T H E INFLUENCE OF ADSORBED FILMS ON RATES O F EVAPORATIOK BY RONALD PERCY BELL
Introduction In a previous paper1 it has been shown that it is possible to investigate the adsorption of solute at the interface of a solution by a study of kinetic phenomena taking place at the interface. I n this case the phenomenon studied was the velocity of a reaction taking place a t the interface, and the present work is an attempt to evolve a method of more general application for the investigation of adsorption from solution, by studying rates of evaporation. As was pointed out in the previous paper,* the most striking general conclusion arrived a t by applying the Gibbs adsorption equation to the surface tension curves of solutions of non-electrolytes is that above a certain limiting concentration, the excess surface concentration becomes constant, presumably corresponding to the formation of a “saturated” monomolecular film such as is known to exist in insoluble films on liquid surfaces and films of gases on solid adsorbents. It would therefore afford valuable support of the Gibbs equation if the existence of stable soluble films over a range of concentrations could be confirmed independently, and the work described in this and the preceding paper is directed especially towards this point. I t has been shown by RideaP and Langmuir‘ that the rate of evaporation from a liquid surface is influenced by the presence of an insoluble monomolecular film. The use of such methods for soluble presupposes a certain degree of stability in such films, which seems justified by the fact that both static and dynamic methods of measuring the surface tension of solutions leads to the same results. The work of Lenard6 shows that adsorption a t a newly formed surface is complete in IO-^ - IO+ seconds, so that any small disturbances of the film will be very quickly repaired. It is probable that at high concentrations of solute a film is formed more than one molecule thick, which will have no further effect upon the surface tension although it may influence the kinetic relationships. It is probable, however, that the forces holding the first layer of molecules together are considerably greater than those for subsequent layers, and that this greater stability of the monomolecular film will give it a prodominant influence upon kinetic processes. The process of evaporation takes place in two stages, the escape of molecules from the liquid phase t o the gas phase, and the removal of vapour from Bell: J. Phys. Chem., 32, 882 (1928).
* Bell: loo. cit., p. 889.
Rideal: J. Phys. Chem., 29, 1585 (1925). ‘Langmuir: J. Phys. Chem., 31, 1719(1927). Lenard: Sitzungber. Akad. Heidelberg, 5A 28 Abhand. 28, p. 16 (1914);also, “Ueber die zeitliche Aenderung reiner Flussigkeitsoberdachen.” Diss. Heidelberg (1913).
IO0
RONALD PERCY BELL
the surface of the liquid. As has been pointed out by Rideall and Adam,2 only the first of these stages will be influenced by the nature of the interface, so that in order to detect this influence experimentally, the rate of removal of vapour from the surface must be an appreciable fraction of the “ideal” rate of evaporation. The “ideal” rate is the rate of evaporation in vacuo, or the rate of interchange between the two phases when the liquid is in equilibrium with its vapour, and according to the kinetic theory is given by the Herz-Knudsen equation, R = P. 0.0583 where R = ideal rate in grams per sq. cm. per second. P = vapour pressure in millimetres of mercury. M = molecular weight. T = absolute temperature. This accounts for the fact that Hedestrand3 found no reduction in the rate of evaporation of water which was covered with an insoluble monomolecular layer of oleic or palmitic acid, since (as was pointed out by Rideal and by Adam) the maximum rate he measured was 5.05 X IO+ grams per sq. cm. per second, while the ideal rate for water a t 20OC. is 0.253 grams per sq. cm. per second. Hedestrand thus only obtained 0.002370 of the ideal rate, and the fact that he obtained a concordance of 1% between the values obtained with and without a film present only shows that the rate of escape was not, diminished to less than 1/5ooth of its normal value by the presence of the film. Rideal studied the influence of films of lauric, stearic, and oleic acids upon the rate of evaporation of water, and by removing the vapour by condensation, he obtained rates of about 0.47~of the ideal rate. Under these conditions he found that the films of acid caused reductions of about 20-soy0 in the rate of evaporation, These positive results, together with the negative results of Hedestrand, show that insoluble surface films exert a large retarding effect upon the rate of escape of water molecules into the gas phase, but that this retarding effect is only apparent in the rate of evaporation when the latter is an appreciable fraction of the ideal rate. It has been suggested, however, that in dealing with the evaporation of a component from solution (as opposed to that of a pure solvent) other factors may lead to a reduction in the evaporation rate in the presence of surface films. Langmuir4 has studied the rate of evaporation of aqueous ether solutions in presence of different insoluble films, using relatively slow air currents. Although the rates of evaporation of ether obtained were only about IO-^ times the ideal rate, it was found that each of these films caused a reduction of the order of 80-90yc. (As would be expected from Hedestrand’s results, the rate of eva’Rideal: J. Phys. Chem., 29, 1585 (1925). *Adam: J. Phys. Chem., 29, 610 (1925). 8 Hedestrand: J. Phys. Chem., 28, 1245 (1924). ‘Irving Langmuir and D. B. Langmuir: J. Phys. Chem., 31, 1719 (1927).
