On the kinetics of coupled sulfur and oxygen transfer through an ionic diaphragm
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AND
I. JIN
Turkdogan and G r i e v e s o n have shown e x p e r i m e n t a l l y by use of the coupled S-O r e a c t i o n in ionic m e l t s that it is possible to t r a n s f e r s u l f u r or oxygen f r o m a low to a high c h e m i c a l potential through an ionic m e m b r a n e . A new rate e x p r e s s i o n has b e e n d e r i v e d by applying the r e l a t i o n s of i r r e v e r s i b l e t h e r m o d y n a m i c s u n d e r the c o n s t r a i n t of e l e c t r i c a l n e u t r a l i t y . The e x p e r i m e n t a l r e s u l t s obtained by Turkdogan and G r i e v e s o n 2 a r e s a t i s f a c t o r i l y i n t e r p r e t e d by m e a n s of the new a n a l y s i s .
IN his Howe M e m o r i a l
L e c t u r e L. S. D a r k e n ~ d i s c u s s e d the n a t u r e of coupled r e a c t i o n s . T h e s e r e a c tions involve the s e p a r a t i o n of a s y s t e m into p a r t s in such a way that there is a weak but definite c o m m u n i cation between the parts. The q u a s i s t e a d y state of the s y s t e m depends on the n a t u r e of the coupling b e tween the s u b s y s t e m s . The example Darken used to i l l u s t r a t e his point of view was the uphill pumping of sulfur by the c o u n t e r flow of oxygen in an ionic m e m b r a n e , an e x p e r i m e n t c a r r i e d out by Turkdogan and G r i e v e s o n . 2'3 The subs y s t e m s c o n s i s t e d of a M n - M n O - M n S pellet and a F e - O - S m e l t in s e p a r a t e i s o l a t e d c h a m b e r s connected by a soda glass diaphragm. The p a r t i a l p r e s s u r e s of oxygen and sulfur on each side of the d i a p h r a g m were a s s u m e d to be in s i m u l t a n e o u s local e q u i l i b r i u m with the s u b s y s t e m and with the s u r f a c e of the soda g l a s s . The c o n t r o l l i n g step for m a s s t r a n s f e r between the s u b s y s t e m s would t h e r e f o r e be diffusion in the ionic d i a p h r a g m . The i s o l a t e d c h a m b e r s were i n i t i a l l y e v a c u ated so that the gaseous phase c o n s i s t e d e s s e n t i a l l y of oxygen, s u l f u r , and t h e i r compounds. In this e x p e r i m e n t the c h e m i c a l p o t e n t i a l s of oxygen and s u l f u r were both lowest on the M n - M n O - M n S side. If the diffusion of ions of oxygen and s u l f u r in soda g l a s s were independent of each other then the fluxes would be in the s a m e d i r e c t i o n , f r o m the m e l t to the pellet. However, the e x i s t e n c e of coupling b e t w e e n the two diffusion p r o c e s s e s has b e e n v e r i f i e d by the o b s e r v a t i o n of equal m o l a r c o u n t e r c u r r e n t fluxes. In the following we p r e s e n t an a n a l y s i s , a l t e r n a t i v e to that given by Turkdogan and G r i e v e s o n . 2 I m m e r s e d a s it i s in the f o r m a l i s m of i r r e v e r s i b l e t h e r m o d y n a m i c s , we b e l i e v e that our a n a l y s i s is the f u n d a m e n tally c o r r e c t one. F u r t h e r m o r e , a
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