(Re&ved 30 January 1978) Dear siis, With reference to our commu&ation on A [email protected]
+Treatment of the Met Boundary Condition for L%pemivr z;low Mo&r[l] two points have baa brought to our attention that deserve mention. The first item concerns the integration of eqn (3) Bird points out that the proper results ought to give eqn (4) as
For the second item we are indebted to Stewart, who notes that it is not necessary to our conclusions that the diffusivity have continuous 6rst derivatives. It can for example be piecewise continuous. The several condusions and comparisons in our communication are not altered by these arguments. but they do set the record straight and may he useful for further study.
This correction will not atTect what follows become3
~artmmt of Chemical and Biochemical Eb&neering Unihsiry of Pennsylvania PhiQddphia PA 19104. U.S.A.
since eqn (7)
CHA Y. CHOI D. D. PERLMUTTER
(11 ChoiCha Y. and Perlmutter D. D., C&m. Eagxg Sci. 1976 31 259.
and still goes to zero in the same way as A + 00.
ChemicdE&mui~Scimcr Vd.33.m.1567~lSt# @FwprmlRusLtd.,1978. PrilncdiacKatBritain
(Received 11 April 1978) Dear
LeCardinal er al. published an interesting paper in Chew. Engng Sci. 32,733 (1977) entitled, “A New Operating Method for the Kinetic Study of Open Systems by Means of Tracer Elemerits”...We have been working on similar problems for a number of years first using steady state tracing and also since 1972 transient tracing of reactions which are occurring under steady state conditions as regards the chemical elements involved[l]. We believe that some of our work and that by other investigators may be of interest to your readers in placing this study in context. In steady state tr& of a reaction, if one assumes no isotopic kinetic &et& the unidirectional velocity of a reaction can be readily identitied by means of the fraction of atoms of a given atomic species which are marked by isotope. In cases where radioactive isotope is employed only a very smaU fraction of marking is necessary. For tracing with stable isotopes such es % or D it is necessary when one has obMned steady state data without tracer to switch to a mixture containing tracer. but with the same total proportion of atoms both marked and unmarked.
Thus the steady state overall reaction is maintained the same both before and after introduction of tracer. This procedure for steady state tracing has been used for a long time. For example, Enemoto and Ho1iuti established equilibrium concentrations of Nz, HZ and NH3 for the ammonia synthesis reaction and then tested a mixture of the same equilibrium concentration but with the nitrogen in NH3 marked with “N to determine unidirectional reaction rates. Later Raneko and Oki studied the mechanism of the water gas shift reaction in which the overall reaction rate was taken as that of water contakdng deuterftnn. which served to identtfy unidirectional rates. We also in a study of sulfur dioxide oxidatfon  employed ‘“0 in which different kvels of marking were used at the same overall reaction velocity. Other examples could be cited. In these cases, of eenrse. the assumption is that no perturbation of the overall reaction occurs by add&on of tracer in this fashion. In 1972 we suggested the extension of this approach to the use of unsteady state tracing. We mentioned that the concentration of reacting species was often perturbed in such experimentation