ADSORBED FILMS AND RATES O F EVAPORBTION
IO1
poration of the water was not affected.) Langmuir therefore supposes that the films cause retardation not directly by influencing the rate of escape, but by preventing convection currents in the neighbourhood of the surface. This may be expressed by saying that in the case of evaporation of a solute, the resistance caused by the presence of a surface film is due not only to the film itself, but also to a layer of solvent molecules adjoining it. The present work uses the evaporation of chlorine from dilute solutions in carbon tetrachloride, thus avoiding complications due to association or ionisation. The vapour is removed from the surface by a current of air, and the rate of evaporation of the chlorine determined by passing the air current into an absorption apparatus containing potassium iodide solution, and titrating the iodine liberated. Before studying the effect of adsorbed films in a quantitative manner, it is necessary to consider the kinetics of evaporation in a current of gas. Very little theoretical or practical work has been done on this subject, and a rigid application of the laws of gaseous diffusion to the problem leads to differential equations which appear to be insoluble. However, by making several amplifying assumptions, Jablczynski and Przemski' have obtained a semiempirical equation which is in good agreement with their experimental results. They deduce the equation - K .\/i log10 -Po - P
Of a different nature is the work of C. Bohr2 on the invasion and evasion coefficients of solutions of gases. He defines the evasion coefficient y as the amount of gas which would escape in unit time from unit surface of a perfectly stirred solution of unit concentration into a space containing none of the gas in question,-Le., the ideal rate of evaporation for a solution of unit concentration. Bohr measures the evasion coefficients for aqueous and alcoholic solutions of carbon dioxide by passing a current of air over the surface of the stirred liquid. It is obvious, however, that the rates which he measures are not true evasion rates. For example, using a saturated solution of carbon dioxide in water a t o°C., he finds for y the value 0.077 ccs. per minute per sq. cm. for a solution containing I cc. carbon dioxide in 1. cc. solution. This equals 2 . 5 X IO^ grams per second per sq. cm., while the value calculated for the ideal rate by the Herz-Knudsen equation (equation (I)) is 10.4grams per second per sq. cm. Thus under the conditions of Bohr's experiments, evaporation takes place a t only about IO-^ times the true rate of evasion, and must therefore be considered essentially as a diffusion phenomenon. Bohr has also defined the invasion coefficient (0)as the amount of gas at 7 6 0 mm. pressure which would dissolve in unit time in unit area of perfectly stirred liquid containing none of the gas in question, and measures these invasion coefficients by passing carbon dioside over stirred water. Here 1
Jablozynski and Przemski: J. Chim. phys., 10,241 (1912). (1899); (4) 1, 244 (1900).
* C. Bohr: Ann. Physik, (31, 68 500
I02
ROSALD PERCYBELL
again it is obvious from the values obtained that the case is essentially one
of diffusion within the liquid, and not of true invasion. If fl and y are respectively the true invasion and evasion coefficients, and LY is the coefficient of absorption, then for equilibrium] Y = LYP Bohr finds an approximate agreement with this relation using experimentally determined values of fl and y, from which he concludes that they correspond to the quantities he defines, and that there is no undisturbed layer at the gas-liquid interface. However, all the experiments were conducted under constant conditions of stirring, air current, containing vessels, etc., and it is certain from the results of other workers that had he varied these factors, different evasion and invasion coefficients would have been obtained. The approximate agreement between y and afl can only be attributed to a chance relation between the velocities of diffusion of carbon dioxide in air and water under the unvarying conditions of the experiments.
Practical Part
Materials. Chlorine was prepared by the action of concentrated hydrochloric upon pure potassium permanganate, and was washed with water and dried with concentrated sulphuric acid and phosphorus pentoxide. It was found that a tenth-molar solution of chlorine in ordinary pure carbon tetrachloride speedily became cloudy and deposited globules upon the glass. This did not occur if the carbon tetrachloride was previously dried over phosphorus pentoxide and distilled, but a solution approximately M/jo prepared in this way was found to undergo a continuous diminution of apparent chlorine concentration on keeping, to the extent of about 1 % per day. This instability of solutions of chlorine in carbon tetrachloride has previously been noticed by Plotnikow’ who attributed i t to reversible photochemical reactions. Griiss2 has shown however, that Plotnikow’s results were due to traces of an unknown impurity in his carbon tetrachloride, and that by a rigorous purification stable solutions could be obtained. Since the method of purification employed by Griiss is very laborious, experiments were carried out with a sample of carbon tetrachloride purified specially for medicinal purposes supplied by Messrs. Albright and Wilson. This was dried over phosphorus pentoxide] distilled, and used to prepare chlorine solutions as before. At intervals I O ccs. of solution was pipetted out and run into an excess of potassium iodide solution, the iodine liberated being titrated with N/IOOsodium thiosulphate solution. It was found that there was no steady decrease in chlorine concentration. The method finally adopted for preparing pure carbon tetrachloride was as follows. The “medicinal” grade was dried for twenty-four hours over phosphorvs pentoxide] and was then poured off and fractionated. Only the Plotnikow: Z. wiss. Phot., 19,
22
(1919).
