Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]
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1 Conept of Atvty Equlbrum onstnt s thermodynm property of n equlbrum system. For heml reton t equlbrum; Conept of Atvty Thermodynm Equlbrum Constnts A + bb = C + dd d [C] [D] [A] [B] b Conentrton equlbrum onstnt. d [ C] [ D] onentrton equlbrum onstnt b [ A] [ B] Expeted exstene of queous ons (del); Strtly, nd n generl, the onentrton 'equlbrum onstnt' s not 'onstnt' nd depends on the envronment n whh the equlbrum exsts. The true equlbrum onstnt s the thermodynm equlbrum onstnt. on on C d D th b A B = for dlute solu tons ( del solutons) C th onstnt for gven T Hydrton shell Prmry hydrton shell s mde of wter moleules. Expeted exstene of queous ons (del); + hyrted shell hyrted shell lph=effetve dmeter The hydrton of ons mkes the effetve sze of the on dfferent (lrger) n omprson to the bre on sze. Cton shells lrger thn the non shells.
2 Relst generl stuton: The extent of ontmnton depends on the onentrton of ll ons (expressed s the on strength, I or ) present n the soluton. I z For low I (=) the ontmnton s neglgble. The hydrted shells get ontmnted wth oppostely hrged ons tht move n nd out of the shell, mkng the hydrton shell frtonlly hrged. Non del soluton. For dlute (on) solutons where the ons re postoned t reltvely lrge nter-on dstnes, ons re essentlly hydrted wth no ontmnton,.e. del soluton. If the on strength of the soluton s sgnfnt; Effet of soluton on onentrton on the equlbrum poston. on Frtonlly (oppostely) hrged Exmple: solublty (equlbrum) of slver hlorde. Ex. AgCl(s) Ag + (q) + Cl - (q) AgCl(s) dssotes n to the queous soluton nd quted ons reombne, equlbr re dynm. AgCl(s) beng rngly soluble n wter, the reetve on onentrtons re very low, but not zero. At sturton pont (equlbrum poston) n pure wter, Hydrton shell ontmnted by oppostely hrged on, overll. Assumng delty [ Ag ][ Cl ] A+BC+D Impled: AgCl(s) Ag (q)+cl (q) Ag Cl Ag + Cl - ons re free exept for hydrton. e.g. [Ag + ] = onentrton of free ons, hydrton only. [ Ag ][ Cl ] [Ag ][Cl ] = = th del system = totl on on. Ions wth len hydrton shell, del soluton
3 Negtve on Postve on AgCl(s) A+BC+D Ag (q)+cl (q) - Ag + Cl - Ag+ Cl - + [Ag ][Cl ] = > Hgher thn n n del soluton Ions wth ontmnted hydrton shell, non-del soluton The expermenter, however, does not know, off hnd whether ll ons dssolved hs hydrton shells re len.e. whether only wter exst n the hydrton shell, or not (ontmnted). In the thermodynm equlbrum onstnt (whh s the true onstnt) the onentrton vlues re those of free ees. In relty, the effetve free on onentrton s only frton of the nlytl onentrton. [ ] usully mples the totl on,.e. nlytl onentrton, the tul onentrton of the ees - wth ontmnted hydrton shells nd free ons - n the system t equlbrum. Reserve [ ] notton to totl on/nlytl onentrton. In soluton: Low [on] Hgh [on] Hydrton shell not shown nly solutons wth very low onentrtons n soluton would led to stuton; where hydrton shells re mde of wter moleules only. IDEAL SLUTIN. In most stutons orreton must be mde to ount for the non-delty,.e. ontmnton of hydrton shells of ons n soluton. Very dlute solutons n be onsdered s del solutons for ll prtl purposes, however. Sgnfntly on solutons mkes the effetve free on onentrton of n on,, less thn the nlytl onentrton [] n the system. The free on onentrton vlble for the equlbrum system should be, [] = + [Ag + ] - [Cl - ] effetve on. of quted 'free' ons n equlbrum wth AgCl(s), dynmlly. [] Atvty tvty oeffent for dlute solutons [] 3
