Nonideality of Binary Adsorbed Mixtures of Benzene and Freon-11 on

Goldsmith, H. L., Mason, S.G.. J. ColbidSci., 18, 237 (1963). Govier, G. W., Omer, M. M., Can. J. Chern. Eng., 40, 93 (1962). Greskovich. E. J.. Shrier, A. L., lnd. Eng. Chern.. Process Des. Dev., 11, 317 (1972). Hewitt, G. F., Hall Taylor, N.S. "Annular Two Phase Flow" Pergamon Press, 1970. Hoogendoorn, C. J., Chern. Eng. Sci., 9, 205 (1959). Hoogendoorn, C. J., Welling, W. A. "Symposium on Two Phase Flows," E x 6 ter, 1965. Hubbard, M. G.. Ph.D. Thesis, University of Houston, 1965. Hubbard. M. G., Dukler, A. E., "Proc. 1966 Heat Transfer 8 Fluid Mech. Inst.," M. A. Saad and J. A. Miller, Ed., Stanford University Press, 1966. Hubbard, M. G., Dukler, A. E., paper presented at the AlChE National Meeting, Tampa, Fla.. 1968. Hughmark, G. A,, Chern. Eng. Sci., 20, 1007 (1965). Johnson, H. A,, Trans. ASME, 77, 1257 (1955). Kosterin. S. I., lzv. Ak. Nauk SSSR, Otd. Tekh. Nauk, No. 12, 24 (1949).

Kordyban, E. S., Trans. ASME, 83, 613 (1961). Kordyban, E. S..Ranov, R . R., "ASME Mukiphase Flow Symposium," p 1, 1963. Marruci, G., Chern. Eng. Sci.. 21, 718 (1966). Martinelli, R. C., Nelson, B. D., Trans A S K , 70, (1948). Neal, L. G.. "An Analyses of Slip in Gas-Liquid Flow" Report of lnstitutt for Atomenergi, Kjeller Res. Est. (1963). Nicklin, D. J., Wilkes, J. O., Davidson, J. F., Trans. lnst. Chern. Eng., 40, 61 ( 1962). Oliver, D. R., Wright, S.I., Brit. Chern. Eng., 9, 540 (1964). Richardson, B.,Argonne National Laboratory Report ANL-5949 (1958). Suo, M.. Trans. ASME, J. Basic Eng., 90, 140 (1968). Suo, M., Griffith, P., Trans. ASME, J. BasicEng., 86, 576 (1964). Vermuellen, L. R., Ryan, J. T., Can. J. Chern. Eng., 49, 195 (1971).

Received for review February 5,1975 Accepted June 5,1975

Downloaded by STOCKHOLM UNIV on August 31, 2015 | http://pubs.acs.org Publication Date: November 1, 1975 | doi: 10.1021/i160056a012

Nonideality of Binary Adsorbed Mixtures of Benzene and Freon-I 1 on Highly Graphitized Carbon at 298.15 K Earle D. Sloan, Jr. and J. C. Mullins' Chemical Engineering Department, Clernson University, Clernson, Sooth Carolina 2963 1

Experimental adsorption isotherms of binary gas mixtures of benzene and Freon-1 1 are presented for comparison with predictions by the ideal solution theory and by a two-dimensional van der Waals equation of state. The homogeneous carbon black, Sterling MTFF-D-7 (310OOC) with a surface area of 9.6 m2/g, was the adsorbent. A commercial electrobalance was used to measure both mixture isotherms at 298.15 K below 10 Torr and pure component isotherms at 273.15 K and 298.15 K at pressures up to 125 Torr. A chromatographic technique was used to correct the mixing rule for the energy parameter crii The calculated isotherms, using the corrected mixing parameter for the van der Waals equation, are shown to agree with the experimental isotherms. A small departure from the ideal adsorbed solution theory was found.

Introduction Many theories of adsorption such as the early BET theory (Brunauer et al., 1938) and a more recent theory by Lee and O'Connell (1972) assume sitewise homogeneity for the adsorbent. In spite of this basic assumption there is a paucity of data for adsorption equilibria of mixtures on either sitewise homogeneous adsorbents or adsorbents with a homogeneous field. The basic difficulty is that the composition of the adsorbed phase, which is frequently less than a monomolecular layer on a relatively small (e.g., 10 m2/g) surface area, must be determined. Friederich and Mullins (1972) obtained data for ideal mixtures of similar molecules using an equilibrium calculation method suggested by Van Ness (1969). The purpose of this paper is to present a different method for determining homogeneous absorbent mixture equilibria and to extend the mixture data available to include components which exhibit nonideality in the monomolecular layer region. Adsorption Equilibrium Relations Two equilibrium relations have been used here in the measurement of mixture equilibria on homogeneous adsorbents: a modification of the Gibbs-Duhem relation for the adsorbed phase and a relation for determining infinite dilution activity coefficients by a chromatographic technique. Gibbs Adsorption Isotherm. The Gibbs-Duhem relation for a two dimensional adsorbed film, restricted to constant temperature, is known as the Gibbs adsorption isotherm (Van Ness, 1969)

N

A n

- -dd.rr

2 xi dpia = 0 i=l

+

(constant T )

(1)

The chemical potential of species i in the ideal gas mixture is given by

pig(^, p , y i ) = G i o ( T ) + RT In P y l

( 2)

Since a t equilibrium the chemical potential of component i is equal in the adsorbed and gas phases, the differential of eq 2 may be substituted into eq 1 to obtain a useful relation.

