374
T. FT, R.
F. E. BARTELL
S. H . I S S E S .\XD
THERM ODYS211\IICS OF ,\DSORPTIOS FROM SOLUTIOSS. I] T H E 110L.lLITY I S D
-ICTIYITT
COCFFICILST O F .iDSORBED
1 7 X G FP,Z ROBERT S. HASSES,?
\XD
LAYERS
F. E. BXRTELL
D e p a r t m e n t of Chenazstry, Cnzverszty o j M i c h q a n , B n n Arbor, J l i c h i g a ) ~ Recezied August 12, 1947 ISTRODUCTIOS
I n the adsorption of gases and vapors the investigations of Emmett, Brunauer, Teller, Deming, and many others have shou-n quite conclusively the existence of multilayer adsorption. Heretofore no satisfactory evidence of corresponding phenomena in liquid solutions, even in the simplest binary solutions, has been presented. This is largely due to the increased complexity caused by the presence of a second component, but in part it has also been due to lack of reliable methods for estimating the specific surface area of the adsorbent. Recent work in this laboratory on the adsorption from aqueous solutions by different graphites of known area indicates that the atlsorbed phaqe is probably more than one molecule thick. In vien- of the fact that the state of a substance may sometimes be revealed from a study of its activity coefficient, it seems that an investigation of the activity coefficient of the adborhate in the adsorbed phase may furnish some valuable information regarding the nature of that phase. It is the purpose of this paper t o suggest methods ior the estimation of surface concentrations and activity coefficients and to present a hypothesis concerning the nature of the adsorption layer correlating the results obtained thereby. THEORCTIC.lL
Let p and a be the chemical potential and activity, respectively, of the solute in the bulk solution. ,usand us tlie corresponding quantities for the solute in the adsorbed layer, and po and p i the chemical potentials of the solute in its standard state in the bulk solution and in the adsorbed phase. Then p = po+ pa
= pi
(1)
R7’lna
+ RT
In as
(2)
whence for equilibrium, po
+ R T In u = p i + IZl’ln as
(3)
or In (as’a) = I n
(1127’ )?if)
= (po - p i )
RT
(4)
in n.hich 7n is the molality anclf the activitv coefficient, and tlie +upervript s again The authors wish t o acknonledge financial assistance from the Board of Governors and the E\ccutive Board of the Horace H Rarbhanl School of Graduate Studies. Horace H Racbhain Research ;Issociate Horace I1 Racliham Predortoral Fcllon
THEHlIODTS.IlII(‘S O F 1 D 5 0 l t P T I O S FRO31 SOLCTIOSS
375
denotes the surface phase. -4ls the activity of the solute in the bulk solution can be determined by appropriate methods, the activity coefficient f” of the adsorbate in the adsorbed layer can be evaluated if ms and ( p o - p : ) / R T are known. 1. Evaluation of
(po - p i )
111’
,It low concentrations the amount adsorbed is a linear function of the concentration. Innes and Rowley (1) have shown that an ideal two-dimensional gas corresponds to a linear adsorption equation. -1similar relation may be shown t o apply t o dilute solutions. Let I’ be the total surface pressure on the solid surface of area A , and n, the number of moles of solute i on the surface, considered identical with the surface excess for dilute solutions. Then by the Gibbs equation, one has
-4dl:,
=
HT n; d In c,
(5)
According t o Mitchell (3), for an ideal two-dimensional solution
ilFi = n; RT
d dF,
=
R T dns
(6)
(7 1
whence d ln n: = d In e , ns = kc, Equation 4 can be rewritten in the forni :
as = a esp
((PO
pi)/RT)
(4a)
- pi)/RT)
(10)
-
In the ideal region this becomes
m’
=
a esp
((po
since for the ideal layer f” = 1. The limiting slope of the plot of m sus. a accordingly is exp ((po - p : ) / R T ) . 2 . Etaluation of nis
Let b represent the number oi molecules per square centimeter in contact with the solid surface, S the total number of moles per liter in the bulk solution, and 2 A4vogadro’snumber; then if there ik no adsorption
b
=
(NZ)2’3/100
(11)
Let B , represent the number of moles of component i in contact with 1 cm.? of the solid surface, and 2 %the mole fraction of component i in the bulk solution; then if there is no adwrption
23, = bXi/Z
(12)
(Table 1.) 13quations 11 and 12 correspond t o a solid surface completely covered with molecules : adsorption of molecwle. of nne species must he accompanied by
376
T. FU, R. S. HXVSES - E i D F. E. BARTELL
displacement of the other. If the area per molecule is knon-n for both species in the case of binary solutions, the number of moles displaced can be calculated from the number of moles adsorbed. I n the case of aqueous solutions, for example, these considerations may be used t o calculate the molality of the adsorption layer as follows:
ms =
h'umber of moles adsorbate/cm.' ___ Numbes of moles solvent/cm
- Original moles adsorbate/cm.'
