SORPTION OF AMMONIA AND CARBOK DIOXIDE BY GLASS
Time and Pressure Relationships BY D. H . BANGHAM A N D F. P. BURT
In a previous paper' we have described an apparatus for measuring the rate of sorption of carbon dioxide by a known surface of glass wool under approximately constant pressure conditions at a temperature of o°C. It wae found that the sorption-value (s) waE related to the time (t) by the equation S" = kt, where m is a number varying from I O a t low pressures to I 4 a t pressures approaching atmospheric. Although the sorption-values exhibited by carbon dioxide were relatively small, the fall of pressure in the sorption-vessel, due to removal of gas, introduced serious complications when the initial pressure was low. Experiments with ammonia, yielding sorptionvalues some five times greater than for carbon dioxide under similar conditions, indicated the necessity of devising some means of correcting the results to constant-pressure conditions, as an alternative to designing a constantpressure apparatus. The present communication, while presenting further data obtained with our original apparatus, deals in the main with an attempt to solve this problem by expressing the sorption as a function of a variable involving both pressure and time. The Sorption Apparatus The apparatus described in the previous paper consisted essentially of a gas pipette A connected by a tap to a sorption-vessel B: X and B were calibrated and provided with manometers so that their gas-content could be determined. The system was kept at 0°C. After measurement of an initial quantity of gas in A the tap between A and B was opened for a few reconds and the disappearance of gas in the sorption-vessel noted a t different intervals. By reversal of the operations just described it was possible at the end of any sorption experiment to examine the gas-content of the glass wool as the pressure was reduced in succesrive stages. Sufficiently long intervals were allowed to elapse between each pressure-reduction to enable the timeeffects to be examined. For sorption experiments a t pressures greater than half an atmosphere a special device was adopted whereby the whole of the gas in A was transferred to B. In such experiments, however, the admission of gas to the sorbent occupied an appreciable time2 (some minutes). At the end of each experiment the glass wool was out-gassed by heating for several hours at a constant temperature in the neighbourhood of 2 0 0 O C . As the gases examined were readily condensible and carefuly freed from permanent gas a high vacuum was achieved during this process by immersing a Proc. Roy. SOC. 105 A, 481 (1924). *Proc. Roy. SOC. 105 A, 482 (1924).
114
D. H. BAh'GHAM AND F. P. BURT
portion of the system in liquid air. As already discussed in the previous paper this treatment mas successful in recovering quantitatively the activity of the glass towards carbon dioxide. It was also successful in the case of all other gases examined with the single exception of sulphur dioxide. Experiments with Ammonia
1;
etorage-bulb. The melting-pressure of this ammonia was 45.6 mm. Before being admitted to the measuring pipette of the
A sorption experiment with ammonia was carried out a t an initial pressure of 360 mm. and continued for a period of 35 days. At the end of this time the rate of sorption, though small was still detectable. Table I gives the reduced pressures and sorption-values observed at different times.
I n Fig. 2 the results are represented by plotting log s against log t, where s is the sorption-value at time t. I t will be noticed that the graph remains linear up to t = 400 mins., but thereafter becomes concaire to the log t axis. The value of m in the equation s"=kt is 12.8. Too much weight cannot be attached to the exact form of the latter part of this graph; not only had the pressure fallen very considerably below its initial value but, owing to a slight melting of the ice near the top of the wool tube that was occasionally noticed, the temperature of this part of the system may have risen temporarily
IIj
SORPTION BY GLASS
TABLEI Time s PO Time s (rnins) (cc.@ N.T.P) (mm.ofHg) (minsj (
[email protected]) 8.7~0 615 5 2 2 360.33 70 ~
4
6 8 I1 I2
I4 16 18 20 22
26 28 32 36 38
40 46 49 55 59 65
6.976 7.195 7,350 7.501 7.584 7.670 7.767 7.840 7.885 7.938 8.044 8.097 8.181 8.261 8.288 8,327
8.415 8.458 8.539 8.581 8.651
-
356.42 354,39 352.92 351.52 350.73 349' 98 349.04 348.38 347.97 347' 47 346.47 345.98 345,I9 344,43 344.18 343'86 343'04 342' 65 341.88 341.47 340 82
~
75 80 85 90 95 IO0
I IO
1-25
I35 I45
I55
I 65
204 212 220
240
322 330 335 364 367
P O
_
8,746 8,786
8.832 8.879 8.911 8.938 9,007 9.104 9.158 9.213 9.270 9,308 9,461 9,486 9.5'9 9.579 9.802 9.821 9.831 9,886 9.891
_
(mmof Hg)
340.33 339.91 339,50 339.07 338,63 338.32 338.07 337.45 336.51 336.00 335.50
335,oo 334.60 333.07 332.87 332.55 331.98 329.84 329.66 329,57 329.05 329,02
Time
_
(Ta3 I .Oj
1.13
4.04
4.12 4.94 5.14 7.07 8.11 9 I3 12,I 0
14.I O Ij.Ij
16.13 17.18 18.05
18.96
3 .