--A

nRT

d n + d l n P + N

( x i d In y i ) = 0 (constant T ) (3) i.1

If eq 3 is restricted to constant gas phase composition, a means for calculating spreading pressure results P

=

n d(ln P) (constant T and y i )

(4)

In eq 4 the number of moles adsorbed may be determined by the mass adsorbed and an average molecular mass

i=1

Ind. Eng. Chem., Fundam., Vol. 14, No. 4, 1975

347

If eq 3 is restricted to constant pressure and applied to a


binary system, a phase equilibrium relation is obtained

By measuring a number of mixture isotherms at constant gas phase composition, the adsorbed phase composition may be determined through use of eq 4,5, and 6. An iterative solution is required since the desired quantity, X I , is necessary for the determination of the moles adsorbed, n, for spreading pressure curves. Friederich and Mullins (1972) used this method as suggested by Van Ness (1969) to determine equilibria for mixtures of ethylene-ethane, ethane-propane, and propylene-propane on graphitized carbon a t 298.15 K. Seven to nine isotherms a t constant gas phase composition were required to determine accurately the equilibrium of each binary pair. In an attempt to decrease the experimental effort, a chromatographic method of determining infinitely dilute activity coefficients is examined in this work. Activity Coefficient Determination. Myers and Prausnitz (1965) developed the concept of adsorbed phase activity coefficients in a manner analogous to that used for liquid phase solutions. An activity coefficient is’defined by

p i a ( T , P , x i ) = p i o ( T ,n) with lim y i = 1 ; x i

+

-

RT In y i x i

(7)

1.0

( 8)

The standard state, p L o ( T , x ) is , the chemical potential of the pure component adsorbed at the same spreading pressure as the mixture. If P L o ( x is ) the equilibrium pressure of the pure adsorbed component at x , the standard state may be related to the properties of the pure gas by p i o ( ~n), =

ci0(0+

RT In pio(.)

( 9)

At equilibrium the chemical potential of component i in each phase may be equated and eq 2, 7, and 9 combined to give

PY, = Y i X i P , O ( ? i )

(10)

The above equation may be used in conjunction with a pulse chromatographic technique by Gilmer and Kobayashi (1964) to determine infinitely dilute activity coefficients. In the chromatographic technique, an elution gas consisting of helium and one of the adsorbates flows through a packed column until steady state is reached. A small sample of the second adsorbent is then injected and the resulting retention volumes are measured. The basic equation for the chromatograph is

In the above equation nj’ is the moles adsorbed of the elution gas, as determined from its partial pressure in the elutriant and a knowledge of its adsorption isotherm. The infinite dilution activity coefficient may be determined from the chromatograph by substituting eq 13 into eq 10

While one can fit y;” to a simple expression for Gibbs excess free energy (e.g., the Van Laar or Margules equation), this is not done here. The excess free energy expression is given by

?(T, n, x i .

. .)

Y

= RT i=l

x i In y i

(15)

In contrast to the slight dependence on pressure encountered with liquid phase activity coefficients, the adsorbed phase is gas-like and the adsorbed phase activity coefficients are strong functions of spreading pressure. Instead of using a free energy expression, the infinite dilution activity coefficient is used here to correct an interaction constant in an equation of state as shown below. Prediction of Adsorption Equilibrium Young and Crowell (1962) present an excellent review of adsorbed mixture prediction methods prior to the work of the last decade. Of these and the more recent prediction methods, all require some experimental measurement of the potential between the adsorbent and pure component adsorbate, usually the pure component isotherms. Two of the most recent prediction methods are examined here. Ideal Adsorbed Solution Theory. The ideal solution theory proposed by Myers and Prausnitz (1965) assumes that y Lis unity, to obtain from eq 10 an expression analogous to Raoult’s law Pyi = YiPiO(.)

(16)

The three basic assumptions incorporated in the ideal solution theory are (1)the thermodynamic properties of the adsorbent are not altered by the adsorption process, (2) an equal temperature invariant area is available to all adsorbates, and (3) the Gibbs definition of adsorption applies. Myers (1968) investigated binary mixtures adsorbed on a number of heterogeneous systems which obey the above three assumptions and found good agreement with the ideal adsorbed solution theory. The equation determining the number of moles adsorbed in an ideal binary solution is 1= $ i + $ fit

The above equation assumes pointwise equilibrium, negligible axial diffusion, Gaussian distribution of the input pulse, and a linear adsorption isotherm in the range of operation. The partial derivative of eq 11 may be used to deo the relation termine ( x J ~ ‘ ) ~ , =by

Imposing the limit ni = 0 and assuming anJay, # m, it may be noted that x , and y I approach the origin simultaneously to obtain for binary mixtures

348


where nl0 is the amount of pure component 1 adsorbed at spreading pressure x . The mass adsorbed may then be determined by eq 5. One major advantage of Myers’ method is that it allows the prediction of binary mixture equilibria from only ‘2 pure component isotherms without assumption of any mixing rules. In the present work the graphical procedure of Myers is replaced with a computer program by Chien (1969). Friederich and Mullins (1972) determined that the ideal solution theory applied on homogeneous adsorbents for similar molecules. Myers and Prausnitz (1965) had previously suggested that nonideality may be more pronounced on homogeneous adsorbents than on heterogeneous adsorbents due to the masking of molecular interaction by heterogeneous adsorbents.

