SOLID SURFACES and the Gas-Solid Interface

Thermodynamics of Adsorption The Barium Sulfate-Water System Y. C. WU and L. E. COPELAND Research Department, Portland Cement Association, Skokie, Ill.

Adsorption isotherms for the system BaSO -H O at 4

2

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch038

three temperatures have been obtained. Thermodynamic study of these data reveals that part of the free energy decrease in the adsorption process involves changes in the partial molal free energy of the adsorbent.

From the three isotherms

differential and integral heats of adsorption were derived

and

compared with

new calorimetric

determinations of the same thermodynamic functions.

In both kinds of measurements exactly the

same system

and exactly the same

materials

were used.

y he primary purpose of this paper is to demonstrate the significance of the thermodynamic treatment developed in the previous paper (6), with an application to a simple binary adsorption system for which isotherms at three temperatures and calorimetric heats of adsorption have been made available. A free energy function, AGt, was defined (6) to be equal to the change in free energy in an adsorption process involving a monodisperse adsorbent in which true thermodynamic equilibrium could be achieved. In this paper we use this free energy function, and functions for enthalpy and entropy defined in a similar manner, for the interpretation of data obtained from the adsorption of water on barium sulfate. Although the samples of adsorbent have a constant specific surface, they are not monodisperse and thermodynamic equilibrium within adsorbent particles probably is not maintained. The approximations that must be made to apply the thermodynamic functions to solid adsorbents were discussed in the previous paper. The agreement between enthalpy changes calculated from adsorption isotherms with calorimetrically determined values shown in this paper indicates that the approximations did not introduce significant errors. A change in the partial molal property of each component has been found to be an essential part of the corresponding integral change usually determined. The discussion of adsorption presented is closely parallel to discussions of solutions presented in familiar thermodynamic treatises. An equation developed in the first paper (6) is identified in this paper by the Roman numeral I, followed by the number of the equation in that paper. 357

In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.

358

ADVANCES IN CHEMISTRY SERIES

Two kinds of thermodynamic process will be discussed: an integral process, and a differential process. The integral process may be written —• [system comprising τζιΧι and 722X2]

«1X1 + W2X2(Hquid)

0)

This process represents the adsorption of n moles of X , initially liquid, upon n moles of X It is equivalent to Process 1 of the preceding paper (6). The differential process is Process 1-4. 2

2

x

v

7Z2X2(adsorbed on X i , — unchanged)

w X2(liquid) 2

(2)


n\

The negative of the enthalpy change for this particular process corresponds to the "net heat" of adsorption, since the process involves the transfer of the adsorbate from its liquid state to the surface of the adsorbent. (The "net heat" of adsorption of liquid adsorbate is in turn the difference between the heat of adsorption of the adsorbate vapor and the heat of condensation of the vapor. ) Enthalpy Changes in Adsorption It has long been realized that the heat of adsorption can be calculated more accurately from determinations of heats of immersion than from equilibrium vapor pressures of adsorbates. Harkins and Boyd (8) and Jura and Harkins (10) have discussed the emersion process and have developed an expression for the enthalpy of desorption that is the negative of the one above. That the immersion process is equivalent to the process we are discussing can readily be shown with the aid of the following two-step process : A. Immerse a clean adsorbent from a vacuum into a liquid adsorbate: wiXi(s) -f- JVX (liquid)

[rziX] saturated with and in an excess of liquid X2]

2

(3)

B. Immerse the adsorbent from a vapor, wherein n moles of X adsorbed n moles of X in equilibrium with vapor at pressure p, into a large amount of liquid adsorbate. x

2

x

2

~n\ mole of X i with /z moles of X " n\ mole of X i saturated~| adsorbed upon it in equilibrium + (N - « )X (/) -+ with and in an excess of (4) with vapor at pressure p L liquid X2 J 2

2

2

2

The difference between these two steps (A expressed above: fliXi(s) + 722X2(0

B) gives the integral Process 1

\ ^ °^ ^ ^ °l of X2 adsorbed upon it: I Lin equilibrium with vapor at pressure p J n i m o

e

w

t n n 2

m

e s

(5)

The integral heat of adsorption is the difference between the heat of immersion of the clean adsorbent and the heat of immersion of the adsorbent, with n moles of X adsorbed upon it. This calorimetric heat of adsorption is to be compared with the heat of adsorption calculated from the temperature coefficient of the integral free energy change by Equation 6. 2

2

The integral free energy is determined from an adsorption isotherm by Equation 1-6. In practice it is sometimes simpler to determine the partial molal