* Griiss: 2. Elektrochemie, 29, 146 (1923).
ADSORBED FILMS AND RATES OF EVAPORATION
103
middle fraction (about 90% of the whole) boiling over a range of not more than o.ofC. was retained. The apparatus used to prepare the chlorine solutions is shown in Fig. I . The ground-in top of the flask A and the ground joints B and D were lubricated with syrupy phosphoric acid, while the top of the vessel G and the joint H were not lubricated a t all, H being held together by an external coating of cement. The concentrated solution thus obtained was a t once transferred
FIQ.I
t o a large glass-stoppered flask and diluted to the required extent. When it was required to transfer from the large flask, it was forced over by dry air under pressure, thus minimising any loss of chlorine. Apparatus. The apparatus used for determining the rates of evaporation is shown diagrammatically in Fig. 2 . The air current used was produced by the rotary blower A, and, the volume of air passing through the apparatus was measured by the meter C. In order to indicate the pressure of the air leaving the meter, a manometer containing carbon tetrachloride was attached to the capillary tube F. The oil-trap E contained glass wool, and during the first few experiments was immersed in a freezing mixture to remove oil spray vapour derived from the blower. However, nothing was found to condense except a little water, so that in subsequent experiments the freezing mixture was omitted, although the oil-trap still formed a part of the circuit. The air wm dried
I04
RONALD PERCY BELL
by passing through the calcium chloride tube G, about 1.5 metres long. The spiral H immersed in the thermostat was of thin-walled glass tubing about 3 metres long and I cm in diameter. It was fused on to the presaturator J, in which the air current passed over the surface of pure carbon tetrachloride. The air current was thus brought to the temperature of the thermostat and approximately saturated with carbon tetrachloride vapour, so as to avoid appreciable loss of carbon tetrachloride or cooling effect in the evaporation bulb. Preliminary tests showed that both the temperature attainment and saturation were practically complete.
J
FIG.2
The tube K was connected to the evaporation bulb L by a short piece of rubber tubing just above the thermostat level. (The air current only passed through rubber joints before it entered the evaporation bulb.) The bulb was designed to give a high degree of hydrodynamic stability, and had a mark etched around the neck. It was always clamped in a fixed position, so that the liquid surface was exactly reproducible. It was found that the surface remained steady with air currents up to 15 litres per minute, provided that the velocity was constant. If, however, any fluctuations took place in the speed of the motor, the surface was immediately disturbed, and no significance could be attached to the results obtained. Many experiments had to be rejected for this reason. To indicate the pressure of the air in the evaporation bulb, a manometer was attached to the capillary tube 0 . The tube between the evaporation bulb and the ground joint 11 was heated electrically.
ADSORBED FILMS AND RATES O F EVAPORATIOlV
IO j
The tap 'c' was lubricated with phosphoric acid, with a narrow layer of vaseline a t the top and bottom to prevent deliquescence. The other taps were lubricated with ordinary tap-grease, as they did not come into contact with chlorine. The spiral, presaturator, and evaporation bulb were in an electrically controlled water-thermostat a t z j.00 =tO . O I O C . Preliminary Experiments. The motor blower was tested for constancy of running and i t was found that after a small gradual decrease in the first 3 - j minutes, the velocihy remained constant with fluctuations of less than 1%. The type of apparatus used for absorbing the chlorine from the air current is shown in Fig. 3 . The ground joint A, lubricated with phosphoric acid,
FIG.3
fits on to ?VI in Fig. 2 . The bulb B was packed loosely with glass wool to prevent splashing, and the flask C served to check the completeness of absorption. The absorbent used was a solution of potassium iodide containing 50 grams per litre, and the back pressure was about 2 - 5 millimetres of mercury with slight fluctuations. The efficiency of absorption was tested under conditions similar to those in actual experiments, and was found to be practically 100%. There was never enough iodine liberated in the small flask to give any colouration with starch solution, which also points to 100% absorption.