Prediction by Equation of State. Hill (1946) proposed a two-dimensional van der Waals equation for description of nonlocalized adsorption

(n

+ $)

(a

For a pure component eq 27 becomes

- 0) = kT

RT In A + nRT

Hill used a statistical approach and later DeBoer (1968) used a macroscopic approach to develop the adsorption isotherm corresponding to eq 18

Ross and Olivier (1964) have used the above isotherm extensively to represent pure component adsorption on homogeneous adsorbents. Hoory and Prausnitz (1967) have extended the method of Ross and Olivier to mixtures by proposing the following mixing rules for the pure component van der Waals parameters

ITA- naRT

na

(28)

The activity coefficient is related to fugacity by

Substituting the two dimensional equation of state given by eq 18 into eq 27 and 28 and the results into eq 29, a relation may be obtained for the activity coefficient.

In the limit of infinite dilution of component 1 the above equation reduces to Downloaded by STOCKHOLM UNIV on August 31, 2015 | http://pubs.acs.org Publication Date: November 1, 1975 | doi: 10.1021/i160056a012

ff,

=

cr1Xi2

+

2ffI2XiX2

+ a2x22

(21)

In ylm = Inu' - P i uz -

where the interaction constant cy12 = With the mixing rules the resulting equilibrium equations are

-.El u -

2 - - (cu1X1 P, UkT

+

0112x2)

(22)

and

When the pure component van der Waals parameters are available, eq 22 and 23 may be solved for the two unknowns, u and X I , a t specified P , T, and y 1 . The number of moles of component 1 may then be determined through use of

Pz

Hoory (1966) gives the following equation for the surface fugacity of component 1 in the adsorbed mixture as

1 -

Pz

- ___ '51 - P i > +

where 6 2 is the area per molecule of species 2 at the gas pressure and u1 is the area per molecule of component 1 if pure 1 were adsorbed a t T and T of the dilute mixture (XI 0). All of the terms in the right-hand side of eq 31 may be determined from pure component isotherms except cy12 which Hoory and Prausnitz assumed to be the geometric mean of the pure component cy values. If the infinite dilution activity coefficient is determined chromatographically using eq 14, the information from pure component isotherms may be added to obtain an experimental measurement of cy12 from eq 31. The experimental values of the interaction constant may be used to correct the geometric mean value by a constant, k l 2 , which is characteristic of a binary pair of molecules

-

0112

and a similar expression for component 2. With the number of moles of each component, the total mass adsorbed may be determined through eq 5. While Hoory and Prausnitz illustrated the calculation, no data were available for comparison. Hoory and Prausnitz made calculations to indicate that for systems of molecules with widely different van der Waals constants (e.g., CFCls and C6H6 on homogeneous carbon) considerable deviation from ideal behavior was possible. Correction to Mixing Rules for Equation of State. From the defining relations for the fugacity of an adsorbed component dpia = RT d l n f i a (at constant T ) (25) and

+ Pi(?

=

- ki2)

(32)

Experimental Section Static Apparatus and Experimental Procedure. A Cahn electrobalance was used to measure the mass of both pure components and mixtures of gas adsorbed on 0.5213 g of Sterling MTFF-D-7 (310OOC) carbon black. The arrangement of the static apparatus is illustrated in Figure 1. The static experimental apparatus and procedure was similar to that described by Friederich and Mullins (1972) with two exceptions: pressures below 10 Torr were measured by a capacitance manometer, and the sample hangdown tube was modified to mitigate diffusion effects. The pure component isotherms were obtained at two temperatures, 298.15 f 0.01 K and 273.15 f 0.01 K, while the environment was maintained a t 298.15 f 0.2 K. The carbon black was pelletized without binder by self impingement on the rotor of a ball mill and sieved to 20-40 Tyler mesh size. Dynamic Apparatus and Experimental Procedure. A chromatograph was used to determine adsorbed mixture p r q e r t i e s a t infinite dilution. The arrangement of the dynamic apparatus is illustrated in Figure 2. Three basic experiments were performed a t 298.15 K. In the first experiment Freon-11 was injected into a pure helium elution stream so that sample purity could be determined. In the second experiment a sample of benzene-argon was injected into an elution gas mixture of helium and benzene to verify Ind. Eng. Chem.. Fundam., Vol. 14. No. 4, 1975