- .
Original moles solvent/cm.
x 55.51
+ moles adsorbate added/cm.'
- moles solvent displaced/cm.2
X 55.51 (13)
3 . Evaluation of f a Once (po - p i ) / R T and m3 are known, the activity coefficientf" is given by: logf
= (pa
CONCENTRATION
+ l o g a - logms
- pi)1'2.303RT
XIOLES O F BUT'IRIC ACID PER SQUARE C E l T I U E I E R
(14)
MOLKS O F WATER P E R SQUARE CEKTIKETER
___
As long as the adsorbed layer remains ideal, the plot of log ms vs. log a should follow a straight line of unit slope (the ideal line). -Any deviation from this line shows the non-ideality of the adsorbed layer. If the actual curve lies above the ideal line, the activity coefficient is smaller than unity, and if the actual curve lies belon- the ideal line, the activity coefficient is greater than unity. 1: SPERIlIEST.\L
I n order t o minimize effwts of capillarity and heterogeneity of the solid surface it seemed advisable t o use adsorbents of definite crystal structure; various graphites (indicated as graphites -A-D, inclusive) Ti-ere selected as best fulfilling these requirements. For purification these graphites n-err subjected to a preliminary leaching \\-it11 1: 1 hydrochloric acid t o remove the major portion of impurities (iron), were then evaporated to dryness n-ith hydrofluoric acid and sulfuric acid, u-ere nest treated repeatedly n-ith hot dihite hydrochloric acid and hot redistilled water, and Ti-ere finally heated in high vacuum at 850°C. for 2 days
377
THERlIOD’I-SA\311CS O F 1DSORPTIOS FROM SOLVTIOSS
I n the case of graphite 11the final heating temperature was 1030°C. -4 loJv-area carbon black n-as included for comparison. The surface areas of thedifferent adsorbents were determined from nitrogen adsorption by the R.E.T. (Brunauer, Emmett, and Teller) method. The ash contents of the different adsorbents were: ADSORBEST
I 1
Graphite A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Graphite 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . j Graphite C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphite D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Carbon G.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~
~
PER C E S T ASK
0.035 0.013 0.000 0.180
0.078
Butyric acid was selected as adsorbate. Eastman’s pure grade n-butyric acid was first distilled, the distillate further purified by two fractional freezings, and the melt collected and redistilled twice, the first and last thirds being discarded. The boiling range mas 163.0-163.2”C. a t 736 mm. The more concentrated solutions were made up by weight with redistilled water, and the most dilute solutions by dilution of the more concentrated. T o 0.5000-g. samples of graphite 15-ml. portions of the acid solutions were added in ground-glass-stoppered flasks. -4 thin layer of silicone grease mas applied around the stopper to prevent evaporation through the joint, and according t o blank runs did not appear t o be a source of error. The solutions Ivere then shaken for about 20 hr., after which portions n-ere removed into stoppered tubes and centrifuged. Immediately following centrifuging the clear supernatant liquid was analyzed interferometrically. The zj’m (number of millimoles adsorbed per gram of adsorbent) values were calculated from the concentration changes in the usual manner. The data are given in tables 2-6. DISCUSSION O F RESULTS
In the calculations given above an area of 20.5 n-as assigned to each butyric acid molecule, this being the generally accepted cross-sectional area for long-chain fatty acids. 1-sing this value for butyric acid and knowing the number of molecules of each species on 1 of the solid surface, the area for each ivater molecule 1va5 found to be 9.9 .%.? These values of the molecular areas proved selfconsistent n-ithin the limit of experimental error, the surface area derived from their use TI ith the previously calculated numbers of molecules per square centimeters deviating from unity by not more than 3 per cent (table LA). These valuea lead to the conclusion that each molecule of butyric acid adsorbed will displace 2.0’7 molecules of n at PI-. n-hich ii an important quantity in the preceding calculations. The activity values of biityric acid wcre taken from the data of Jones and 13ury ( 2 ) . Rigorously, their values are valid only at the freezing points of the solutions. Since the partial molal heat contents and specific heats nere not knon-n, it was not possible to convert their data to the temperature of our experiments (22-23°C). Hon-ever, it is believed that n-ithin the range of concen-
trations covered in this investigation the error introdiicecl thereby is within the experimental error. The log m s 1's. log n curves (figure 1) show the folloning characteristics. *it lower surface concentrations the curve$ are convex ton-ard the ideal line; as the surface concentration becomes higher, the ciirves become linear; at still higher T.LBLE 1.1 A r e a occupied b y b u t y r i c acid ni?d b y water
Equilibrium molality
Area of butyric acid
Area of water
Total
-
cm.?