First Series of Experiments. Thwe experiments were all carried out with the same solution of chlorine, using different velocities of air current. The solution was brought to the temperature of the thermostat in a small glass-stoppered flask, while the motor was allowed to attain constant running, by blowing air through the first by-pass D (Fig. 2 ) . The solution was forced over into the evaporation bulb by dry air under pressure, and the air current was passed for about one minute through the bulb and out via the second by-pass N in order to evaporate the chlorine from any solution adhering to the walls of the bulb. The thermostat heating current and the thermostat stirrer were both switched off for a few minutes, so as to avoid electrical disturbances of the blower and mechanical disturbance of the liquid surface. Absorption was then carried out by closing the tap 'c' for 1-3 minutes, the exact time being taken by a stop-watch. During the absorption the two manometers were read to the nearest 0.5 millimetres. The absorption apparatus was removed and its
I 06
RONALD PERCYBELL
contents washed out into a titration flask: it was then refilled again with potassium iodide solution and fitted again to the rest of the apparatus. The run was then immediately repeated, proceeding exactly as before, and the two lots of iodine titrated. Calculation shows that the amount of chlorine evaporated during a pair of runs was always less than 1% of the total chlorine in the bulb, so that it was legitimate to consider the concentration of chlorine in the solution as constant throughout each pair of runs. Every time the flask in the thermostat was refilled, IO ccs. of the solution was titrated, and the chlorine concentration for the first series of experiments was taken to be the mean of the values thus and no downward trend. obtained, which shows an extreme variation of 17~ The barometer was read and the temperature of the meter taken directly after each run. The pressure of the air leaving the meter (PA)and the pressure in the evaporation bulb (PB) were calculated, and the volume of air which passed through the meter, corrected to 2 j C. and pressure PB. The following is a typical example of the figures obtained for one determination (first half only). Run No. X Meter Manometer Time Barometer Temp. 96743 A 18.0 - 3.0 = 15.0 mm. I min. 41.7secs. 763.3 mm. 13.6c. 96748 B 2 2 . 0 - 11.0 = 11.0mm. = 1.70 mins. Titrations Bubbler 1st 0.00 ccs. and 27 .IOccs. 2 7 .IO ccs. Flask
None
+ X 1.63/13.6} = 763.3 + 1.8 = 765.1 mm. Pg = 763.3 + (11.0 X r.63/13.6) = 763.3 + 1.3 = 764.6mm. PA = 763.3
(15.0
Velocity of air current (v) = { 15/1.7o) X (298.0/286.6} X (765.1/764.6} = 9.18 litres per minute.
Msss of chlorine absorbed
= 27.10 X 0.0002371 =
0.006428 grams.
Rate of evaporation (R’) = o.oo6428/101.7 = 0.00006322 grams per second. When the values obtained for R’ were plotted against the corresponding values for V, it was found that the points become more and more erratic as V becomes greater, probably owing to disturbance of the surface a t these high velocities. I n the final results, therefore, only points cotresponding to a velocity of air current less than I1 litres per minute were retained. “Ceteris paribus,” it is obvious that the rate of evaporation will depend upon the pressure of the gas passing over the surface, since this will affect the diffusion coefficient of the chlorine. Therefore, in order to make the above results strictly comparable, it is necessary to apply a small correction for the variations in PB, the pressure over the surface. Since the theoretical
ADSORBED FILMS AND RATES OF EVAPORATION
107
equation connecting the rate of evaporation with the diffusion coefficient is not known, the true form of the correction is not known, but since the total correction is small, it has been assumed that the rate of evaporation is inversely proportional to the pressure. (Jablcaynski and Przemski' state that R CY P*, but since their experimental results give values varying from 0.289
FIG.4
TABLE I Concentration of chlorine = 0.8658 grams per litre V
Ps
7.90 8.16 8.17 8.24 8.49 8.85 9.07 9.13 9.18 9.65 9.66 9.81 10.09
764.2 748.7 748.7 762.9 764.1 762.8 764.7 754.2 764.6 764.2 j68,2 765.4 768.3 765.3 767.0
10.55 11.02 ~~
J. Chim. phgs., 10, 241 (1912).
R' X
101
5.097 5 ' 488 5.428 5.376 5.608 6.042 6.082 6.028 6.322 6.617 6.438 6.612 6.744 7.036 6.993
R X
IO
5,125
5.406 5.347 5.398 5.640 6.065 6.119 6.061 6.359 6.655 6.j07 6.659 6.823 7.087 7.058
I08
ROXALD P E R C Y B E L L
to 1.014 for the index, the matter seems very doubtful). Table I summarises the results, where R = R' X P ~ / 7 6 0
V
=
R'
=
velocity of air current in litres per minute. observed rate of evaporation in grains per second.