349

Pressure,

P

(D (0

0

0

0

A

A

27315 29815 29815

torr

4

x


@Y

Figure 1. Schematic diagram of gravimetric adsorption apparatus: A, electrobalance; B, signal conditioner for electrobalance; C, recorder for electrobalance; D, constant temperature bath for adsorbent sample; E, thermostat for water bath; F, input bulb for adsorbate; G, Barocel capacitance manometer pressure sensor; H, 16-mm U-tube manometer; I, mercury seal; K, liquid nitrogen trap; L, oil diffusion pump; M, mechanical vacuum pump; N, McLeod gauge; 0, gas inlet needle valve; P, stop valve; Q, feed bulb for adsorbate; R, ice trap; S, McLeod gauge; T, calibrated flask; U, signal conditioner for Barocel manometer; V, recorder for Barocel signal; W, DVM indicator for Barocel signal; X, Glass to metal fitting; 1,2,3,vacuum stopcocks. GAS PREPARATION APPARATUS

Pressure. torr

Figure 3. Low-pressure Freon-11 isotherms on Sterling MTFFD-7 carbon black with Hill-deBoer fit t o isotherm data.

0

20

Ressure. 60

40

torr 80

100

120

140

CHROMATOGRAPH

uds des

75-7 0 0 0

0

n a

T. K Run 2735 T 273 I5 2 29815 3 29815 4

I

Pressure, torr

Figure 4. High-pressure Freon-11 isotherms on Sterling MTFFD-7 carbon black with Hill-deBoer fit to isotherm data. Figure 2. Schematic diagram of chromatograph and gas preparation apparatus: A, elution gas cylinder; B, sample gas cylinder; C, pressure gauge, 0-30 psig; D, pressure gauge, 0-300 psig; E, sample valve with 0.25 cm3 sample loop; F, mercury manometer; G, mechanical vacuum pump; H, hot wire detector; I, power supply and amplified for hot wire detector; J, two-speed recorder; K, adsorption column; L, water bath; M, thermostat; N, oil manometer; 0, thermometer; P, rotameter; Q, Vol-U-Meter; R, Barocel pressure sensor or manometer; S, major component cylinder; T, minor component bulb; U, mixed gas cylinder. Valves: 1 to 11, %-in. valves with Kel-F stems; 12, %-in.needle valve; 13 to 25, %-in.valves with Kel-F stems; 26, %-in. stainless steel needle valve. that the elution gas was at the proper composition. T h e third experiment consisted of injecting Freon-11 and argon into an elution mixture of benzene and helium to determine infinite dilution properties. The second and third experiments were performed at three different partial pressures of benzene to account for each end and the middle of the spreading pressure range of interest. T h e column was operated at atmospheric pressure and the temperature was controlled to 298.15 f 0.01 K by a liquid bath thermostat. T h e column mass of pelletized carbon black was degassed at 473 K by heating in a furnace while flowing helium through the column at 30 cm3/min. Elution mixtures and sample mixtures were prepared from pure gases by first introducing the minor component (benzene or Freon-11) into an evacuated gas storage tank, measuring the pressure on the capacitance manometer, and 350


then introducing the major component (helium or argon) until the desired final pressure was obtained. After mixing thoroughly, the final pressure was determined using a bourdon tube pressure gauge calibrated in increments of 0.1 psig. T h e virial equation of state truncated after the second coefficient was used to calculate the final gas compositions. T h e elution gas flow rate was first determined by volume displacement of a mercury sealed piston and flow fluctuations were observed with a rotameter. The elution gas was allowed to come to steady state in the column by observing the constancy of the signal from the hot wire detector. Pressure drop through the column was always less than 3 Torr. T h e sample of 0.25 cm3 at pressures between 230 and 3 Torr was injected into the column and extrapolated to zero sample size. The benzene and Freon-11 used had purities quoted by the vendors of 99.98 and 99.9% (min), respectively, and no impurities could be detected by the chromatograph. Results

Pure Component Isotherms. The adsorption isotherm data for benzene and Freon-11 at 273.15 and 298.15 K are presented with the Hill-deBoer isotherm fit in Figures 3 through 6. Tabulated data for pure component and mixture isotherms are given elsewhere (Sloan, 1974).

P r e s s u r e , torr

0 38

-

34

-

X

0 3 0

-

\"

X

24

W

020

Z16 E 0

2

v 4

12

-

ID

4

8

12

16

I

I

I

I

P

-

-

26

-

0

-

0

i 22ads des --

4

p

0 0 0 h

18-

0

(D

8 A

T. K 273 15 273 15 298 15 29815

% 5 6 7 8

4

O0W

I

02

I

04

I

06

I

IO

08

1 I '



oL

Figure 5. Low-pressure benzene isotherms on Sterling MTFF-D-7 carbon black with Hill-deBoer fit to isotherm data. Equation 19 was rearranged to a linear form in order to fit the experimental isotherms 2cY 8 In P - In- - = In K - - 8 (33) 1 - 8 1 - 8 k TP All pure component isotherms were fitted by the method of least squares to eq 33 by an iterative procedure. A value of rima was found which minimized the sum of the squares of the deviations of the quantity in brackets. The constants K , 2 a/& and rima for the pure component isotherms of the present work as well as the data reductions for other investigators of the pure components on similar carbons, are given in Table I. Assuming the area of the carbon to be constant, the values of 6 are related by

..