(cc.@
PO
N.T.P) :mm.of Hg)
10.949
318.85 318.27 12.031 309.76 12.062 309.33 12.187 308.20 12.213 307' 56 12,328 306.47 12.388 306.35 12,441 306.00 1 2 . 519 304,85 12.585 304.41 12.604 304.26 12.624 303.08 12.644 302.69 12.675 302.50 12.678 303.57 11.011
21.I 0
12.705
303.11
22.04 24.03 28.11 34.99
12.710
303.12 302.92 302.45 302,32
12.732
12.765 12.786
a few degrees above zero. In the light of independent evidence, however, there is little reason to doubt that a similar departure from the linear woula have been observed under ideal conditions.
FIG.2
Desorption The sorption run was extended for the long period of five weeks in the hope that the change of sorption with pressure could afterwards be examined under equilibrium conditions. It is clear from the foregoing that this was not actually realized, but on the thirty-fifth day, the rate of sorption, though still detectable, was so far reduced that it could be neglected without involving serious error. The procedure consirted in repeatedly distributing the gas in the wool tube to the evacuated gas-pipette. The pressure was thus in the
116
D. H. BANGHAM AND F. P. BURT
course of some hours reduced to about 5 mm. Fig. 3 show the course of the desorption process as carried out. Both the sorption-value ( 8 ) and the pressure (p) are shown plotted against the time, the zero of time coinciding with the moment of the first distribution. The graphs indicate that an instantaneous or very rapid evolution of gas accompanied each fall of pressure, and was followed by a slow further desorption. The evolution of gae was in no case complete when the next step was made, and this is indicated by the course of the extrapolation of each line beyond the experimental region. The desorption at each stage ie thus a composite quantity representing the cumulative effect of the pressure history. In order to elucidate any relationships
12.4 11.6
10.8 10.0
FIG.3
existing between s and p it seemed best to select for comparison values corresponding to equal times after each distribution; and further, to isolate the specific effect due to each individual fall of pressure from the surviving effects on which it was superimposed. In the following table (Table 11) the logarithms of the 2 - and ro-minute values of s and p as read (in the latter case) from the graph a t A1, A2, A3 . . . and B1, Bz, Bat . . . are shown in comparison with those of the corresponding values of s’ and p’, taken from the overlying extrapolated sections of the graph at A’l, A’z, A’S . . . and B’l, B’2, B’3 . . . The vertical lines across the diagram indicate the times at which the successive pressure reductions were made. The constancy of the quotient Alog p/Alog s (which is the index of s in the Freundlich equation s”/p = constant) implies the validity of this expression over the range of s covered by the experiment. Although this range was small the agreement is surprising in view of the wide departure from equilibrium conditions. On account of the difficulty of obtaining accurate early readings it was to be expected that the deviations would be greater in the 2 minute table; but, even here, the two most discrepant values are those in-
SORPTION BY GLASS
TABLEI1 t = 2 mins. log 8‘
1st distribution 2nd ” 3rd ” 4th ” 5th ” 6th ” 7th ” 8th ”
I . 1067 I ,0931 I . 0766 1 . 0 6 1j 1.0484 I . 0364 1.0249 1.0154
1st distribution 2nd ” 3rd ’’ 4th ” 5th ” 6th ” 7th ” 8th ”
I . 1067 I . 0930 I . 0763 I ,0611 I . 0481 I . 0361 I .0244 1.0149
log s
1,0945 1.0799 I . 0661 I .OSIO
I . 0380 I
,0276
I
,0170
I
,0090
1% P‘
log P
n*
2,479
21.3 20.4
1.957 1.699 1.459 1 ‘ 243 1,059 0.903
2.219 1.951 I ,687 1.446 I . 230 1.023 1.875 0.740
2.479
2.220
20. I
2.220
.952 1.693 1.455 I . 236 1.049 0.892 0.778
18.9 20.3
2.220
25.7
24. I 22.1
25.0
23.3 25.4
t = 10 mins. I ,0938 I . 0788 1 ,0634 I ,0489 I . 0367 I ,0256 I ,0162 I . 0079
1.957 I . 701 I . 462 I . 248 I ,061 0.908
I
20.2
19.8 19.0 20.6 18.7
volving the most serious extrapolations. It is further evident that n is a decreasing function of the time, tending towards a final lower limit. In attempting to arrive a t this value we extended the observations after the eighth distribution for a period of two days at the end of which the rate of desorption was barely detectable. The final values of log s and log p were :log S=0.9919 log p=1.029 and these, taken in conjunction with the initial values log s=1.1067 1% P = 2.479 lead to the value n = 12.6, which is remarkably close to the constant of the time equation for the sorption process, viz: m = 12.8.