The corrected values are plotted in Fig. 4 (curve A ) and give points which lie far better on a curve than do the uncorrected values. Second Series of Experiments These experiments mere carried out in exactly the same manner as the first series, but with a chlorine concentration of 0.5801 grams per litre. The results obtained are summarised in Table 11, and the corrected values of R are plotted against V in Fig. 4 (curve B ) . TABLE I1
v
PB
7.88
758.7 760.4 758.3 757.1 747.4 747.9 757.6 758.4 749.5
8.03 8.29 8.58 8.65 8.79 8.88 9.21 9.35 9.71 9.88 10.31 10.73 10.98
R' X
106
3.337 3.446 3'723 3.870 3,991 3.940 4.103 4.170 4.472 4.597 4.410 4.689 4.558 4.857
750.2 750.2
759.2 759.1 758,8
R X
105
3.332 3.448 3.715 3.856 3.924 3.877 4.090 4.161 4.411 4.538 4.353 4.684 4.553 4.840
I n order to determine whether any simple relation exists between the rate of evaporation and the chlorine concentration in the solution, the values of R for round values of V were read off from the two curves in Fig. 4 and are tabulated in Table 111. TABLE I11
v
8.00 8.50
9.00 9.50 10.00
10.50 11.00
R'X
105
RII X
105
3.45 3.80 4. I O 4.34
5.19 5.68 6.11 6.48 6.76 6.96 7.08
R1/RI1 I . 50
1.49 1.49 1.49
4.52
I . 50
4.65 4.71
I . 50 I . 50
-
Mean = 1 . 4 9 6 Ratio of concentrations
=
0.865810. j801
=1.492
ADSORBED FILMS AND RATES OF EVAPORATION
109
It is thus established that for values of V between 8.0 and 11.0 litres per minute, and solutions of chlorine having concentrations between 0.5801 and 0.8658 grams per litre, RaC where C = concentration of chlorine in solution.
Experiments with trichloracetic acid solutions. The solute used for the study of adsorption was trichloracetic acid, which has a strongly polar carboxyl group .and does not react with chlorine. It was found by analysis to be a t least 99.9870 pure.
FIG.5
I n order to investigate the effect of trichloracetic acid on the evaporation rate under different conditions, the following scheme was adopted. A solution was made up by weight from a stock solution of trichloracetic acid (concentration known exactly), a stock solution of chlorine (concentration known approximately), and carbon tetrachloride. After determining the chlorine concentration of this solution by titrating a I O cc. sample, the rate of evaporation was determined by carrying out a double run as described before. The solution was then poured back into the flask, thereby losing a little chlorine, and the chlorine concentration again determined. The rate of evaporation was then again determined, and this procedure was repeated until the concentration of chlorine fell below the lower limit of the range previously investigated. Thus for each solution, a series of results was obtained corresponding to the same concentration of trichloracetic acid, but different velocities of air current and concentrations of chlorine. I n each case the rate of evaporation corresponding to the same values of V and C (in absence of the acid) was calculated from curve A in Fig. 4 and the relation
RONALD PERCY BELL
I10
This calculated rate was called R,, and the fractional decrease in rate caused by the presence of the acid is given by
x
=
(Ro
-
R)/Ro
where R = rate observed in presence of acid. At first solutions containing about I O grams of trichloracetic acid per IOO grams were used, but it was found impossible to obtain reproducible results. More dilute solutions were then used, and a series of preliminary experiments showed that the fractional reduction ‘x’was dependent upon the velocity of the air current (as would be expected), but not upon the chlorine concentration. I t was also found that for any one solution, on plotting the fractional reduction (xj against the velocity of air current (V), approximately a straight line was obtained in each case. A typical graph obtained in this way is shown in Fig. 5 . After each of the tables of results which follow is given the linear equation obtained by applying the method of least squares to the experimental results for x and 5’. The values of x corresponding to 5’ = 8.5 and 5’ = 9.0 as calculated from this equation are also given in each case.