WU AND COPELAND

359

Barium Sulfate-Water System

free energy of the adsorbent, AG^, by integration of Equation 1-12 (cf. 1-4, 6) and then to obtain AW by Equation 7

A—\ «ι (

\

-JL J T

à

= ΔΗ+

( 7)

/ «ι,&,σ

Equation 1-14 expresses the equality of A G ^ with the surface excess free energy, Δ 7 . If, as is customary, the film pressure, ττ, is used for — Δ γ , and the vapor can be considered to be a perfect gas, Equation 7 can be rewritten in its more familiar form Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch038

σ

-JH

= ΔΗ+

(7a)

where χ is the relative pressure of the vapor in equilibrium with the adsorbate. The differential enthalpies can be deduced either by differentiation of the integral enthalpy with respect to the amount of each component or from the expressions for the corresponding differential free energies. The partial molal enthalpy of the adsorbent is

\

Τ

/

n n ,a h

2

This equation is similar to Equation 7, except that n

l9

variables rather than n

1 ?

G , and T. 2

n , and Τ are the independent 2

Similarly, the partial molal enthalpy of the

adsorbate is (9)

where χ is the relative pressure of vapor in equilibrium with adsorbate. Equation 9 says that the net "isosteric" heat of adsorption is the negative change in partial molal enthalpy of the adsorbate. The "net" integral heat of adsorption could also be obtained by integration of the isosteric heat of adsorption over the range n = 0 to n . 2

2

Entropy Change in Adsorption As with enthalpy changes, entropy changes are determined from appropriate temperature coefficients of the corresponding free energy changes. The change in partial molal entropy of the absorbate is determined directly from the tempera ture coefficient of the change in free energy of the differential process (Equa tion 2). Λ5, =

-

( ψ )

-

( ψ )

;

,

(10)

The integral change in entropy, Δ δ * , is determined from the temperature coefficient of AG+. The change in differential entropy of the adsorbent, AS^, can be de termined either from the difference between the changes in entropy of the integral In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.

360


process and the differential Process 2, or from the temperature coefficient of A G ^ . These two procedures give precisely the same result, because the Gibbs-Duhem relation is applicable to A S and AS^. 2


Experimental Procedures and Results The Adsorbent. The barium sulfate used in these experiments was one of the finely divided materials prepared for the adsorption studies made by W . D . Harkins and his coworkers. This material was chosen for this work because we expected the barium sulfate-water system to be a simple system to investigate. That it is not a simple system became evident when the initial area determinations were obtained. Table I contains areas determined by adsorption of water on samples outgassed at 2 3 ° and 4 5 0 ° C ; by adsorption of nitrogen on a sample outgassed at 4 5 0 ° C ; and by the heat of immersion of a sample saturated with water. The molecular area of the water molecule was taken to be 11.4 sq. A. In experiment 2, the barium sulfate was outgassed at 4 5 0 ° C. and the area determined by adsorption of water. The sample was then outgassed by evacu ation at room temperature and 10 mm. of H g for 24 hours and the area re determined (experiment 3). The agreement was poor. The fair agreement between the area calculated from experiment 3 and the area calculated from the heat of immersion (experiment 4) of the saturated sample suggested that barium sulfate might be slightly porous or that some water might be chemisorbed. -6

Table I. No. 1 2 3 4

Measurements of Area of BaS0

Method N adsorption H 0 adsorption H 0 adsorption Heat of immersion 2

2

2

Outgassing Temp., °G. 450 450 23 450

4

σ, Sq. M . / G . 5.0 4.5 2.9 2.7

A vacuum thermogravimetric balance was then used to determine necessary conditions for outgassing. The result is shown in Figure 1. The sample was held at the temperatures indicated until the sample weight appeared to be constant over an interval of at least 4 hours. The results show that the water cannot be removed completely at any temperature below 6 0 0 ° C. Since our adsorption apparatus is not made of quartz, the outgassing temperature could not be as high as 6 0 0 ° C. The results reported here were obtained on samples out gassed in the temperature range 4 9 0 ° to 5 1 5 ° C. for 24 hours at lO^ mm. of Hg. It is evident in Figure 1 that even this treatment did not remove all the water. The area determined from nitrogen adsorption (5 sq. meters per gram) was used to calculate the surface pressure, π. The changes in free energy, enthalpy, and entropy for the processes being discussed are reported for the system contain ing 1 mole of barium sulfate, so any uncertainty pertaining to the accuracy of the area is not reflected in the results reported here, except for the absolute values of 7r. Walton and Walden (15) have explained the behavior of barium sulfate. These authors suggest that the water coprecipitated with barium sulfate is held in pockets in the crystallites, where 3 molecules of water substitute for one BaS0 ion pair in the crystal lattice. In some instances, they found that more than 25% (mole basis) of water was held in this manner and could not be removed com pletely below 5 0 0 ° C . A small but measurable expansion of the lattice results from 7

6

4



WU AND COPELAND


Ό

200

400

361

600

t.°c.