Other Sorption Experiments with Ammonia As a first attempt to interpret the empirical time equation and at the same time to introduce the pressure as a variable, the assumption was made that a controlling influence in the sorption process was the number of molecular impacts received by the wool. Under constant pressure this number would be proportional to the product pt, and under varying pressure to
s
p.dt
which could be evaluated from our data.’ This idea proved of great service The use of this integral expression enabled us to evade the difficulty of assigning a time origin to the high presmre experiments, in which the gas was introduced to the wool by the necessarily slow process of evaporation. During this process frequent observations of pressure and time were made and the value of Jp.dt determined by a graphical method.
118
D. H. BAKGHAM A K D F. P. BURT
since it enabled us to impose conditions resulting in a much wider variation in the sorption than would have otherwise have been possible. While we have found it convenient to apply the same treatment to the data for other gases it should be remarked that the results leave it an open question whether the above kinetic assumption is entirely justifiable. Three further experiments were carried out, at initial pressures of 16, 20, and 600 mm. respectively. As a result of these experiments the following regularities became apparent :( I ) log s plotted against log
s
p.dt yielded in each case lines which were
initially straight and parallel, with slopes leading to values of m not very different from 12. (2) The Freundlich expression when applied to s, p values for times equidistant from the beginning of each experiment led to a value of about 6 for the index constant. (3) The Freundlich expression when applied to s, p values for times corresponding to equal values of constant.
s
p.dt led to a value of about
(4) For equal values of the product pt
12
for the index
s:
p.dt, where pt represents the
momentary pressure, the value of s was found constant. t
Srn
These four relationships are summarised in the equation - = k S p.dt, Pt 0 where the value of m is about 12. This equation implied :( I ) That in experiments carried out at constant pressure the values of log s and log t would be related by a linear equation. The effect of the falling pressure would be twofold, and while the device of plotting log
s
p.dt in place
of log t would eliminate one cause of deviation, that due to desorption known to accompany fall in the value of the momentary pressure, pt., would still remain. ( 2 ) That if a number of sorption experiments were carried out a t different constant pressures, then for equal times s ' ' ~ should be directly proportional to those pressures. (3) That the equation s"/p = constant (n = 1 2 approx.) found to hold in the desorption experiment described, was a necessary consequence of the
absence of any further significant increase in the value of
s
p.dt while
desorption wae proceeding. (4) That if the values of log s from all four sorption experiments were collected and plotted against (log pt should result.
+ log
s:
p.dt), a single straight line
119
SORPTION BY GLASS
Fig. 4 shows how nearly this last requirement is fulfilled. To avoid confusion only typical points from each experiment are shown, these being indicated by different symbols for each of the four series; but in actual fact (neglecting the latter part of the half atmosphere experiment) every single one of the 140 observations taken yields a point lying between the boundary lines drawn. The ranges of time and pressure covered in these experiments are given in the following table which is arranged in the order of decreasing pressures.
FIG.4
TABLEI11 Experiment
I
(25
Jan. 1922) 2
Pressure (mm. of Hg)
Time (mins)
3.5 236. j
{ {
initial final
610.45 588.20
initial final
360.33 318.27
{
initial final
64.97 25.92
4.0 5760
{
initial final
16.25 5.47
57
2.0
1627
(25 Nov. 1921) 3 (IO Jan. 1922)
4 (20
Feb. 1922)
0.5
While the points referring t o each separate experiment are in better alignment t,han the series considered as a whole, the deviations are throughout small
D. H.
I20
B A N G H A M AND F. P . BURT
i.d4
mduchbn
hPforPprP5ssrP
o/im
0
1)
1.00 /d
,Q
))
y
.9G 4
111
*
4 ’0
o(
.9 2
,/
p’”’
g’
I
I
9.4
..
