This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 4.11. EQUILIBRIUM IN A TWOCOMPONENT SYSTEM 143 One can also eliminate Î¶ to get n N in terms of n N 2 : n N = 2 ( n N 2  t =0 âˆ’ n N 2 ) . (4.439) Now for the reaction, one must have, for second law satisfaction, that Î¼ N 2 dn N 2 + Î¼ N dn N â‰¤ , (4.440) Î¼ N 2 ( âˆ’ dÎ¶ ) + Î¼ N (2 dÎ¶ ) â‰¤ , (4.441) ( âˆ’ Î¼ N 2 + 2 Î¼ N ) dÎ¶ â‰¤ (4.442) ( âˆ’ Î¼ N 2 + 2 Î¼ N ) dÎ¶ dt â‰¤ . (4.443) In order to satisfy the second law, one can usefully, but naÂ¨ Ä±vely, hypothesize that the nonequilibrium reaction kinetics are given by dÎ¶ dt = âˆ’ k ( âˆ’ Î¼ N 2 + 2 Î¼ N ) , k â‰¥ , convenient, but naÂ¨ Ä±ve model (4.444) Note there are other ways to guarantee second law satisfaction. In fact, a more complicated model is well known to fit data well, and will be studied later. For the present purposes, this naÂ¨ Ä±ve model will suffice. With this assumption, the second law reduces to âˆ’ k ( âˆ’ Î¼ N 2 + 2 Î¼ N ) 2 â‰¤ , k â‰¥ , (4.445) which is always true. Obviously, the reaction ceases when dÎ¶/dt = 0, which holds only when 2 Î¼ N = Î¼ N 2 . (4.446) Away from equilibrium, for the reaction to go forward, one must expect...
View
Full
Document
This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Parksou during the Fall '11 term at FSU.
 Fall '11
 ParkSou
 Dynamics

Click to edit the document details