REDUCING TUNGSTEN OXIDES since part of the oxygen being removed is being supplied by the W4011 + WOZ reaction proceeding in the interior. The differential equation for the progress of phase boundaries is now k3r2 = pbr2 dr/dt
+ (pb/4)(r1)~(dri/dt) (9)
Since the reaction W4011 -+ is faster than WOZ W it proceeds to completion fairly rapidly, T I becomes zero, and Equation 9 becomes -f
ka = pb dr/dt
(10)
This, of course, is the same as Equation 4. Consequently, it should be possible to superimpose the later parts of the reaction curves of Figure 1 onto these cf Figure 2, with the zero time points or Figure 1 placed a t times on Figure 2 corresponding to somewhere near 33l/s% reduction. Superposition is almost perfect escept for the 770’ C. rate data. Figure 5 shows that the rate a t this temperature deviates widely from the Arihenius plot and may be somewhat inaccurate. It is readily shown that k2
E
p
(11)
bR/‘lbt‘
Comments o n
where t’ is the time from 8.4% total reduction to 22.8% total reduction. I t is difficult to get accurate values of t1 from Figure 2 due to the steep slope of the reaction curves. Figure 5 gives estimated rate constants as a function of inverse temperature. The specific rate constant for the reaction W4011 + WO? is thus estimated as kz = 0.75 exp (-15.5/RT) g. 0 cm.-* set.-' Discussion of Results
Although this type of experimental technique cannot be expected to be very precise, carefully performed experimental work by Hougen, Reeves, and Mannella (2) has produced data which form a consistent pattern of results. I t seems likely that the over-all rate is controlled by the moving phase boundary areas since this gives a mathematical model which explains the data quite well. Application of internal diffusion control concepts, either for diffusion of gas in pores or diffusion of ions within the solid, does not give the correct form of rate equations. Diffusion of oxygen. probably as ions, appears to occur so fast
as to have no control on the rate. Large oxygen diffusion gradients can occur in these materials without phase change because of the relative stability of nonstoichiometric tungsten oxides (7). T h e frequency factor term in the rate equations may be considerably in error due to the assumption made concerning the density of WOs in the pellet. The values of the activation energies for kl and ks are probably accurate to =t1 kcal. per g. mole. No information is available on the order of the reaction with respect to hydrogen but the suggested model implies that a t 1 atm. of hydrogen, the slow step in the process is the rearrangement of oxide t o a more reduced phase. Consequently, the reaction would be expected to be zero order with respect to hydrogen a t this pressure. literature Cited (1) Anderson, J. S., Ann. Repts. on Progr. Chem. (Chem. Soc. London) 43, 115 (1946). (2) Hougen, J. O., Reeves, R. R., Mannella, G. G., IND.ENG. CHEM.48, 318 (19 56).
RECEIVED for review August 16, 1960 ACCEPTED February 20, 1961
...
Reducing Tungsten Oxides SIR:
M r . Austin refers to discrepancies in the reduction data “for the 805”C. case where it appears that the starting pellets had been overreduced in their preparation from W03” and in his conclusion says “Although the experimental technique cannot be expected to be very precise.. . .” Several years were devoted to developing the experimental technique and the work was done by some very skilled and talented personnel. The technique was found to give reproducible data and much of the information reported represents results from duplicate, triplicate, and more observations. M r . Austin can find a detailed discussion of
the experimental procedure in the original theses upon which the published data were based. Because we used the technique of starting each reduction with a new pellet and permitted the reactions to proceed progressively farther each time, experimental data for a given reduction curve is based on the reaction of many pellets. This helps to eliminate erroneous data as well as to “average out” the differences in individual pellets. Of course, we would have preferred to use the differential technique of investigation rather than, or in addition to, the integral method. We were very limited in capital and equipment and under the conditions of the experimenta-
tion, differential techniques may have been even more time consuming to develop. In view of the fact that the esperimenters are confident that all data are equally reliable, care should be taken not to reject summarily those which d o not fit a n assumed model. Perusal of the original theses might help to elucidate certain facets of the work and clarify somc of the discrepancies.
JOEL0. HOUGEX Research & Engineering Division Engineering Department Monsanto Chemical Co. St. Louis 66, Mo.
VOL. 53, NO. 8
AUGUST 7961
661