A = (n,"P)I = (nmaP)2 = . (34) If Ross and Olivier's (1964) value of 31.2 A2/molecule is taken for the Freon-11 value of p, the area computed with the value of rima a t 298.15 K is in agreement with the area

0'4

0'8

1'2

I

I

16

2 0


Figure 6. High-pressure benzene isotherms on Sterling MTFF-D7 carbon black with Hill-deBoer fit to isotherm data. quoted by the vendor (Goulston, 1973) and obtained by nitrogen adsorption (BET measurement). The area is taken as 9.62 m2/g. With this area and the value of nmaof benzene at 298.15 K, the @ value of benzene is calculated as 30.00 A*/molecule. Limiting isosteric heats of adsorption are compared in Table I. The heats of adsorption were determined for the present work by

(35) Standard entropy changes on adsorption from a gas phase pressure of 760 Torr to an adsorbed phase spreading pressure of 0.338 dynlcm were calculated by an equation derived by Ross and Olivier (1964) for the Hill-DeBoer isotherm

Table I. Comparison of Hill-deBoer Parameters and Limiting Isosteric Heats of Adsorption for Pure Component Isotherms of Benzene and Freon-11 on Homogeneous Carbon Black

van der

Component

Investigator

Adsorbent

Benzene

Olivier (1964) Pierotti (1966)

Sterling F T

Kiselev (1961) This work Ross (1964) This work

Sterling MT

Benzene Benzene Benzene Freon-11 Freon-11

Sterling F T

Sterling MT Sterling F T Sterling MT

Waals Monolayer concoverage, stants, Henry's law rima, 24p, constant, Temp, K pmol/g kcal/g-mol K , Torr

273.15 308.15 273.15 298.15 303.15 293.15

75.94 75.94 76.02 76.44 77.21 51.19

1.06 1.10 1.18 1.08 1.15 0.916

0.705 4.75 0.6797 3.33 4.31 2.029

273.15 298.15 273.15 286.15 273.15 298.15

52.03 53.10 82.0 82.0 46.0 51.2

0.927 0.904 2.74 2.63 2.73 2.69

0.6133 2.834 15.2 28.8 15.6 51.62

Limiting isosteric heat of ads. qSt,

kcalig-mol 9.12 (calcd) 10.1 (calcd) 9.8 (calorimeter) 9.91 7.9 (calcd) 7.75


351

Table 11. Summary of Experimental and Calculated Retention Volumes for Determination of Sample Gas Purity and Elution Gas Concentration

Run

1c 2c 4c 6C

Column mass, g

Elution gas

Sample g=

1.5427 0.7047 0.7047 0.7047

He C,H,-He CgHg-He CsHg-He

CFC13 C6H6 C6H6

C6H6

Mole fraction adsorbate in elution gas

Equation used to compute

0 0.001845 0.00145 0.00105

(37) (38) (38) (38)

(Vr -

v,)

Calcd (V,. - V g ) ,

cm3 28.45 94.2 124.3 150.5

Exptl

(v, - v,), cmR 27.02 90.27 122.2 150.7

Table 111. Comparison of Experimental and Calculated Activity Coefficients and Interaction Force Constants for Infinitely Dilute Freon-11 in Benzene on Sterling MTFF-D-7 Carbon Black at 298.15 K


Infinite dilution activity coefficients

Exptl

Calcd from eq 31 with geom. av for cyij

1.086 1.075 1.117

1.276 1.213 1.183

Spreading pressure TA/RT,

Run

Pmol!g

3c 5c

21.58 17.71 13.34

7c

b.,) - R

Interaction force constant Exptl, erg cm2/molecule2 1.962 x lo-'' 1.965 x lo-*' 1.817 X

