Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]

Size: px

Start display at page:

Download "Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]"

Alexandra Goodman
7 years ago
Views:

1 onept of Atvty Equlbrum onstant s a ermodynam property of an equlbrum system. For a hemal reaton at equlbrum; onept of Atvty Thermodynam Equlbrum onstants aa + bb = + dd d [] [D] [A] a [B] b onentraton equlbrum onstant. d [ ] [ D] onentraton equlbrum onstant a b [ A] [ B] Expeted exstene of aqueous ons (deal); Strtly, and n general, e onentraton 'equlbrum onstant' s not a 'onstant' and depends on e envronment n whh e equlbrum exsts. The true equlbrum onstant s e ermodynam equlbrum onstant. on on d D a b A B = for dlute solu tons ( deal solutons) onstant for a gven T Hydraton shell Prmary hydraton shell s made of water moleules. Expeted exstene of aqueous ons (deal); + hyrated shell hyrated shell alpha=effetve dameter The hydraton of ons makes e effetve sze of e on dfferent (larger) n omparson to e bare on sze. aton shells larger an e anon shells.

2 Realst general stuaton: The extent of ontamnaton depends on e onentraton of all ons (expressed as e on streng, I or ) present n e soluton. I z For low I (=) e ontamnaton s neglgble. The hydrated shell gets ontamnated w oppostely harged ons at move n and out of e shell, makng e hydraton shell fratonally harged. For dlute (on) solutons where e ons are postoned at relatvely large nter-on dstanes, ons are essentallyhydrated w no ontamnaton. If e on streng of e soluton s sgnfant; Effet of soluton on onentraton on e equlbrum poston. on Fratonally (oppostely) harged Example: solublty (equlbrum) of slver hlorde. Ex. Agl(s) Ag + (aq) + l - (aq) Agl (s) dssoates n to e aqueous soluton and aquated ons reombne, equlbra are dynam. Agl(s) beng arngly soluble n water, e reetve on onentratons are very low, but not zero. Hydraton shell ontamnated by oppostely harged on, overall. At saturaton pont (equlbrum poston) n pure water, [ Ag ][ l ] Impled: ons are free exept for hydraton. e.g. [Ag + ] = onentraton of free ons, hydrated only. [ Ag ][ l ] deal system The expermenter, however, does not know, off hand wheer all ons dssolved has hydraton shells are lean.e. wheer only water exst n e hydraton shell, or not (ontamnated). [ ] usually means e free + ontamnated on onentraton. Analytal onentraton, e atual onentraton of e ees - ontamnated and free ons - n e system at equlbrum. In realty, e effetve free on onentraton s only a fraton of e analytal onentraton.

3 In soluton: Low [on] Hgh [on] Hydraton shell not shown nly solutons w very low onentratons n soluton would lead to a stuaton; where hydraton shells are made of water moleules only. IDEAL SLUTIN. In most stuatons a orreton must be made to aount for e non-dealty,.e. ontamnaton of hydraton shells of ons n soluton. Very dlute solutons an be onsdered as deal solutons for all pratal purposes, however. Sgnfantly on solutons makes e effetve free on onentraton of an on,, less an e analytal onentraton [] n e system. The free on onentraton avalable for e equlbrum system should be, [] = + [Ag + ] - [l - ] effetve on. of aquated 'free' ons n equlbrum w Agl(s), dynamally. a [] Atvty atvty oeffent for dlute solutons a [] Atvty oeffent s a measure e effet of dverse ons n soluton on e avalablty of ees to engage n hemal equlbra. d [ ] [ D] = a b [ A] [ B] onentraton equlbrum onstant In hgh on onentraton systems s effet s sgnfant. a d D b A B onstant for a gven T Thermodynam equlbrum onstant for dlute (deal) solutons; = 3

4 In solutons w larger on. of ons (all types of ons), e hydraton shells gets 'ontamnated' by oppostely harged ons. Thus eah on (of nterest) loses ts effetve harge. Ths redues e ablty of on omponents to reombne,.e. more ons (predted from ), an o-exst n soluton. Thus effetve on. of ees n equlbrum n soluton wll be hgher n hghly on solutons an n non-on solutons. Agl (s) = Ag + (aq) + l - (aq) Now, = a a. Ag l substtutng for on. of free ons = [ Ag ] [l ] = [ Ag ][l ].e. = n on. terms atvty fator for dlute solutons fator = = n on. terms rgn of s non deal behavor s due to e hange n e atmohere of e hydrated on. Non-dealty s sgnfant at hgh on onentratons. As e total on on. nreases; deal non deal and ve versa. s a measure of devaton from dealty of real systems. 0 for non deal (not =0) for deal 0<<, n general. As e on on. rses; 0. = f(on on.) on on. measured by on streng. Ion streng of solutons, : nludes all on types n soluton,. s a measure of e total on onentraton n e soluton. = f(); z Debye-Hukel lmtng law on ees ( 0.0M) 0.5z log ( ) / 305 atvty oef. of ees z harge of (ntegers) at 5 effetve dameter of ees (pm) For ons of same harge and effetve sze, n e same on envronment (soluton), s are e same. If harge = 0, log () = 0, = (true for most part beause suh ees (moleules) arry a mnmal on atmoheres around t). 4

5 0.5z. log ; 0,, log 0.33 =, 0, log 0 <. log - (see fg.) dereases w z z 3. log (see table) nreases w 5

6 Mean atvty oeffent of an eletrolyte A m B n ; For eletrolyte AB; mean atvty oef., ( ) s defned as; mn m n ( mn) m n m n AmBn The Debye-Hukel equaton atually breaks down for large values. Indvdual atvty oeffents annot be measured by experment but an be alulated. Mean atvty oeffent of an eletrolyte an be measured expermentally. For eletrolyte AB m n; mean atvty oef., ( A ) mbn s defned as; m n m n m n mn ( ) Maematally solublty of Agl(s) n on solutons; ermodynam ; = a + a - Ag l = + [ Ag ] -[l ] = [ Ag ][l ] =on. fator = = ; low solutons (onentraton equlbrum onstant) must be rased so at ermodynam (ermodynam equlbrum onstant) attans e true value..e. analytal (atual) onentratons of e ees are hgher an at would have been predted by n hghly on solutons. Equlbrum poston for solublty shfts forward (for ). For solublty equlbra: > n hghly on solutons. In ase of on ompounds an nrease of solublty n hgh solutons s observed. Thermodynam equlbrum onstant s e fundamental property defnng e equlbrum onstant!!. Fe SN Fe( SN) Fe( SN ) Fe SN Fe SN [ Fe( SN) ] [ Fe ][ SN ] [ Fe( SN) ] [ ] [ ] Fe( SN ) Fe SN H H H H = + H H I 6

7 Thermodynam onentraton n hghly on solutons. At very low, and are same.?! H H H H = + H H In general; [ ] [ D] True [ A] [ B] onstant d D ' a b d d D a b a b A B A B Debye-Hukel lmtng equaton an be used to alulate e for eah on ees, for < 0. M. ( = for neutral moleules) Ion streng dependent. use [ ] for all ees for ver low, n plae of atvty. 7

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3

Series Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3 Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons