-
2.1 . 1 3 6.5 20 9 12 41 13 54 23 103 22 125 22 190
given in table 3. Though the agreement is not perfect in the high-pressure region, it may be stated that no other equation gives as good an approximation over so large it range. We therefore feel justified in applying Sips’ deductions further. Sips deduced by statistical methods that the distribution of heats of adsorp-
DESORPTIOS OF ETHYL CHLORIDE FROM CARBON
37
tion among the total adsorption sites is very nearly Gaussian about a heat of maximum frequency (p), expressed by the following formula:
where po = RT In a, a is a constant for all adsorbents of similar nature (derived from the Langmuir b ) , and the other letters have the same meaning as above. As n decreases, the Gaussian-type peak flattens, the heats of adsorption being more evenly distributed over a wider range; as n is increased the peak becomes sharper, finally becoming infinitely sharp (i.e., all sites having identical energies) when n = 1. This change, it seems, might parallel rather closely the activation process, since during activation a more or less heterogeneous mass of carbonaceous material having very fine porosity becomes more and more ordered and approaches a pure graphite structure with a larger average pore size and a sharper pore-size distribution. It would therefore seem that a flat distribution (n low) about a high heat of adsorption (high value of A , low n) would correspond to underactivated chars like PN 208 and PN 98. The other extreme would be represented by PN 112W (where n is 0.49). Here the distribution is sharper, but the heat of adsorption is still far from uniform over the entire surface. This may be seen readily in figure 8, where the frequency distributions of heats of adsorption (q) among adsorption sites as calculated from equation 3 are plotted: 1 F ( q )=
?rRT 1
e"' sin rn
+ 2 cos mc'*+ c
(3)
where
x = 2n(q, - q ) RT F(ql is the fraction of total sites having a heat of adsorption (site energy) between p and (p dp). The other letters have their usual or previously designated meanings. I n figure 8 the F values have been multiplied by the respective N , values of the chars, which should be proportional to the total number of sites available for adsorption on each char. The p values have been plotted from right to left for comparison with figure 9, where the distribution of surface area over the micropore diameter range has been plotted. The surface areas associated with pores of a given size were calculated from the volumes of water adsorbed within a small p / p o increment (taken from Juhola's water isotherms). The pore diameters corresponding to particular pressures were calculated from the Kelvin equation (cos 0 = 0.49) (5), and the conversion from pore volume to surface area made by simply assuming cylindrical pores of the diameter calculated. The correlation between site energy (heat of adsorption) and pore diameter appears to be surprisingly good. If the qm of PN 112W is said to correspond to a
+
38
EDWIN 0. WIIG AND STAXTOPU’ B. SMITH
maximum area in por$s of 19 b. diameter (d, = 19) and the pm for PN 98 similarly matched at 16 A., then a simpleJinear interpolation for the q, value of PN 102 predicts an area peak a t 16.8 A., which coincides exactly with the observed area peak calculated from the water isotherm. The calculated and observed values of the d, are shown in table 2. The isotherms of PN 110 and P N 94 were not determined with sufficient accuracy to yield reliable values for n and so could not be compared. The PN 208 sample does not correlate well, as no real peak appears in its area-distribution curve. Since Juhola felt that the pore-size distribution calculated from water adsorption data was meaningless
FIG.8. Adsorption site energy distributions calculated from ethyl chloride isotherm constants. q - qo = site energy minus constant PO, kcal./mole; F(ql = fraction of total sites having energies between q and ( q dq); N , = capacity for ethyl chloride a t monolayer coverage, mg./ml.; D = correlated pore diameter, A.
+
for such nonactivated chars, perhaps this lack of agreement should not be allowed to detract from the correlation of the other samples. The fact that such a correlation exists permits of two explanations: (1) either the sites having a given energy are confined to, and are completely within, the pores of the prescribed diameter range, or (2) the energies are distributed evenly over the entire char surface, but the state of the surface (i.e., the particular site energy distribution), which is the direct result of a certain degree of activation, is coincident with (but not necessarily dependent upon) the pore-size distribution. The first explanation might be preferred in the light of the potential theory of Polanyi (g), in which the greater proximity of the adsorbed molecules to the pore walls and nearest neighbors, as would be found in small pores, would lead to high heats of adsorption.
39
DESORPTIOS OF ETHYL CHLORIDE FROM C A R B O X
Though the determination of the position of qm is not sufficient to establish both A and n in equation 2, the height and breadth of the heat curves together with the value for surface area do fix them. The heights of the peaks in figures 8 and 9 are related in a fair approximation by a factor of 1.17. The width of the area-distribution curves was not treated quantitatively, but inspection of the two figures shows that it correlates, roughly at least, with that of .the heat curves. Whether or not the correlation of a definite pore diameter with a particular heat of adsorption extends to charcoals prepared from other raw materials and by other methods would depend on the heat of adsorption scale, the zero point leal,
1
,
,
I
1
1
I
I
I
,
1 1
D FIQ.9. Differentiated surface area distribution curves, calculated from t h e water isotherms assuming cylindrical pores. D = pore diameter, 11.; A A / A D = surface area (m.2/ml.) associated with pores of diameter between D and (D + A D ) .
of which is fixed by the constant a, which was assumed to be the same for all sites in Sips’ original presentation. A value of a may be calculated theoretically, but the calculation is rather involved and includes a somewhat doubtful oscillation frequency term. Instead, a value was calculated semiempirically by matching the average heat of adsorption for a completed monolayer (as calculated from the heat-distribution data) with an experimentally determined average heat of adsorption obtained by integration of the isosteric heat curve (figure 6) for PN 112W. A value for a of 2.32 X 1oj was obtained. The objection has been raised on theoretical grounds that a should not be assumed constant even for sites of different energies on the same surface. We prefer, however, to assume that the variation, if it exists, is small, and we oFfer
40
E D W I N 0. WIIO A N D STANTON B .
SMITH
this semiempirical treatment of results as evidence for the veracity of this assumption.
B. Vacuum desorption measurements The relation of the vacuum desorption curves to one another is not evident if they are plotted linearly. The curves appear to level off rather abruptly, the less active material retaining a much higher proportion of its initial load than the others. It is therefore apparent how the retentivity of a char came to be considered a static fixed quantity. However, if the data are plotted logarithmically, as in figure 5, the rate of desorption is more clearly evident. All curves approach straight lines even up to 100 min. A very regular progression is evident as the activation time of the sample is increased. Changes in temperature do not alter the shape of the curves, but only its relative position. The effect of an increase in temperature seems to be equivalent to a shift to the left by a constant amount TABLE 4 Time-temperature f a c t o r s f o r v a c u u m desorption rates a n d derived apparent activation energies APPAXENT A C I N A I I O N ENERGY ~ A C I I O N Or I N l l l U . CAPACIIY (NIh'a) AT poim OF C O ~ A P I S O N
-
9i
0.5 0.3 0.2 0.1 0.05 0.02 0.01
-1 -
PN 200 PN ll2W TI 290' Ti = 290 Tr = 329.JdT1 = 329.5'
I -
F" llZW Ti 290' Ti = 323'
-
PN ll2W TI = 290'
kcal./molc
2.5 2.6 3.2
3.0 2.6 2.5 2.5 2.8 3.0
2.3 2.1 2.0 2.0 2.1
2.3 2.5
I
PN 112Wo TI = 290
329.5* Tr = 323' T. --
-5.8 5.9 7.2
krJ./nrolr
kcal./wwlo
6.7 6.0 5.6 5.7 6.3 6.8
6.5 5.9 5.2 5.2 5.8 6.5 7.0
with respect to the log of the time. This is shown in table 4, where the ratios of desorption time at equal relative capacities are recorded. If the difference in overall rate is considered to be due to an activation energy which is required to attain translation on the adsorbent surface, then its value can be calculated as shown in table 4. The values are quite constant but do not show as much variation from sample to sample as might be expected. The magnitude of the values seems reasonable with respect to the total heat of adsorption. An attempt was made to derive an equation which would describe the experimental results, thus establishing an assumed mechanism and giving the true explanation for the temperature and pressure dependence of desorption. Wicke (12, 13), working along the lines pioneered by McBain (8) and Damkoehler (2), derived an equation based on diffusion of mass to and from the interior of. spherical granules of adsorbents which possess a Langmuir-type isotherm. It is based on Fick's diffusion law applied to a combination of gaseous and surface diffusion. Since on the linear portion of the Langmuir isotherm the
DESORPTION OF ETHYL CHLORIDE FROM CARBON
41
surface concentration is always directly proportional to the vapor concentration, the diffusion coefficients can be lumped together in a linear combination to yield a single overall diffusion coefficient. If the resulting differential equation is integrated within the boundary conditions of these experiments, the equation expressed in terms of the fraction of original adsorbed material remaining after a given desorption period is:
where fi = fraction of initial capacity retained in entire granule after desorption, D, = generalized diffusion coefficient, K = isotherm constant for the linear portion of the isotherm (ratio between vapor and surface concentration a t equilibrium), R = radius of the granule, and t = time. As T becomes large, then the expression may be approximated by the leading term of the series. A plot of the log of the fraction of adsorbed phase remaining us. time should therefore approach a straight line at long desorption times. Such a curve calculated from Wicke's equation, assuming reasonable values for the constants involved insofar as possible, is shown as a dotted line in figure 5, and the difference between it and the experimentally observed behavior is clearly evident. We therefore attempted the derivation of the analogous equation for the case of the Freundlich isotherm, basing it on the following assumptions similar in most cases t o Wicke's: ( 1 ) The granules are spherical and of equal radii, R. (3) The granules are permeated throughout with large interconnecting pores (macropores), through which Knudsen diffusion and surface diffusion can occur. (3) A second-order pore system (micropores) exists, but serves only to increase the total surface areas available to each macropore, and the mass transfer from the micropore to the macropore is assumed to be nearly instantaneous and therefore not rate determining. (4) The sorption is considered to be isothermal. Though this probably is not strictly true initially, it is probably a good approsimation after desorption has proceeded for a short time. (6) Mass transfer obeys Fick's law and for gaseous diffusion in pores small in diameter compared to the mean free path of the molecules it becomes:
where C = gas concentration, z = linear distance along pore in direction of flow,
42
EDV'IS 0. WIIG AND STANTON B. SMITH
D , = gaseous diffusion coefficient, d = pore diameter, zio = average molecular velocity, and M = molecular weight of adsorbate.
The analogous equation for surface diffusion is:
where N = concentration of adsorbed material on the surface, D. = diffusion coefficient on the surface, which Damkoehler gives as:
D, = 3A.zi.
(7)
A. = mean free path on the surface, and & = average velority on the surface.
The molecular velocity should be proportional to d/T/IMas in the gaseous state, but is also subject to hindrance by potential barriers between adsorption sites. If the average height of the potential barrier is E then:
Damkoehler assumed E to be constant over the entire surface concentration range, but this is doubtful in our case since the heat of adsorption shows such wide variation. Ufiing the above assumptions and transforming to radial form we obtain:
% at+ ? ! !at= D g [ 2 ? ! Cr +ar-
aT2 a'c]
f D a [2r- a,v ar+ -
31
(9)
where r = the radial distance from the center of the granule. If we make use of the equilibrium postulate to interrelate the gaseous concentration to the surface concentration we can make a substitution for C from the Freundlich eauation :
N
=
KC"
or
(3"
C = -
(10)
where n = the slope as read from the log-log plot of the isotherm and m = l/n. It is also advantageous to eliminate dimensions by transforming to relative distance and concentration terms: y = N / N o = relative surface concentration = relative radial position within granule a = r/R When the above substitutions are made and the terms combined one gets:
[Comrrn-'
+ No1 = [mBy'"-l + GI at
DESORPTION OF ETHYL CHLORIDE FROM CARBON
43
where
B = -D,CO and G = -Do No R2 R* The boundary conditions for this vacuum desorption experiment are : at t = 0 ,
y = l
at t = t,
y = f(t,a) for y = O
for O < a < l 0
5
a
1. However, as y and a y / a a become small, its contribution will become negligible. Therefore if we confine our. selves to long desorption times we may drop the final term, thus leaving:
According to this expression either gaseous or surface diffusion will occur, depending on the relative magnitudes of mBym-l and G . Since m varies from 2 to 5 in this Eeries of samples, the B term will be very small for small values of y. However, if the B term is dropped (which is equivalent to saying that gaseous diffusion is negligible), then we are left with an equation the same in form as Wicke's differential expression. As shown in figure 5, the observed data are clearly in disagreement with this equation in its integrated form. We are therefore faced with two alternatives, if our basic premises (which, incidentally, were used by Wicke in interpreting adsorption of carbon dioxide with reasonable success) are correct. Either the G term changes in value with decrease in surface concentration, the B term remaining negligible, or the G term varies in such a way that the B term does not remain negligible, in which case both gaseous and surface diffusion occur together to a measurable extent. Equation 11 as it stands has not been integrated. However, it served as a guide in planning other experiments to be reported later, which served to differentiate more critically between surface diffusion and gaseous diffusion. If the surface diffusion coefficient could be accurately described as a function of surface concentration, then possibly a solution could be worked out which, when compared with the observed results, would test the validity of the assumptions made in its derivation and lead to a more rational concept of sorption rate behavior. \'. SUMMARY AND CONCLUSIONS
1. Ethyl chloride isotherms of coal base chars agree with Sips' equations
reasonably well over an extended concentration range. 2 . The activation series of chars show great heterogeneity with respect to surface energy; this leads to differences in isotherms not explained by surface area alone.
44
W. 0.MILLIGAX, G. L. BUSHEY, AND A. L. DRAPER
3. The shape of the isotherms is well explained by Sips' theory if the heat of adsorption is said to vary linearly with pore diameters. 4. Vacuum desorption rates are greatly dependent on the degree of activation. The explanation for the wide variation is evident not in macropore structure, but rather in the micropore distribution, providing surface diffusion with restricted molecular motion on the char surface is assumed. REFERENCES
(1) BRUNAUER, S.: The Adsorption of Gases and Vapors. Physical Adsorption, pp. 21823. Princeton University Press, Princeton, IUew Jersey (1945). (2) DAMKOEHLER, G.: Z. physik. Chem. A173, 35 (1935). (3) EMMETT, P. H., A N D KRAEMER, E. 0.: Advances in Colloid Science, Vol. I, Chap. I. Interscience Publishers, Inc., New York (1942). (4) FREUNDLICH, H.: Colloid and Capillary Chemistry, p. 111. Methuen and Co., Ltd., London, England (1926). (5) JUHOLA, A. J., A N D WIIG,E. 0.:J. Am. Chem. Soc. 71,2069,2078(1949). (6) LANGMUIR, I.: J. Am. Chem. SOC.40, 1361 (1918). J. J . : Ph. D. Thesis, University of Rochester, 1946. (7) MADISON, (8)MCBAIN,J. W.: Z. physik. Chem. 88, 471 (1909). (9) POLAXYI, M . : Z. Elektrochem. 26, 360 (1920). (10) SIrs, R . : J. Chem. Phys. 16, 490 (1948). D., AND DOYLE,G.: OSRD Report No. 5236,April, 1945. (11) VOLMAX, (12) WICKE,E . : Z. Elektrochem, 44, 587 (1938). (13) WICKE,E.:Kolloid-Z. 86, 167 (1939). (14) ZEFFERT,B., A N D DOLIAN,F.: TDMR 864,July, 1944. J . : Acta Physicochim. U. R. S. S. 1, 961 (1934). (15) ZELDOWITSH,
ISOBARIC AND ISOTHERMAL STUDIES I N THE SYSTEM SOAP-WATER. I' W. 0. MILLIGAN, GORDON L. BUSHEY,z AND ARTHUR L. DRAPER' Department of Chemistry, The Rice Institute, Houston, Tezas Received August 10, 1060
Studies of the physical chemistry of soaps are complicated by the fact that even pure soap constituents, such as sodium palmitate and sodium stearate, occur in a multiplicity of polymorphic crystalline forms, each of which is considered by some investigators to exist as various hydrates. Thiessen and Stauff (14,15, 16) were the first to recognize that relatively pure sodium stearate and palmitate exist in a t least two crystalline forms, designated as alpha and beta. Although 1 Presented before the Twenty-Fourth National Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the American Chemical Society a t St. Louis, Missouri, June 15-17, 1950. Proctor & Gamble Fellow, 1947-48. Present address: Department of Chemistry, University of Illinois, Urbana, Illinois. a Proctor & Gamble Fellow, 1948-50. Humble Oil and Refining Company Fellow, 1950-51.
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