cm.2
0.0072 . 0.0159 0.0436 0.097 0.194 0.284 0.496 0.730 1.oao
'
0.106 0.162 0.249 0.340 0.443 0.494 0.615 0.716 0.843
cm
0.920 0.865 0.776 0.683 0.576 0.523 0.396 0.288 0.154
1
Equilibrium molality
Area of but>ric acid
Area of water
cm 2
2
1 026 1.027 1.025 I ,023 1.019 1 017 1.011 1.003
0.0090 0.019 0 048 0.095 0.203 0 291 0 511 0 778 1.050
0.998
Total
1
0.163 0.221 0.323 0.429 0 496 0.578 0.719 0 871 0.981
1
cm 2
cm.2
0 861 0.804 0.701 0.594 0 523 0.439 0.289 0 133 0.015
1.024 1.025 1.023 1.023 1.019 1.017 1.008 1.004 0.996
TXBLE 2 A d s o r p t i o n of b u t y r i c cicid b y g l u p h i t e A PO - P i Specific area = 9.15 X 106 cni.2; = 2.628 2 30312T ~
I
EQUILIBRIUM MOLALITY 1
1
0.0436 0.097 0.194 0.284 0.496 0.730 1.040
1
,
ADDED
x,'m
a
1
lVATER DISPLACED
1
W'AIER REXAINISG
'
~
I
LoGf
I
j4
___
,
0.0524 '0,10951 0.227 10.327 '0.548 '0.773 1 1.038
millimoks,' gram
0.078 0.119 C . 183 0.248 0.321 0.357 0.430 0.507 0.593
__ moles cm X 1011, E!$! cm
0 855 1 31 2 01 2 73 3.53 3 92 4 82 5 57 6 52
X
J(J'
1 78 2 71 4 16 5 64 7 30 b 12 9 99 11 53 13.49
males X Jill' crn 2
!?Aes cm X JV' 15 42 14 4q 12 99 11.45 I) 67 8.76 6 65 4 83 2 58
I
0 861 1.31 2 03 2 76 3 59 4 01 4 98 5 80 6 83
I
3.10 0 078 1.20 5 0A1 0.210l 1.62 8.661 0.411 2.58 13.4 1 0 541' 3.48 20.6 1 0.671 4.69 26.4 0.737' 5.46 41.5 0.7491 5.62 66.7 0.692 4.92 146.8 0.477) 3 00
concentration the curvature of the curve is reversed and the curve becomes concave ton-ard the ideal line. The change in curvature is also exhibited b y the log f" vs. log v z s plots (figure 2 ) . .Ifter increasing regularly with log msthe log f" values begin to decrease very rapidly a5 the surface concentrations become higher and higher. Considering equation 14, there is no reason t o suspect that concentration variables ( a and m8)are directly responsible for this abrupt change,
THER3IODYSAIIICS O F .\DSORPTIOS FROM SOLrTIOSR
379
and we are therefore forced to the conclusion that it must be due t o a similar abrupt change in pi, which in turn must hP due to an abrupt change in the forces whereby the adsorbate molecules are held t o the adsorbent. Such n change may be explained by supposing that the adsorption becomes multimolecular, with the attractive forces of the solid being such that the first layer is essentially complete before the second layer is developed to any appreciable magnitude, and also that the adsorbate molecules are much more strongly held in the first layer than in the second. X similar explanation is generally accepted for many solid-gas adB
A
3
3
2
2
I
I
0
-3
-2
-I
0
0
-3
-2
c
-I
0
-1
0
U
3
2 1
0 -3
-2
-I
-3
0
-2
G 3
2 I
0
-3
-2 -I 0 LOG A C T I V I T Y
FIG.1. Plot of log ma against log a
sorption isotherms. Such an explanation ~ r o u l drequire a sharp increase in n-ith the essential completion of the first layer. causing a sharp don-nil-ard trend in log f”. That this does not produce an actual discontinuity in log f” could Ire11 be due to the fact that the first layer is still in the process of completion when the second begins to form. From this viewpoint, the logfs us. log m 5curve consists in reality of two curves (in the range of concentrations covered by this work), one a function of the potential of the first layer and one a function of the potential in the second, and the intersection of there curves represents the molality of the adsorbed phase when the first adqorption layer is completed. Granting this cupposition, it should be possible to calculate the molalities and pi
activity coefficients of the ueconcl adsorption layer, m;,f l . Subtracting the amount adsorbed in the first layer from the total s m , the molalities in the second layer can be calcidntect n ithout difficulty. The evaluation of ( P O - plo"'),'RTis less simple. Even if TIP siipposp the adsorption in the second layer to be zero a t the concentration corresponding t o (x'm),,, (the value of z m corresponding t o a completed monolayer), it is still necessary to extrapolate
- 0.5
0
I .o
2.0
3.0
4.0
LOG MOLALITY, ms FIG.2. Plot of log f" against log ma
m i to zero equilibrium concentration in order t o obtain ( b o - $ ' ) / K T .
