CHARACTERIZATION OF ADSORPTION RATESON HETEROGEXEOUS SURFACES
Feb., 1963
Because magnesium is soluble in liquid aluminum,25 the usual expression m0208 --
TABLE I11 HEATOF REACTION FOR 4MgO(s) f 2Al(l) + MgA1204(s)
A(FTO - H m O )
T
T
- R I n -p a M g U2A1
(OK.)
for calculating the heat should include the reduction in A1 activity produced by the solution of magnesium. This can be done by solving the equationP
X M-~ (1600/RT)(X~1)~
In
aMg
= In
In
aAl
= In XAI
-
T
(1600/RT)(X~,)~
to obtain the composition and activity of aluminum in equilibrium with magnesium vapor. The results are given in Table 111. Omission of the activity correction would increase the heat by 0.5 to 1.5 kcal./mole. The lower heat value, 127 kcal./rnole, yields a heat of formation for MgA1,04 from the oxides of - 6 kcal./mole and for the upper limit of 131 kcal., a heat of formlation of -10 kcal./mole. Other than possible errors in the values of the free energy functions used in these calculations, no explanation for the decreasing heat value is apparent. Ifowever, these results lead to an (25) A. Sohneider and E. K. Stoll, Z. EEektrochem., 47, 519 (1941). (26) “Selected Values for the Thermodynamic Properties of Metals and Alloys,” Minerals Research Laboratory, Univ. of Calif., Berkeley, Calif ., 1958.
Pnaga (mm.)
+ 3Mg(g) - A(FTO H%ss)/TC
a
d
XM,~
1143 3 . 5 5 0.047 0.085 1194 7.56 .OS5 .095 1232 13.3 .065 .lo9 1271 23.6 .078 .117 .095 .146 1345 56.0 .114 .170 1379 89.0 .119 ,177 1388 100.1 1390 102.5 .120 .177 .139 .200 1414 143.2 Reference 26 a Reference 18.
aAib
369
(e.u.)
aH0298
(koal./ mole)
0.910 .900 .884 .877 .843 .816
82.94 130.9 82.47 130.8 82.20 130.4 81.94 129.8 81.48 129.6 81.26 128.6 .808 81.10 128.2 .808 81.10 128.1 .782 81.07 127.3 References 7, 13, and 27.
estimate of the heat of formation of magnesium aluminate from the elements of -552 kcal./mole, but ithe error limits of this value are difficult to assess. Acknowledgments.-This work was performed under the auspices of the U. S. Atomic Energy Commission at the Department of Mineral Technologyof the University of California, Berkeley, and LRL-Livermore. The author is indebted to Professor Alan W. Searcy of .the Department of Mineral Technology for his guidance a,nd support during this investigation. (27) K. R. Bonnickson, J . Phys. Chem., 69, 220 (1955).
A NOVEL TECHNIQUE FOR CHARACTERIZATIOS OF ADSORPTION RATES ON HETEROGENEOUS SURFACES BY L. M. NAPHTALI AND L. M. POLINSKI Polytechnic Institute of Brooklyn, Brooklyn 1, hr. Y . Received August 10,1962 A novel technique is proposed for obtaining and interpreting data on adsorption rates to a catalyst surface. The method is illustrated by actual data from a hydrogen-on-nickel system. The amount of adsorbed gas on a catalyst which is part of an isothermal system varies with time when the pressure changes. The variation depends on the adsorption kinetics and the hetero,geneity of the surface. For a sinusoidally varying pressure, the dependence of the adsorption amplitude and phase lag on the frequency is one way of characterizing adsorption kinetics. The “frequency response” to an induced sinusoidal pressure variation of the moles of gas adsorbed on a uniform surface having first-order kinetics can be computed theoretically. A heterogeneous surface is assumed t o be an assembly or series of “different uniform-surfaces” randomly interspersed. An assembly of such surfaces, characterized by different rate conetants, has an out-of-phase component of the adsorption which resembles a spectrogram, separating the effect of different types of surface sites irrespective of the fact that adsorptions are occurring simultaneously on &like sites. As an illustration of the technique, hydrogen adsorption was studied on a supported nickel catalyst. The effect of oxygen addition t o the catalyst on the adsorption kinetics of hydrogen was studied. It was found that an increase in oxygen content reduced the amount of fast adsorption and increased the slow adsorption. It was possible t o characterize and separate the rates of adsorption of both the fast and the slow types.
Introduction The problem to be discussed is, essentially, how to interpret data on adsorption rates to a catalyst surface. Frequently during chemical adsorption on a catalyst surface, several processes occur simultaneously. This may be due to the heterogeneous nature of the surface or to the existence of different adsorbed states. I[n either case, the tools of automatic control theory can be used to separate the phenomena and give further information on their nature. I n order to determine the dynamic characteristics of an unknown system, ,the control engineer uses or induces certain forms of disturbances of “inputs” and observles or interprets their effects or “outputs.” Two of the
most useful types of inputs for the study of process dynamics are the step-function and the sine wave. I n the study of the kinetics of adsorption, the input commonly used (though not usually thought of in this sense) is the step-function, or instantaneous jump in a system variable. A typical example of a step input is an evacuated chamber containing catalyst which is instantaneously opened allowing the adsorbing gas to enter freely. The sine wave input, however, has been overlooked in studies of adsorption kinetics.1 The sinusoidal disturbance is particularly useful when the surface being investigated is expected to be hetei~o(1) L. Polinski, Doctoral Dissertation, Polytechnic Institute of Brooklyn, 1961, p. 29.
L. 31. KAPHTALI A~YDL. M. POLINSKI
370
An/Ane,
T'ol. 67
=
sin wt
1
- (w/a)cos w t
+ (./a>z
+
(3)
1 (w/ai)2 where a is the adsorption rate constant and w is the angular frequency of pulsation in radians/unit time. The sine term is the in-phase or real part and the cosine term is the out-of-phase or imaginary part of the frequency response. This equation may also be written in complex notation
An/An,,
0.2-1 0. I
-0
I
I
where i
I
=
=
+ w')
(az- iaw)/(a2
(3a)
d z ;the real part, R, is expressed R
TIME.
+ wz)
= a2/(a2
(3b)
Figure 1.
and the out-of-phase or imaginary part
Figure 2.
I = - aw/(a2 w2) (3c) One notes a very useful property of the imaginary or out-of-phase part; namely, that it reaches a local maximum when the angular frequency w equals the adsorption rate constant a aiid that it approaches zero both when w >> a and when w