Results I n the following tablesC = chlorine concentration in grams per litre. V = velocity of air current in litres per minute. R’ = observed rate of evaporation in grams per second. Pg = pressure over the liquid surface in millimetres of mercury. R = rate of evaporation corrected to 760 mm., in grams per second. R, = calculated rate of evaporation in grams per second. x = fractional decrease in rate, i.e. (R, - Rj/R,. TABLE IV Solution H Concentration of acid = 0.5253 grams per C
V
0.8598 0.8598 0.7554 0.5829 0.5829 0 ’ 4994 0.4994
8.15 9.02 9.04 8.73 8.02
9.72 8.76
R‘ X 1 0 6 5.286 5.577 4.978 3.808 3.617 3.263 3.191
Pa
758.6 758.3 759.7 758.8 758.9 759.0 759.5
Equation of straight line is x = 0.0983 x = 0.029 x = 0.079
WhenV = 8.50 When V = 9 . 0 0
R X 105 5.277 5 ’ 565 4.976 3 ’ 784 3.612 3.259 3 . I88
v -- 0 . 8 0 6
IOO
grams
R, x 106 5.302 6.078 5.357 3.968 3.510 3.813 3.409
X 0.005
0.085 0.072
0.042 -0.028 0.146 0.065
ADSORBED FILMS AND RATES OF EVAPORATION
I11
TABLE V Solution J Concentration of acid = 0.8594 grams per
v
C
0.8702 0.8702 0.7739 0.6037 0.6037 0.5145
8.93 8.61 8.21 8.44 9.97 7.91
R’ X
5.580 5.526 4.691 3.695 3.910 3.144
761.7 761.4 759.1 756.4 756.5 756.5
Equation of straight line is x = WhenV = 8 . 5 0 x = 0.045 WhenV = 9 . 0 0 x = 0.104
0.I I 5
100
R X 105 5,593 5,537 4.686 3.677 3.892 3.129
PB
10’ 5
V
grams R,X
10)
6.081 5.809 4.755 3.932 4.246 3.031
X
0.080
0.047 0.015
0.065 0.106 0.032
- 0.934
TABLEVI Solution N Concentration of acid = C
S‘
o 7543
8.63 8.92 8.11 8.50 8.39
0.7543 0,6829 0.6829 0 5500
R’ x 1 0 6 4.576 4.598 4.062 4.119 3,312
165 grams per IOO grams R X IO) R, x 1 0 6
761.4 761.5 760.3 760.4 759.8
Equation of straight line is x = WhenV = 8 . 5 0 R h e n V = 9.00
I. PB
x
= 0,079
x
= 0,137
0 .I 16
4.584 4.608 4.065 4.122 3,311
V
5.054 5.272
4.181 4.480 3,545
X
0,093 0.126 0.036 0.080
0.066
- 0.907
TABLE VI1 Solution F Concentration of acid = C
v
0.6616 0.6616 0.5619 0.5619 0.4820
8.66 8.12 8.33 9.11 7.94
R’ X IO) 3.894 3.923 3.302 3.394 2.732
I . 375 grams per 100 PB R x 105 760.0 3.894 760.0 3.923 759.6 3.299 759.5 3.391 758.2 2.726
Equation of straight line is x = 0.102 V WhenV = 8 . 5 0 x = 0.099 WhenV = 9 . 0 0 x = 0 . 1 5 0
- 0.857
grams R, x IO) 4.455 4.142 3.583 4.005 2.856
X
0.126 0.053 0.079 0 .I54 0,047
RONALD PERCY BELL
112
TABLE VI11 Solution K Concentration of acid = I . 800 grams per C
V
0.5364 0.5364 0.4751 0.4751 0.4634
8.97 8.11
8.37 8.87 8.49
R' x 1 0 5 3.301 3.114 2.784 2.840 2.851
PB
R
IOO
105
grams R, X
3.266 3.082 2.791 2,847
752.0
752.1
762.0 761.7 748.7
Equation of straight line is x = 0.083 V WhenV = 8 . 5 0 x = 0 . 1 0 0 WhenV = 9 . 0 0 x = 0.141
x
2.808
-
IO&
3.767 3.315 3.052 3.294 3.153
X
0.133 0.070
0.085 0.136 0 . IO1
0.604
FIG.6
TABLE IX Solution M Concentration of acid = 2 , 2 5 7 grams per C
V
0.8226
8.72 8.65 8.47 8.35 7.94 9.12
0.8226
0.7311 0.7311 0.6419 0.6419
R' x 10: 5.098 4.790 4.177 3.322 3.629 3.843
PB
765.4 765.5 765.6 765.7 764.0 764.1
Equation of straight line is x = 0 . 1 0 8 V When V = 8 . 5 0 x = 0 . 0 9 6 WhenT' = 9 . 0 0 x = 0.150
5.028
grams R, X 105 5 j77
4.826 4.207 4.348 3.648 3.864
5.524 4.799 4.696 3.804 4.597
R X
105
- 0.822
IOO
X
0.098 0.126 0.120
0.074 0.041 0,159
ADSORBED FILMS AND RATES O F EVAPORATION
T ~ LXE Solution L Concentration of acid 3.302 grams per C
v
0.7879 0.7879 0.6987 0,5435 0.5435
8.67 8.47 8.48 8.00 8.25
R
x
4.792 4.718 4.241 3.234 3.283
IOO
R X 105 4.805 4.732 4.252 3.251 3.298
P
105
763.0 763.0 761.9 763.8 763.6
grams R
X
XIO'
5.307 5,151
4.566 3.258 3.445
0.095 0.081 0.069 0.002
0.043
Equation of straight line is x = 0 . 1 3 0 V - 0 . 9 1 9 WhenV = 8 . 5 0 x = 0.095 W h e n V = 9 . 0 0 x = 0.148 The values of x corresponding t o V = 8 . j o and V = 9 . 0 0 are plotted against the concentration of trichloracetic acid in Fig. 6.