Geometric mean, erg cm2/molecule2

Correction to v7 cYi(Yj as in eq 32

1.658 X lo-'* 1.658 X lo-'' 1.658 x lo-" Av k i j =

-0.1837 -0.1853 -0.0964 -0.155

dictions by ideal solution theory and by the van der Waals ~ equation ~ with and without experimental corrections to cy12 are presented in Figures 7 through 9. The data are correct(36) ed by the van der Waals equation to constant gas composiStandard molar entropy changes on adsorption for benzene tion in each figure, but the correction to each data point is by Ross andolivier and the present work were determined never more than 2 pg. as -10.6 and -12.8 eu, respectively. Kiselev and Poshkus A computer iteration was performed to determine the (1963) have calculated a value of -13.3 eu for the adsorpcorrection value, 1212, to the van der Waals interaction contion of benzene on Sterling M T based solely on properties stant which would predict the experimental data exactly. of the adsorbent and adsorbate. The entropy change for These individual 1212 values are presented along with the Freon-11 calculated from eq 36 from the data of Ross and 1212 values obtained by chromatography in Figure 10. Olivier and this work were in agreement with values of -11.43 and -11.8 eu, respectively. Discussion Chromatographic Measurements. The retention volPure Component Isotherms. Ross and Olivier (1964) ume for dilute Freon-11 in helium elution gas may be calhave determined that the Hill-deBoer equation successfulculated as indicated by Ross and Olivier (1964). ly correlated experimental data below 0.65 monolayer. This limit was not exceeded in the 273.15 K isotherms, but is il(37) lustrated at 298.15 K for benzene and Freon-11 a t 1 2 Torr' The equation relating the retention volume for benzene and 32 Torr respectively in Figures 4 and 6. The average injection into a benzene-helium elution mixture is given by deviation in pressure of the experimental data, above 0.5 Haydel and Kobayashi (1967). Torr for benzene and above 0.1 Torr for Freon-11, from the calculated isotherm is about 1%.The accuracy of the low( 3 8) pressure data is limited by the accuracy of the electrobalance, estimated to be 6 pg. The discrepancy of rima of Freon-11 a t the two temperatures is due to the fact that the where yj is the gas phase mole fraction of helium and the 273.15 K isotherm data only extend to 0.49 monolayer. partial derivative is the slope of the benzene isotherm a t Pierce (1968) has noted for a similar molecule adsorbed on the partial pressure of benzene in the elutriant. Agreement a similar carbon, that a change in rima of 20% is possible of chromatographic data with the calculations using graviwithout affecting other Hill-DeBoer parameters if the covmetric isotherms in eq 37 and 38 is indicated in Table 11. erage is limited to 0.5 monolayer. The chromatographic measurements of infinite dilution Prediction of heats and entropies of adsorption is a necactivity coefficients for Freon-11 in benzene are presented, essary indication of the applicability of an equation of along with the correction to the interaction force constant, state. The isosteric heat of adsorption and entropy change in Table 111. An average value of the correction constant on adsorption of Freon-11 determined by Ross and Olivier was taken as -0.155. and this work are in acceptable agreement. The limiting Mixture Isotherms. Mixture isotherms along with preASSa = - lim-qS 9-0

352

T

iR

(1

-

pn

k -

Ind. Eng. Chem.,Fundam., Vol. 14, No. 4, 1975

K I

IIOOL

-

1300

1000W

I200

0

-

x

;1100-

.o

d

.o U

a IO00

900.

D

10

c

800

I

n

U

I"

A

900-

Boot

'

r

700

A E C

R u n 80

E

von der

Waals e q n k l l = ' O I

C

von der

Waals eqn k , , = 0

O

Ideal S o l u t i o n

van der W o o l s e q n von der W o o l s eqn

Y

a

k = - 0 15 0

k

'=

I

I

I

5

6

7

Pressure, t o r r I

I

I

Figure 9. Benzene-Freon-11 isotherm at Y c ~ =H0.1583 ~ at 298.15 K on Sterling MTFF-D-7carbon black.

Pressure, torr

Figure 7. Benzene-Freon-11 isotherm at Y Q H ~= 0.065 at 298.15 K on Sterling MTFF-D-7carbon black.

05


000 I2O0

r

*=

r

o e a m ~ o o e

Run 9

IO 1 1

I

I2 I3 3C 5C 7C

I l

a

-05

1100 -

(o

1000-

E? x

Spreoding

900-

; Z

coo-

s 700 -

/ 600

Solution

A

Ideal

8

van der

Waals e q n h , ] = - 0 I5

C

van d e r

Wools eqn hi,:

I

0 3

Pressure, T r A / R T ,

moles/g X I O 6

Figure 10. Correction constant k;, as a function of spreading pressure for mixtures of benzene and Freon-11 at 298.15 K on Sterling MTFF-D-7carbon black.

n

5

I

I

6

7

0

Pressure, t o r r

Figure 8. Benzene-Freon-11 isotherm at Y c ~ H=~0.1295 at 298.15 K on Sterling MTFF-D-7 carbon black. isosteric heat of adsorption of benzene for the present work is in agreement with two of the three investigators. If the heat of adsorption by Ross and Olivier for benzene were increased to agree with the other investigators, then the calculated standard entropy change would agree with that of the present work and the calculation by Kiselev and Poshkus. Pierotti and Smallwood (1966) present data to indicate that the entropy loss of benzene on adsorption does not support the concept of localized adsorption. Chromatographic Measurements. The experimental results presented in Table I1 indicate satisfactory agreement between the chromatographic measurements and the gravimetric isotherms used for the calculation of retention volumes. The error in the determination of the chromatographic retention volume, estimated a t f3.5% is the largest error involved in the determination of y Lin eq 14. The values of y L are estimated to be accurate to f5%. The negative k 12 values for correction to the interaction force constant are relatively uncommon in three dimensions except in cases of dimerization or charge complex formation. Ross and Olivier (1964) have carefully studied the pure component adsorption of CFCls as well as the similar