9.2Q,0°
9.0 D o
0
60
do
‘88 ’6;.
Boo
6.6
7.0
,,.*:*
1 100
..e*
I20
Yoti177d 077!!775)
1.4
.
I
7.8
140
8.2
SORPTIOK BY GLASS
121
( a ) A sorption experiment at a very low pressure was continued for about an hour when the pressure was suddenly raised from 5 . 5 mm. to 346 mm. : after a further 79 minutes the pressure was increased again to 51s mm. and 13 minutes later was suddenly reduced to 82 mm. by immersing a part of the system in liquid air. Frequent observations were taken throughout and extended until the following day. While the large number of operations involved in this experiment made it difficult to attain a high degree of precision, it is clear from the graph (Fig. 6) that here again the values of s throughout correspond closely to the demands of the formula. A straight line drawn through the points has a slope very much the same as that of the lines in Figs. 4 and s., the value of m being 12.1. The same figure shows inset the last portion of the graph considerably magnified so as to indicate more clearly the individual observations taken after the sudden lowering of the pressure. The passage of s through its minimum value is much more clearly defined than in the previous experiment and is further illustrated in the following table.
TABLEIY Time (reckoned from moment of lowering pressure) -
2.83 5.0
7.5 18.5 42.5
71.5 76.5 150.5 154.5 I365
7
c .e.
N.T.P.
8.058 8.015 7,987 7,942 7.943 7.984 7,993 8.082 8.090 8.825
log s
log (Pt Jbp.dt) (reckoned from beginning of exp.)
0.9062 0.9039 0.9024 0.8999 0.9000 0.9022
6 . 507 6.509 6.512 6.525 6.546 6.567 6.571 6.620 6.623
0.9027
0.9075 0.9079 0.9457
7 . 0 ~ 2
While the integral term necessarily increases throughout this period, it will be noticed that after the pressure reduction the increase per minute is so small (very much smaller, in fact, than the previous experiment) that the points in this neighbourhood suggest the temporary derangement of a steady state and not the final breakdown of the relationship. Experiments with Carbon Dioxide The paper already referred to contained the results of ten sorption experiments carried out at a series of nearly constant pressures ranging from 6 mm. to 655 mm. A desorption experiment with this gas was also described, in which, however, considerably longer and approximately equal times (24 hours) were allowed to elapse between the successive pressure reductions. Under these conditions the quantities of gas remaining fixed at the end of each
I22
D. H. BANGHAM AND F. P. BCRT
step were found to be related to the corresponding pressures by the Freundlich equation s”=k’p, n having the value 4 . 2 . Although, qualitatively, the behavior of this gas suggested close analogy with that of ammonia, two complicating features presented themselves. ( I ) A conspicuous variation of the index m. Since this index assumed larger values a t higher pressures, the variation could not be attributed to the fall of pressure accompanying sorption, because this fall of pressure, being relatively greater in the low pressure experiments, would have tended to depress the later sorption values in such cases.