Figure 1.

Weight loss of BaSO^ in outgassing at dif ferent temperatures

the substitution. If the surface of barium sulfate contains a proportionate share of these pockets, the results shown in Table I are explainable. Adsorption Isotherms. Adsorption isotherms (Figure 2) were determined at three different temperatures, 1 2 . 3 ° , 2 3 . 5 ° , and 3 1 . 5 ° C , by two procedures, one volumetric, the other gravimetric. In the volumetric apparatus, the amount of water distilled from a calibrated capillary tube was determined by measurement of the change in level of the water in the capillary with a slide micrometer. The estimated error is about 1% of the amount adsorbed at low coverages, and less than 0.2% at high coverages. In the gravimetric apparatus, a fused silica spring with a sensitivity of 2.8 mg. per mm. was used. Elongation of the spring was measured with a slide micrometer. The sample was suspended from the spring in a bucket, weighing 17 mg., formed from borosilicate glass wool. The error in weight of adsorbed water is estimated to be ± 0 . 0 1 mg. per gram of sample. The water was purified by a vacuum distillation from alkaline potassium permanganate solution, followed by repeated vacuum sublimation from ice until the vapor from the water showed no residual permanent gas in a McLeod gage. Pressure in the volumetric apparatus was measured by a McLeod gage and by a wide-bore (30-mm.) mercury manometer. Pressures measured with the McLeod gage were corrected for capillary depression of the mercury meniscus. Pressure in the gravimetric apparatus was controlled by regulation of the temperaIn SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.

362



70,

Γ

1

ι

ι

V .2 m

I

.4

I

L

_ .6

1.0

.8

P/P° Figure 2.

Adsorption isotherms of H 0 2

on BaSO

h

ture of the water source, except at one pressure (8.5 microns of Hg) where a mixture of magnesium perchlorate dihydrate and tetrahydrate was used (5). Heat of Immersion. The adiabatie differential calorimeter used was similar in design to the isothermal differential calorimeter used by T . F. Young and somewhat like that used by Lange and Robinson (12). It will be described in detail elsewhere. The calorimeter was submerged in a water bath, the temperature of which was maintained the same as the mean temperature of the calorimeter to within 0 . 0 0 0 5 ° C. The experiments were made at 2 3 . 5 ° to 2 4 ° C. Samples were held in evacuated glass bulbs designed by Pierce (13). The sample bulb in the reference compartment contained water vapor at the same pressure as that in equilibrium with the sample, to compensate for the heat of condensation of water vapor in the sample bulb. Because of the design of the bulbs, no heat of breaking appeared in the calorimeter. The amount of water adsorbed after the samples were outgassed was con trolled by adjustment of the pressure in one of three ways: use of a sensitive Cartesian diver manostat, use of a water source at a controlled temperature, or use of the mixed magnesium perchlorate hydrates mentioned above. The amount of water adsorbed by the sample was measured either by the gain in weight of a companion sample or by interpolation from the isotherm at 2 3 . 5 ° C . The heat of immersion of samples with no water adsorbed was determined with samples sealed off from the vacuum line while they were still in the furnace at 5 0 0 ° C. There is some evidence that the heat of immersion of the well outgassed samples was liberated during a rather long time. Consequently, the heats of immersion of these samples, and also of some of the samples with small amounts of water adsorbed, were determined by integration of the recorded timetemperature curve from the time the samples were wetted until the temperature of the calorimeter had returned to its steady state. Sixteen hours were required in the case of the freshly outgassed samples instead of the 5 to 6 hours normally required. In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.

WU AND COPELAND

363



The heat of immersion results are plotted in Figure 3. The precision of the measurement depends upon the magnitude of the heat developed, and varies from about ± 5 % at saturation to about ± 2 % for the outgassed sample.

h—
• [system consisting of wiBaS0 and /z H 0] 4

2

4

2

2

(11)

can be obtained by Equation 1-6, although it is frequently more convenient to use the identity expressed in Equation 12. rn

2

Jo

G dn ~n G2 2

2

-

2

rG n dGi I 2

JO

2

(12)

The use of this identity is equivalent to the integration of the Gibbs adsorption equation (1-4),

"

(13)

Jx = O

ni


364


Satisfactory integration cannot be performed unless adsorption data are ob tained at very low pressures (II). The lowest pressure that could be measured reliably in this series of experiments was 8.5 microns of Hg. A n empirical equation fitted to the experimental points at low pressure was used to extrapolate the isotherm to zero pressures, π calculated from each of the isotherms is plotted in Figure 4. Values of the decrease in surface energy, ττ, range upward to 200 ergs c m . at room temperature, a value about the same as is found in other solid-vapor adsorption systems and less than ten times as high as is obtained by the spreading of insoluble monolayers on water (7).