Discussion of Results The only equation previously obtained to express the variation of rate of evaporation with velocity of air current is that of Jablczynski and Przemski (Equation 2 , Introduction). I n terms of the present notation this becomes
where C, = concentration of chlorine in saturated vapour, in grams per litre. K = a constant. This equation has been applied to the results of the first series of experiments. From the present data it is impossible to obtain an accurate value for C,, but an approximate value has been obtained by extrapolating to V = zero the C - V curve calculated from the results, giving C, = 7 x IO^ (approx.). This value was used in calculating the constants given in Table XI.
TABLE XI V
8.00 8.50
9.00 9.50
R x 105 5.19 5.68 6.11 6.48
X
v
1.63
IO.00
1.71
10.50
1.76 1.78
11.00
R x 105 6.76 6.96 7 .OS
Mean =
X
1.76 1.72 I .63 -
I.
71
Thus an approximate constant is obtained although there is a distinct up and down trend in its value. (A similar degree of constancy is obtained by using values of C of 6.80 X IO-^ or 7 . 2 0 X IO-^). It was not expected to obtain exact confirmation of this equation since it only applies strictly to the evaporation of a pure liquid, and takes no account of diffusion of a solute towards the surface. For a constant value of V, equation 4 leads to the relation RaC,
114
ROSALD PERCY BELL
If we assume that the partial vapour pressure of chlorine is proportional t o its concentration in solution, (a reasonable assumption since the solutions are dilute), this relation corresponds to that which was found t o hold accurately in comparing the results of the two first series of experiments, namely, Rc.C where C = concentrat,ion of chlorine in solution. Taking the partial vapour pressure of chlorine as corresponding to a concentrat'ion of 7 X IO-^ grams per litre, the Herz-Knudsen equation (Equation I Introduction) gives 2 . 0 X I O + grams per sq. cm. per second as the ideal rate of evaporation of the chlorine. The actual rates measured in the first series of experiments were about 2 . 0 X IO-^ grams per sq. cm. per second, so that the rates of evaporat'ion measured represent about 1% of the ideal rate. The fact that reductions up t o 15% were caused by the addition of trichloracetic acid shows that the rate of evasion must have been changed very considerably, either directly or indirectly. The methods used for measuring the amount' of the retarding effect' caused by different concentrations of acid are purely comparative, so that the theory of the kinetics of evaporation is immaterial for this point. I n calculating the values of the fractional reduction 'x' given in the tables, the only assumption is that RaC which relation has been shown to have both theoretical and experimental support'. The curves in Fig. 6 therefore represent the relation between the concentration of trichloracetic acid and the retarding influence of the film formed, under strictly comparable conditions. The points do not lie very well on the curves, but since an error of 1 7in~the determination of the value of R or C will cause an average error of 10% in the value of 'x' obtained, the results are as accurate as could be expected. The form of the curves for V = 8.jo and V = 9.00 is essentially the same in both cases, and the most important point is that for concentrations above about 1.4grams per I O O grams the curve becomes parallel to the concentration axis: i.e., over this range the retarding power of the film is independent of the concentration of the acid. If we can take the retarding power as a measure of the surface density of the film, it seems very probable that this range corresponds t o the existence of a stable monomolecular surface film of trichloracetic acid. This result is in agreement with the general evidence obtained from surface tension curves, and the results of previous work upon heterogeneous reaction velocity.1 It was mentioned in the practical part that preliminary experiments with solutions of trichloracetic acid containing about I O grams per I O O grams failed to give reproducible results. The reason for this is not certain, but it is suggested that at these high concentrations a second, less stable, layer of molecules begins to form, which is partly destroyed by the slight agitation caused by the air current, thus giving erratic results. Bell: loc. cit.