( 2 ) Values of s for equal times, taken from the ten sorption experiments, were not related, even approximately, to the corresponding pressures by the Freundlich equation. The graphs obtained by plotting log s against log pt, (where pt is the momentary pressure a t time t ) for t = minute ~ and t = 3 0 0 0 minutes, are represented in Fig. 7 by black circles and heavy lines. For purposes of comparison the desorption line obtained after sorbing for 3000 minutes at about % atmosphere pressure is also depicted. The marked divergence between this line and the sorption curve for 3000 minutes emphasizes the reluctance of the sorption to assume a value dependent only on the pressure and independent of the past history. Thus after 3000 minutes the rate of sorption is extremely slow, while the rate of desorption is barely detectable 2 4 hours after the pressure reduction has been made. From the above considerations it will be clear that the pressure-sorption curve for 3000 minutes is subject to systematic error which, though negligible a t the high pressure end, is considerable for lower pressures where the pressure-fall is relatively great. A comparison of the straight desorption line with the sorption curve for 3000 minutes clearly indicates that an experiment which starts a t a higher
SORPTIO?; BY GLASS
123
and ends at a lower pressure will lead (other thinps being equal) to larger sorption values than one carried on throughout at the lower pressure. To make the proper correction for this pressure irregularity would almost certainly demand complete knowledge of the mechanism of the processes involved. Failing this, we have used a method of treating the data which, we believe, leads to results considerably closer t o the ideal than the experimental ones. The method of correction was, briefly, an attempt to reduce the timesorption measurements to constant pressure, the initial pressure being chosen in each case. The corrections involved were twofold :-
0.7
0.1
-1.9
-1.7
-1.5
-1.3
-1.1
( I ) The sorption value was assumed a t any time to adapt itself to the momentary pressure in accordance with the (Freundlich) equation found t o hold in the desorption experiment : deviation of the “momentary” pressure from the initial value was corrected for on this basis. These corrected sorption vadues will be given the symbol s,. ( 2 ) Following the indications of the ammonia experiments that the number of molecular bombardments, rather than the time, was the controlling
factor, values of the expression log (-
I
J;p.dt)
were plotted instead of
PinitisI
log t. These corrected times will be given the symbol t,. As regards assumption
(2)
evidence ill presently be given that
s
p.dt is
D. H . BANGHAM AND F. P. BURT
124
possibly not without significance in the case of carbon dioxide. In any case the correctjons involved here are small. In defense of assumption ( I ) may be urged the experimental evidence that Freundlich’s law is obeyed when the pressure is lowered by successive steps, but it is more difficult to justify the use of the index 4.2, found in the desorption experiment, as a fundamental constant depending only on the nature of the gas and the sorbent. I t is possible that this index varies with the previous history of the sorption; that is to say, with the time of contactj of the sorbent with the gas, and with the pressure of the latter. It should be remarked, however, that a large variation of this index would affect the corrected results but little. The effect of these corrections was to make the lower pressure log s, log t graphs somewhat steeper : whatever the pressure, linearity was not visibly affected between log t , = o and log t,=3, but it was noticed that for log t,= 3.477 (tj,=3000 minutes) the points fell a barely perceptible distance below the straight lines drawn. The values of both the experimental and the corrected reciprocal slopes are given in Table V.
TABLETT
a log t a log s
Values of m =m=-
Initial Pressure (mm. of Hg)
a log t a log s
from experimental log s, log t graphs
384
13.9 13.2
346 231.5 111.7 54.5
13.1 12.35 11.8 10.6
23.3
10.3
17.2
IO. I
655
6.19
IO.
5
m=(
-)
a log to a log sc
from corrected log E, log t graphs
13.8 13.2 13 . o 12.2 11.5 IO. I
9.5 9.4 8.9
From the constant pressure graphs (which are not reproduced here) a series of corrected log s, log p values was deduced for t, = I O , 100,1000 and 3000 minutes respectively: these are indicated by the white circles in Fig. 7. For t, = I minute the corrections are negligible and the points therefore coincide with the uncorrected ones. I n drawing smoothed curves through the points, licence greater than experimental error was required only in the case of one experiment, namely that in which the initial pressure was I I I . 7 mm. It is noteworthy that this was the first experiment of the carbon dioxide
SORPTION BY GLASS
12j
series, and for that reason may not have been quite comparable with the others.' The corrected log s, log p curves show certain well-marked regularities: not only are the horizontal intercepts between any pair of curves independent of the ordinate value, but they are actually proportional to the difference in value of log t, for the pair considered. These relations are manifest in Table VI which was compiled from the smoothed curves.
TABLEVI Carbon dioxide. (1)
(2)
logsc
(3)
Data from corrected log sc, log p curves. (4)
-----log---p-
(5)
(7)
(6;
to =IO00
1 .50 1 .40 -I .30
-
I .20
j 2.627 2.393 2.185 1,985 1.423 1,246 1.072 0.897
2.677 2,426 2.200
1.985 1.787 1.223 1.050 0.875
2.757 2.475 2.226 2.003 I . 791 1.591 1.032 0,855
(10)
A 1% P
~
0.40 0.30 0.20
(9)
(8)
to =SO00
2.852 2.551 2.275 2.029 1.805 1.590 1.392
2.747 2.450 2.172 I . 930 I . 708 1.498 1.301
0.835
0,740
For over-all range from t = I to t = 3000,
I{
(horizontal intercepts between pairs of curves) t c = i o t c = I o o tc=Iooo ' t c = 3 0 0 0 to to to to tc = I t c = I O to = I O 0 t c = I O 0 0
{
{
{
,206 ,201
,193 ,200
.I98
I
,200
,196
(,"il: :),.