-2

300

1

1

1

1

l2.3 C^ e

oj . 200 Ε ο

£

^

^

^

^

^

^

look

1

1

1

.4

1

.8

.6

1.0

P/P° Figure 4.

Reduction in surface free energy, π, caused by adsorption of water

The integral change in free energy, AG*, and the contribution to AG * by barium sulfate, n^G^, and by water, n AG , are plotted in Figure 5. The dashed lines are extrapolations to zero coverage based upon the empirical equations fitted to the data at low pressures. The integral change in free energy, AG^, decreases monotonically with in creasing coverage, as it must because the adsorption process is spontaneous for an increase in vapor pressure of the adsorbate. The curve for n AG has a slope of — oo at zero coverage and decreases with increasing coverage in the low coverage region, but passes through a minimum and increases with increasing coverage in the region where experimental points could be obtained. The difference between these curves gives the curve for n-^AG^. This curve decreases monotonically with coverage, and shows that BaSG is not an "inert adsorbent" (9) for water. The behavior of n^G^ and n AG at low coverages suggests that in systems where Henry s law is obeyed, and perhaps in systems that give a Type III isotherm, the "inert adsorbent" approximation might be satisfactory for some purposes even though AG]t is not zero. 1

2

2

2

2

4

2

2


WU AND COPELAND


365

1

A \\ -20

^

\ \

1

*"""

n

2

A G

?

^

x\


-40

η, Δ Gj"

-60

1

-80

, 20

Figure 5.

1 .

1

40

30

50

Free energy change of adsorption of water on barium sulfate

Integral change in free energy, AGt, is for system containing 1 mole of barium mlfate - - - Extrapolations Enthalpy Change. The enthalpy change measured by the heats of im mersion (smooth curve) and calculated with Equation 7 (plotted points) is compared in Figure 6. The agreement is satisfactory, since the integration of the Gibbs adsorption equation depends so strongly upon the extrapolation of the adsorption isotherm to χ — 0. The differential enthalpies are shown in Figure 7. The line through the chords represents Δ Η from heats of immersion. The plotted points are calculated from the isotherms with Equation 9, and agree satisfactorily with the curve. The curve for ΔΗ ΐ was calculated from ΔΗ+ and Δ Η . In general, the changes in partial molal thermodynamic properties of adsorbents are smaller than for adsorbates, because partial molal properties are average properties of the respec tive component. Figure 7 shows that ΔΗ^ is smaller than Δ Η ; nevertheless, the contribution of barium sulfate to the integral enthalpy change is larger than that of water, except at coverages lower than about a half of a monolayer (Figure 6). 2

χ

2

2

It was pointed out (6) that the partial molal properties of the adsorbent are average properties. The change may not be so large near the center of an indi vidual particle as at its surface. Because the adsorbent is a solid, complete equilibrium of each part of a given particle with other parts of it cannot be assumed. The center of a large particle at a depth to which the effect of adsorbate does not penetrate may sometimes be regarded as entirely inert material—of no more importance to the problem than a phase of an entirely different inert sub stance. The changes in the partial molal properties of regions near the surface therefore are likely to be somewhat larger than the quantities calculated. The phenomenon therefore is one which must not be ignored in a completely thermo dynamic treatment of adsorption. For some purposes, however, the effects may be ignored—and the procedures will be entirely adequate for those purposes. In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.


366


^

n , m M H 0/M 2

Figure 6.

2

BaS0

4

Enthalpy change for adsorption of water (I) on 1 mole of barium sulfate Ο

Data determined calorimetrically Results calculated from temperature coefficient of π

The maximum magnitude of the change in partial molal enthalpy of the adsorbent at its surface may be estimated from the following speculations. We have used η as the number of moles of solid in the system. We know that the contribution to the surface energy from the respective layers in the lattice de creases rapidly as the distance from the surface increases. In fact, a large fraction of the surface energy is contributed by the first layer (14). About 1.6% of the B a S 0 in this sample is in the first surface layer of ions. If we assume that only this first layer is affected by adsorption, the partial molal change in enthalpy of the adsorbent would be 70 times as great as shown in Figure 7. Several layers can be affected by adsorption, and the value of Δί/χΐ at a monolayer coverage would still be of the same order of magnitude as that of ΔΗ . λ

4

2

As pointed out above, ΔΗΐ for the process studied here is the net heat of adsorption. AH is then a net diflerential heat of adsorption. AH^ is the same as it would be for the adsorption process involving adsorption of vapor instead of liquid. 2

Entropy Change. The entropy change in the adsorption of water on barium sulfate is shown in Figure 8. The integral entropy, Δ St, calculated from AG * and ΔΗΐ decreases monotonically with increasing amount adsorbed. AS* can also be calculated from the temperature coefficient of π by 1

ASf = ηισ (^)

- n R In χ 2

Points calculated by Equation 14 are plotted on the curve for ASK In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.