ADSORBED FILMS AND RATES O F EVAPORATION
”5
Besides any action caused by modification of surface conditions, the presence of trichloracetic acid will also have some effect upon the activity of the chlorine in solution, and hence upon its partial vapour pressure and its rate of evaporation. The order of magnitude of the effects observed is however much greater than would be expected from this cause, and the fact that a constant fractional reduction was observed over a range of concentrations makes it probable that this factor can be neglected. I n two experiments (see results for solutions H and J ) , using abnormally small velocities of air current, a small but probably real negative value of x was obtained. I t seems probable therefore that the addition of the acid causes a slight increase in the partial vapour pressure of the chlorine, and that with low velocities of air current the reduction in evaporation rate caused by the surface film is so small as to be masked by this secondary effect. Cases are known’ in which the addition of a third component to a two-component system causes an increase in the activity of one of the components, and this is probably an example. I n any case, the main conclusions with regard to the extent of adsorption are not affected. If, as Langmuir2 supposes, the primary factor in the reduction of rate of evaporation of solute by a surface film is a reduction in the rate of diffusion of the solute towards the surface, we should expect the reduction to be apparent at quite low rates of evaporation. In the present work it is found that the reduction becomes zero when the rate of evaporation is still nearly 1% of the ideal rate. This seems to show that a t least in the present instance the reduction is primarily caused by the resistance of the film itself, as it must have been in Rideal’s experiments on the evaporation of water.
Measurements of Surface Tension I n order to discover whether the conclusions arrived a t above concerning the adsorption of trichloracetic acid from carbon tetrachloride solution were in accordance with the findings of the Gibbs adsorption equation, a series of surface tension measurements was carried out by the drop-weight method. The apparatus used was a modification of that described by hark in^.^ In order to eliminate losses due to evaporation, each drop-weight was calculated by difference from two determinations in which the time taken was the same, but the number of drops different. I n this way the drop-weight could be reproduced to within o.gyG. I n Table XII, each value of the drop-weight represents the mean of five results, which showed an extreme divergence in each case. of less than 0.57~ Harkinsl has shown that under the correct conditions, the surface tension is directly proportional to the drop-weight, so that the w - logloc curve plotted in Fig. 7 has the same form as the u - In c curve. The Gibbs equation for adsorption is a
Lews and Randall: “Thermodynamics,” p. 239 (1921). Irving Langmuir and D. B. Langmuir: loc. cit. Harkina and Brown: J. Am. Chem. SOC.,38,246 (1916). Harkins and Humphrey: J. Am. Chem SOC., 38, 228 (1916).
116
RONALD PERCY BELL
TABLE XI1 w = drop-weight in grams. c = concentration of acid in grams per IOO grams. log10c
C
-0.558
0.277 0.458 1.00 1.26
-0.331 0.000
0. I O 0
W
C
loglac
0.02974 0.02965 0.02957 0.02946
2.04
0.310
3.26
0,513
0.02912
5.15
0.712
6.61
0.820
0.02900 0.02891
W
0,02934
0.0300
0.0295
0.0290
0
-0.5
0.5
1.0
FIQ.7
r where
= -
I _.-
RT
da dlnC
F = excess concentration at the surface in gram-moles per sq. cm. u = surface tension c = concentration of solute.
It is seen from Fig. 7 that the w - logloc curve is a straight line for higher concentrations, while the slope falls off for low values of c. This means that for increasing d u e s of c, du/dlnc and therefore r increases to a limiting value a t which it remains constant, this limiting value presumably corresponding to the formation of a monomolecular layer. Owing to the small changes of surface tension involved, it is impossible to determine exactly where the curve becomes a straight line, but it is certainly between c = 1 . 0 and c = 1.6 grams per I O O grams, thus agreeing with the value found in the experiments on rates of evaporation, c = 1.4, as the minimum concentration necessary for the formation of a complete monomolecular layer.
ADSORBED FILMS .4ND RATES O F EVAPOR.4TION
117
Summary The possibility of employing measurements of velocity of evapora(I). tion for studying adsorption from solution has been discussed, and previous work on the subject reviewed. A method has been evolved for measuring the rate of evaporation (2). of chlorine from its solution in carbon tetrachloride. Measurements have been carried out at z jC under different conditions of chlorine concentration and velocity of air current, and the results compared with previous equations for the kinetics of evaporation in a current of gas. (3). The reduction in the evaporation rate caused by dissolving trichloracetic in the carbon tetrachloride has been measured under different conditions, and attributed to the surface adsorption of the trichloracetic acid. (4). It has been deduced from these measurements that a saturated surface f ilm of trichloracetic acid is formed a t all concentrations greater than about 1.4grams per IOO grams. ( 5 ) . Measurements of the surface tension of solutions of trichloracetic acid in carbon tetrachloride have been carried out by the drop-weight method. By applying the Gibbs adsorption equation to these results, it was found that the lower limit of concentration for the formation of a saturated film is between 1.0and 1.6 grams per IOO grams, thus agreeing with the value previously found. (6). I t is suggested that the measurement of rates of evaporation may prove of general utility in the investigation of adsorption from solution. I n conclusion, the author wishes to express his best thanks to Sir Harold Hartley for his advice, encouragement and assistance throughout the work. Physzcul Chemistry Laboratortes, Balliol and Trznzty Colleges, Ozford. August 9, 1928.