compound CHC13 and concluded that both molecules upon adsorption follow very closely a model which presumes that both molecules are adsorbed with their symmetry axis normal to the carbon surface and with the fluorine or hydrogen atom pointing away from the surface. The greatest effect of this orientation on adsorption of the pure Freon-11 is to reduce the value of CY from an ideal value of 343 X erg-cm2-molecule-2 based on its gas phase properties assuming random orientation (Ross and Olivier, 1964) t o erg-cm2-molecule-2. A an observed value of 294 X calculation of the electric field imposed by the carbon for both benzene and Freon-11, as well as the fact that the for benzene is 33% less than the area of the ring, 39.5 A2/ molecule, tend to indicate that the benzene molecule is oriented with the plane of the ring normal to the surface. With the above pure component orientation either of two effects may occur to cause an increase in a12 over the geometric mean value. The benzene and Freon-11 may form a charge complex with benzene as electron donor and Freon11 as acceptor. The second effect which may occur arises from the fact that the adsorbed orientation of two neighboring Freon-11 molecules causes the dipoles to repel each other and the effective value of a is decreased as noted above. When a molecule of benzene replaces one molecule of Freon-11 the dipole repulsion is not present so that the Freon-11 a is effectively greater and the interaction force constant, a 1 2 , is greater than the geometric average. T h e estimated uncertainty in k l 2 is determined from Figure 10 as -0.155 f 0.06. Equilibrium Prediction. The predicted equilibria are based on the fact that the k 1 2 determined by the chromatograph allows the corrected van der Waals mixing rules to predict more accurately the total mass adsorbed as indicatInd. Eng. Chem., Fundam., Vol. 14, No. 4, 1975

353

___

14

+

.I

v a n der der

- non

I. 3

P

Benzene

B

Freon-ll

0.5-

W o o l s eqn h = O Waals eqn. k l i = -0.15

//

a

0.4

-

/

0"

-.

L

//

". + /

1.2 /

/ /

4

1.1

0

02-

1.0

0.2 Adsorbed

0.6

0.4

0.8

1.0

P h a s e M o l e Fraction B e n z e n e , x

6' H6

Figure 11. Activity coefficient of benzene and Freon-11 at 298.15 K and 6 Torr adsorbed on Sterling MTFF-D-7carbon black.

o!

A

Ideo1 S o l u t i o n

B

v a n der W a a l s eqn

hij

C C

van van dd ee rr Waais Waais

kii kii = 0

0'2 Adsorbed

0'4

eqn eqn

0:s

:

-0.15

018

I

Phose M o l e Fraction B e n z e n e , xc

6

6


Figure 13. Binary adsorption equilibrium for the system benzeneFreon-11 at 298.15 K and 6 Torr on Sterling MTFF-D-7 carbon black. volatility. This is best illustrated by utilizing eq 10 to obtain

For small values of the ratio, Pi0(r)/P,the value of y; will have little effect on the shape of the curve.

C

'

van d e r

Waals eqn k l l = 0

-

"0

0'2

0'4

016

Adsorbed Phose Mole Fraction

0'8

I O

F r e o n - 4 , xcFCl3

Figure 12. Relative volatility for Freon-11 in benzene at 298.15 K and 6 Torr on Sterling MTFF-D-7carbon black. ed in Figures 7 through 9. In each figure the deviation of the experimental data from the prediction of the ideal solution theory is about 4% while experimental error can only account for 1%(maximum) of the observed deviation. The activity coefficients, relative volatilities, and equilibrium diagram for the system at 298.15 K and 6 Torr are presented in Figures 11through 13. The predictions for adsorbed phase benzene mole fractions greater than 0.92 required extrapolation beyond the accepted van der Waals limit of 0.65 monolayer. This does not affect any predictions in Figures 6 through 9 where all benzene adsorbed phase concentrations are less than 0.75 mole fraction. The effect of a negative k 12 is to decrease the activity coefficient predicted by a geometric mean interaction force constant. For this system at 273.15 K and 6 mm Hg on a similar carbon Hoory and Prausnitz (1967) predicted relative volatilities as a function of adsorbed phase composition, based on the van der Waals equation which were quite different (the curves were nearly orthogonal) from the values predicted by the ideal solution theory. At these conditions most of the pure component coverages were greater than 0.65 (0.63 0.78 for Freon-11 and 0.4 0.72 for benzene) so that the mixture van der Waals prediction is not likely to be accurate. As seen in Figure 12 no such radical behavior was observed at the conditions encountered here. The relative insensitivity of Figure 13 to the method of calculation is typical of binary systems with a large relative

-

354

-


Conclusions The binary mixing rules for the van der Waals equation proposed by Hoory and Prausnitz (1967) have been corrected by a chromatographic measurement and a deviation from the ideal solution theory has been measured. Nonideal binary mixture equilibria may be estimated with a minimum of experimental data consisting of two pure component isotherms and one chromatographic measurement. Acknowledgment The authors wish to express their indebtedness to Mr. B. L. Ornitz for valuable assistance with the electronics involved with this work. Dr. W. R. Smith, retired Senior Scientist of the Cabot Corporation, kindly provided the adsorbent for this work. Nomenclature A = specific surface area of adsorbent c = total concentration of gas phase Go = molar Gibbs free energy of pure component in ideal gas state at one atmosphere g = molar Gibbs free energy K = Henry's law constant k = Boltzmann constant M = molar mass ma = mass of adsorbed gas per gram of adsorbent m = mass of adsorbent N = number of components n = dumber of moles per gram of adsorbent no = moles of pure component adsorbed at mixture spreading pressure in absence of other component n m = monolayer capacity per gram of adsorbent P = pressure PO = equilibrium pressure of pure component a t mixture spreading pressure p = partial pressure in elution gas q = heat of adsorption R = gas constant S = entropy