(14)

WU AND COPELAND

Barium Sultate-Water System

367

0,

-4h


< Ο

-8h

-12

-16 0

10

V.

m

Π , mM H 0 / M 2

Figure 7.

40

30

20 2

BaS0

4

Differential enthalpy changes for adsorption of water (I) on barium sulfate

AH2. Change in partial molal entropy of water Chord plot of calorimetric data 0__ Results calculated from temperature coefficient of χ Δί/it. Change in partial molal entropy of banum sulfate

The partial molal entropies are calculated from the partial molal free energies and enthalpies. The change in the partial molal entropy of water increases monotonically to a value near zero with increasing amount adsorbed. The partial molal entropy of barium sulfate decreases with increasing amount adsorbed. Conclusion Data from two types of experiments have been used to calculate changes in thermodynamic properties of adsorption systems. The agreement is within experimental error and indicates that a complete thermodynamic treatment is as useful for adsorption systems as for solutions. In the very low coverage region we used an empirical equation to obtain π. The integral heat of adsorption calculated from isotherms is very sensitive to the temperature coefficient of ττ. Figure 6 shows that agreement between heats of adsorption calculated from the temperature coefficient of π and those measured calorimetrically is good, and Figure 8 shows that ASt calculated from the integral free energy and enthalpy changes agrees within experimental error with AS"ï calculated from the temperature coefficient of i r . The enthalpy change depends upon the temperature coefficient of π, and the free energy change depends upon the magnitude of τ τ . The agreements indicate that the temperature coefficient, as well as the magnitude, of π was estimated satisfactorily. Much more work on many systems is needed to achieve an adequate under standing of the low coverage region of adsorption systems. In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.


368


I

0

ι

10

V

m

• 20

ι

ι

30

40

n , m M H 0/M BaS0 2

Figure 8.

Ο

2

I

50

4

Entropy change for adsorption of water (I) on barium sulfate

Entropy functions calculated from free energy changes and colonmetrically determined enthalpy changes Entropy changes calculated from temperature coefficient of π

Acknowledgment We express appreciation to T . F. Young and to Stephen Brunauer for many helpful discussions and constructive criticism. We are indebted to Conway Pierce for suggestions improving our experimental techniques, and to Robert Landgren and Fletcher Klouthis for aid in preparing this manuscript. Literature Cited (1) Armbruster, Μ. Η. Α., Austin, J. B., J. Am. Chem. Soc. 66, 159 (1944). (2) Bangham, D. H., Trans. Faraday Soc. 33, 805 (1937). (3) Bangham, D. H., Razouk, R. I., Proc. Roy. Soc. (London) A166, 572 (1938). (4) Bangham, D. H., Razouk, R. I., Trans. Faraday Soc. 33, 1463 (1937). (5) Copeland, L. E., Bragg, R. H., J. Phys. Chem. 58, 1075 (1954). (6) Copeland, L. E., Young, T. F., ADVANCES IN CHEM. SER. NO. 33, 348 (1961). (7) Harkins, W. D., "Physical Chemistry of Surface Films," Reinhold, New York, 1952. (8) Harkins, W. D., Boyd, G. E., J. Am. Chem. Soc. 64, 1195 (1942). (9) Hill, T. L., Advances in Catalysis 4, 212 (1952). (10) Jura, G., Harkins, W. D., J. Chem. Phys. 11, 561 (1943). (11) Jura, G., Hill, T. L., J. Am. Chem. Soc. 74, 1598 (1952). (12) Lange, Ε., Robinson, A. L., Chem. Revs. 9, 89 (1931). (13) Pierce, W. C., University of California, Riverside, Calif., private communication. (14) Van der Hoff, Β. M. E., Benson, G. C., J. Chem. Phys. 22, 475 (1954). (15) Walton, G., Walden, G. H., Jr., J. Am. Chem. Soc. 68, 1750 (1946). RECEIVED

October 2, 1961.


SOLID SURFACES and the Gas-Solid Interface

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