I 05 ,101
202 ,200
,200
,197 ,194 ,196
,198 ,199
,103 ,099 ,097 ,092 ,091
,191 ,195
,197
,095
. I97 ,201
= 3.477 = 5.04
~
0.690
Column ( I ) gives selected ordinate values and columns ( 2 ) to (6) the corresponding abscissa values for log t, = o , I .o, 2.0, 3.0 and 3.477, while columns ( 7 ) to ( I O ) give values of the intercepts (Alog p) between pairs of adjacent curves: these values therefore correspond to differences in log to of 1.00,1.00, and 0.477, respectively. The ratio
1.00
t, (-aa log ) log p
sc'
or in the limit, the
1 At the end of this experiment the gas expelled from the wool by heating was condensed in a small bulb a t liquid air temperature and afterwards measured in the pipette when the original volume was recovered to within about 50 cc. This small discrepancy may have been due to the presence of residual traces of ammonia in the wool, since a minute white deposit (poxsibly ammonium sulphate) remained in the small bulb after evaporation of the carbon dioxide.
D. H. BANGHAM A S D F. P. BURT
126
quotient
a log (””””> / (-) log p t a log t, S,
is remarkably constant’ and approxip’ mates very closely to the integer 5. These considerations imply that log s, log t graphs for strictly constant-pressure experiments would have the same properties as the log s,, log p, graphs in Fig. 7 , the curvature being only a question of degree; so that for equal values of s the tangents to the curves would be parallel instead of forming greater angles with the abscissa axis as the pressure diminished. It follows that in such a series of experiments the 8
rates of scrption for equal values of s should be proportional to - - . (;::)P, that is to p5.0,since, at constant s, the partial differential coefficient is con-
’t
I
stant, while - varies as p5.0.
t
.4 0
30
.2G
.l c
C
FIG.8
Since the above relationships lead to the unlikely conclusion that any limiting value of s would be independent of the pressure it follows that they can be characteristic only of the initial stages of sorption; those stages, in fact, with which our experiments deal.
Complex Experiments The above considerations may be summed up in the statement that, as far as constant-pressure experiments are concerned, log s is a single-valued function of the expression (5.0 log p+log t), over the experimental range. Thuslogs,plottedagainst (5.0 log plnltlitl +log t,) yields a smooth curve embracing observations at all times and pressures; this complex curve being built up overlapping sections contributed by the various sorption experiments. h 1This relationship recalls a t once the behaviour of ammonia since it implies that, in the event of the sorption values (for equal times) obeying Freundlich’s equation, the coefficient d log t or index should be independent of the pressure. d log s p
(-)
SORPTION BY GLASS
127
section of this curve appears in Fig. 8 and will be referred to later. The curvature is everywhere so slight that a variaticn in s of 2 : 1 (the order of variation observed in our experiments at nearly constant pressure) is required before it becomes noticeable. The above expression could hardly apply to experiments in which the pressure was varied discontinuously if p is taken as representing the momentary pressure a t time t. The equation log s = f(4.0 log pt+log
s:
p.dt), on the other hand, while yielding a graph identical
with the first as far as constant-pressure experiments are concerned, is also sensitive to variations in the past pressure-history : it should hold accurately if such past history is fairly represented by the number of molecular bombardments received by the surface. I n order to test the validity of this second equation an experiment was carried out in which the pressure was varied discontinuously. The nature of this complex experiment may be indicated as follows: From
)’
s
”
o to 2866 minutes pressure = 111.71 falling to 104.44mm. 9 ) ,, 373.42 ,’ 2866 to4410 ’) ‘377.1 4410 to 4530 ” =531.86 ” ” 531.55 ,’ ’)
)>
p.dt was evaluated up t o the time of each observation, and the log s values
plotted against the expression (4.0 log pt+log
s:
p.dt. Fig. 8 shows the
result of this treatment, the white circles referring to the experiment in question. The full line is the graph of log s, against ( 5 log pln,tl,!+log t c )and , if the equation log s =f(4.o log pb+log[p.dt)
were strictly valid, all points should
0
lie on this curve. The diagram indicates how, after each pressure-increase, the points, widely divergent at first, approach the curve gradually. The final, isolated point, obtained after the first pressure-increase, is seen to approach the curve very closely. After 1497minutes at the new pressure the sorption has reached a value which it would have attained only after 578 days a t the lower pressure. Following the second pressure-increase the observations were continued for a further 1 2 1 minutes only, yet the divergence of the final point from the curve is very small. To reach this value of s a t the original pressure would have required nearly seven years (assuming the relationship found to be valid throughout). On this evidence one may reasonably regard