T = absolute temperature V , = volume of elution gas evolved after sample injection until appearance of peak centroid V , = volume of gas in column x = adsorbed phase composition, mole fraction y = gas phase composition, mole fraction Greek Letters (Y = constant of two-dimensional van der Waals equation p = constant of two-dimensional van der Waals equation y = adsorbed phase activity coefficient 0 = fractional coverage p = chemical potential po = chemical potential of pure component T = spreading pressure u = molecular area of adsorbate


Subscripts i = component i m = monolayer adsorbed s = standard condition 1 = component one 2 = component two 12 = interaction parameter

s t = isosteric ' = elution adsorbate property ~0 = infinite dilution L i t e r a t u r e Cited Brunauer, S., Emmett, P. H., Teller, E., J. Am. Chem. Soc., 60 309 (1938). Chien, M-T. W., M.S. Thesis, Clemson University, Clemson, S.C., 1969. deBoer, J. H.. "The Dynamical Character of Adsorption," 2nd ed, Oxford University Press, London, 1968. Friederich. R. O., Mullins, J. C., lnd. Eng. Chem., Fundam., 11, 439 (1972). Gilmer. H.B.. Kobayashi, R.. A.l.Ch.E.J., 10, 797 (1964). Goulston, P. H., personal communication, 1973. Haydel, J. J.. Kobayashi, R., lnd. Eng. Chem., Fundam., 6, 546 (1967). Hill, T. L.. J. Chem. Phys., 14, 441 (1946). Hoory, S.E., Ph.D. Dissertation, University of California, 1966. Hoory, S. E., Prausnitz, J. M., Chem. Eng. Sci., 22, 1025 (1967). Isirikyan. A. A.. Kiselev, A. V.. J. Phys. Chem., 65, 601 (1961). Kiselev, A. V., Poshkus, D. P., Russ. J. fhys. Chem., 37,312 (1963). Lee, C. S., O'Connell, J. P., J. Colloldhterface Sci., 41, 415 (1972). Myers, A. L., lnd. Eng. Chem., 60, 45 (1968). Myers, A. L., Prausnitz, J. M., A.l.Ch.EJ., 11, 121 (1965). Pierce, C., J. Phys. Chem., 72, 1955 (1968). Pierotti, R . A., Smaiiwood, R. E., J. Colloid Interface Sci., 22, 469 (1966). Ross, S..Olivier, J. P., "On Physical Adsorption," Interscience, New York. N.Y., 1964. Sloan, E. D., Ph.D. Dissertation, Clemson University, Clemson, S.C.. 1974 Van Ness, H. C., lnd. Eng. Chem., Fundam., 8, 464 (1969). Young, D. M., Croweil. A. D., "Physical Adsorption of Gases," pp 365-406, Butterworths, London, 1962.

Superscripts a = adsorbed phase E = excess

Received for reuieu! March 10, 1975 Accepted July 8,1975

E XPE RIMENTA 1 TECHNIQUES

Light Scattering as a Method for Measuring Turbulent Concentration Fluctuations in Liquids Triantafiilos D. Vavanellos and Jon H. Olson* Department of Chemical Engineering, University of Dela ware, Newark, &la ware 197 I 7

The light scattering method for measuring the concentration spectral density function provides a nondisturbing method for measuring eddies of critical importance to turbulence theory. However, interpretation of these data requires very careful consideration of background scattering to recover the spectral information.

The spectral density distribution function for isotropic concentration fluctuations or the corresponding scalar correlation function are the object of a large body of theoretical work (Batchelor, 1959; Beran, 1968; Gibson and Schwarz, 1963b; Kraichman, 1965; O'Brien, 1968) on turbulence. Experimental determination of these functions will continue to be of substantial value in the development of the statistical theory of turbulence. In liquid systems very fine probes have been developed for these measurements (Gibson and Schwarz, 1963a). These probes make a significant perturbation in the velocity field, and the data are suspect in a size range important to liquid mixing. Therefore the potential development of a probeless technique has the exciting possibility of overcoming the disadvantages of probes in liquid turbulent studies. The capstone of this research appeared in the Wilhelm memorial issue of this journal (Christiansen, 1969). It is therefore with some sadness that we report here a severe weakness of the probeless light scattering method.

Background Clemons (1962), Kim (1963), and Christiansen (1967) developed a series of theses in a small-angle optical scattering technique for measuring the spectral density of turbulence. The full development is given elsewhere, but in summary the concentration spectral density function is obtained from a measurement of the variation of scattered light intensity with angular position

where E , ( k ) is the spectral density function, (IlIo) is the ratio of the scattered beam intensity to the transmitted light intensity, the next group is a constant formed from basic physical parameters, V is the sample volume scattering into the counter, and k is the wave number. The scattering sample volume is a weak function of scattering angle U


355

Nonideality of Binary Adsorbed Mixtures of Benzene and Freon-11 on

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