ri%i5 is due t o the fact that only at very low mi can n e be asLured that the activity coefficient is unity, and at the concentration corresponding to the completion of the first layer the molality of the second layer i j the bame us that of the hulk solution (if there is no adsorption at all in the -evond layer), and this molality is too high t o permit omission of log Si. This extrapolation introduces considerable un-
O F .\D-ORPTIOS
THER1IODTS.i1IIC'h
381
FRO11 SOLUTION$
certainty as a considerable concentration range is involved. It is i m f h noticing that the ( P O - ,.$*),/RTvalues for thP different adsorbents are of the same order for the first and second layers, although that for the former is considerably larger. T.1BLE 3 A d s o r p t i o n of butyric ncid b y graphite R Specific area
i 0.0090 0.019 0.045 0.098 0.203 0.294 0.511 0.778 1.050
-
0.023 0.031 0,045 0.060 0.069 0.080 0.099 0.119 0.133
'0.0101 10.022; 0.058( IO. 117 0.237 10.338 10.564 0.815 11.039
=
1.32 1.78 2.50 3.45 3.97 4.60 5.69 6.84 7.64
1.74 X 105
2.74 3.68 1 5.38 7.14 8.20 9.52 1 11.i9 1 14.13 I 15.82
1
'2 3R1
= 2.816
~111.~;
14.46 13.51 11.77 9.96 8.77 7.36 4.85 2.23 0.249
0.1361 1.37 7.3: 0.3091 2.04 0.4881 3.08 1 12.3 0.5981 3.94 I 19.4 1 25.6 0.783 6.07 I 34.7 0.805~6.39 0.743~ 5.54 66.9 172.1 0.4921 3.10 11775.0 -0.434, 0.384
1.32 1.i9 2.62 3.48 4.03 4.69 5.84 7.07 7.96
5.0;
~
,
I
TABLE 4 A d s o r p t i o n of butyric acid by g r a p h i t e 8
Specific area = 1.1 X 105 cm.
2 . PO
,
~
- Po
2.3RT
TOTAL BUTYRIC
WATER REMAINING
moles - x 10'3 cm.2
0.0094 i0.0115 0.0187 10.02261
0.203 0.293 0.508 0.770 1.047
'0.238 10.337 0.562 0.806 11.037
I ~
1
i
0.015 0.025 0.036 0.045 0.052 0.056 0.067
O.Oi8 0.096
1.37 2.29 3.27 4.09 4.73 5.09 6.06 7.09 8.72
I
I
2.93 4.74 6.78 8.47 9.78 10.53 12.55 14.66 All gone
14.27 12.45 10.37 8.63 7.19 6.35 4.09 1.70
- 2.685
moles cm.2
, ~
x
1 'l
I ma
i
i
LoGf'
1
fa
1~1010
1.37 2.30 3.29 4.12 4.73 5.18 6.21 7.32 9.04
1
1
I
I
I
5.33~ 0.007 10.231 0.021 1 17.6 ' 0.1971 26.5 0.300 37.1 0.484 45.3 0.549 84.3 0.502l 1238. 0.2081 1
I
~
~
i
1.02 1.05 1.58 2.00 3.05 3.54 3.18 1.62
This is, of coiirse, to be expected, for the effect of the adsorbent on the adsorbate, manifesting itself in the lowering of the standard chemical potential, must be much more pronounced in the first layer. In contrast with those for the first layer the activity cvefficients for the seconcl layer are smaller than unity and decrease with concentration. Qualitatively this is in agreement with the results of Jones and Bury for butyric acid in the bulk solution (figure 5 ) , an agreement
382
T. FG, R. S. H.4KSES -4h-D F. E. BARTELL
which is to be expected, since the second layer must bc much more similar t o the bulk liquid than the first. The data for in; and j"; are rrcorded in tahle 7 ancl plotted in figure 4. _Idditional support foi, the interpretatioiib given a h o w i:, furnisliecl by the fact that the adsorption isotherms for thc aclsorption of biityric acid from aqueous solutions by the graphite? studied do not follon- the Lnngniuir or Freuridlich equations, biit can be represented 1)y :I motlificd 13.1