s
p.dt as a useful measure of past pressure-history when the pressure changes
have not been too large or too sudden: it fails immediately after an abrupt pressure change through not being sufficiently sensitive to small time-increments a t the higher prcssurc. The black circles in Fig. 8 indicate the results of the desorption experiment when plotted in the manner outlined above. The isolated black circle refers to the last observation taken before the first pressure reduction was made. The tendency to approach the line, but this time from the opposite side, is
I28
D. H. BANGHAM AND F. E’. BURT
again apparent. The first points, immediately after the first pressure reduction, lie well above the line, while subsequent ones approach it. The last observation of this series was made 24 hours after the first pressure reduction, and immediately before the pressure was reduced for the second time. At each pressure reduction the process repeats itself, the divergence from the curve becoming greater each time. As was the case with ammonia, the equation arrived at on the basis of the sorption experiments fails on reducing the pressure, through its inability to account for the slowness of the desorption process. It was remarked in the previous paper1 that the amount of gas disengaged a t each desorption step is adequately represented by the equation r log E = log t+constant ( 4 being the quantity desorbed at time t after the last pressure reduction) as long as t is not too great. For large values of t those of [ were found greater or less than demanded by the equation, according as gas was being desorbed or sorbed a t the moment the pressure reduction was made. It is interesting, therefore, to note that similar regularities apply tc the sorption-increment in the experiment in which the pressure was suddenly raised after two days sorption at a steady lower pressure. Thus log (sorption increment) plotted against log (time from moment of increasing pressure) yields a line initially very straight (over the time-range one) to some hundreds of minutes) but thereafter becoming definitely convex to the log t axis. While this behaviour points to considerable analogy between the process of sorption and that of thermal conduction, or diffusion, attempts to apply the same principles in resolving into simple “waves” the sorption effects following abrupt pressure changes have so far led to disappointing results. It is interesting to note, however, that certain other very simple phenomena display these curious characteristics of the sorption process. Thus the slow stretch of rubber, glass, and of metal wires, under constant load, has been shown to follow a logarithmic instead of an exponential law.2 Philips3, who further investigated this subject, makes the following remarks:--“When two loads are put on successively their effects are not exactly superposable, but just after the second load is put on, the effect is a s if the last load only were acting, and then it gradually alters till finally the effect is the same as if both loads had been put on simultaneously.” If one substitutes “pressure-change” for “load,” this statement summarises not inaptly the results of the complex experiments described in this paper. We are anxious to express our great indebtedness to Mr. W. Sever, not only for the large amount of assistance which he gave us in the experimental work, but also for the many ingenious devices leading to increased accuracy and saving of time which he invented and made. 1 Proc. Roy. SOC.105 A, 487 (1924). 2Phil. Mag. 8, 538 (1904). Phil. Mag. 9, 529 (1905).
SORPTIOR- BY GLASS
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\Ye wish also to acknowledge here the receipt of grants from the Royal Society‘s Committee and from the Brunner Mond Research Fund, which partly defrayed the expenses of this investigation.
Summary The rate of sorption of ammonia by a glass surface a t o°C. was measured a t a number cf different and approximately constant pressures. The ret
latjonships”=k p . 1 p.dt, where s js the sorption-value a t time t , pz the 0
momentary pressure and .m a (nearly) constant number of about 1 2 , was found to hold for all pressures and times over the experimental range investigated. Except for a temporary derangement, the equation was still found applicable when the pressure was suddenly increased or diminished in the middle of an experiment. Similar experiments with carbon dioxide yielded analogous results. With this gas, however, the index m was not constant but varied appreciably with the pressure, to which the sorption-value was much more sensitive. While for strictly constant pressure experiments with ammonia it was concluded that log s would be a (nearly) linear function of log (pt), for carbon dioxide, under the same conditions, log s would be a (non-linear) function of log (p,”). Chemistry Department, I‘nir-ersity of Manchesier