4 Atvty oeffent s mesure the effet of dverse ons n soluton on the vlblty of ees to engge n heml equlbr. d [ C] [ D] =C b [ A] [ B] onentrton equlbrum onstnt In hgh on onentrton systems ths effet s sgnfnt. th C d D b A B onstnt for gven T In very low on onentrton systems ths effet my be neglgble. Thermodynm equlbrum onstnt for dlute (del) solutons; = C th In solutons wth lrger on. of ons (ll types of ons), the hydrton shells gets 'ontmnted' by oppostely hrged ons. Eh on (of nterest) loses ts effetve hrge. Ths redues the blty of on omponents to reombne,.e. more ons (predted from ), n o-exst n soluton. Thus effetve nlytl on. of ees n equlbrum n soluton wll be hgher n hghly on solutons thn n non-on solutons. AgCl (s) = Ag + (q) + Cl - (q) Now, =. + - Ag Cl substtutng for on. of free ons = [ Ag ] [Cl ] = [ Ag ][Cl ].e. = n on. terms tvty ftor for dlute solutons ftor = = n on. terms rgn of ths non del behvor s due to the hnge n the tmohere of the hydrted on. Non-delty s sgnfnt t hgh on onentrtons. As the totl on on. nreses; del non del nd ve vers. s mesure of devton from delty of rel systems. 0 for non del (not =0) for del 0<<, n generl. As the on on. rses; 0. = f(on on.) on on. mesured by on strength. 4
5 Ion strength of solutons, : nludes ll on types n soluton,. s mesure of the totl on onentrton n the soluton. = f(); z Debye-Hukel lmtng lw on ees ( 0.0M) 0.5z log ( ) / 305 tvty oef. of ees z hrge of (ntegers) t 5 C effetve rdus of the ees (pm) For ons of sme hrge nd effetve sze, n the sme on envronment (soluton), s re the sme. If hrge = 0, log () = 0, = (true for most prt beuse suh ees (moleules) rry mnml on tmoheres round t). 5
6 0.5z. log ;.33 0,, log 0.e. =, 0, ;z nd would determne. l og -z (see fg.) dereses wth z 3. log (see tble) nreses wth Atvty oeffent drops s on tmohere (strength) nrese. Men tvty oeffent of n eletrolyte A m B n ; For eletrolyte AB; men tvty oef., ( ) s defned s; mn m n ( mn) m n m n AmBn The Debye-Hukel equton tully breks down for lrge vlues. Indvdul tvty oeffents nnot be mesured by experment but n be lulted. Men tvty oeffent of n eletrolyte n be mesured expermentlly. For eletrolyte AB m n; men tvty oef., ( A ) mbn s defned s; m n m n m n mn ( ) Mthemtlly solublty of AgCl(s) n on solutons; thermodynm ; = + - Ag Cl + - = + [ Ag ] -[Cl ] + - = [ Ag ][Cl ] =on. ftor = = ; low solutons (onentrton equlbrum onstnt) must be rsed so tht thermodynm (thermodynm equlbrum onstnt) ttns the true vlue..e. nlytl (tul) onentrtons of the ees re hgher thn tht would hve been predted by n hghly on solutons. Equlbrum poston for solublty shfts forwrd (for ). For solublty equlbr: > th n hghly on solutons. In se of on ompounds n nrese of solublty n hgh solutons s observed. Thermodynm equlbrum onstnt s the fundmentl property defnng the equlbrum!! 6
7 Fe SCN Fe( SCN) [ Fe( SCN) ] Fe( SCN ) [ Fe ] [ SCN ] Fe SCN [ Fe( SCN) ] Fe( SCN ) [ Fe ][ SCN ] Fe SCN H H H H = + H H I Thermodynm th Conentrton th n hghly on solutons. At very low, th nd re sme. [ Fe( SCN) ] [ ][ ] Fe SCN Fe( SCN ) Fe SCN [ Fe( SCN) ] [ Fe ][ SCN ] Fe( SCN ) Fe SCN?! In generl; [ C] [ D] True [ A] [ B] onstnt d C D ' b d d C D th b b A B A B Debye-Hukel lmtng equton n be used to lulte the for eh on ees, for < 0. M. ( = for neutrl moleules) Ion strength dependent. H H H H = + H H use [ ] for ll ees for ver low, n ple of tvty. 7
8 HA N H H A N V b, C b H H H Ions present n soluton s ttrton rehes V e. Mterl for next Lb exerse. V e Con. of d = C Con. bse = C b Volume of soluton fter ddton of V b ; = V +V b V, C Equvlene pont volume = V e At eq. pt. C V = C b V e monoprot d. At 95% ompleton of reton, V b = 0.95V e = V.95 (sy) C V [ ] V V.95 C b 0. 95V e [ N ] V V C V V V [ A ] C V V V [ HA ]. 95 [ H ]& [ H ] very smll to ontrbute to! Exmple Clulton Ion Molrty, M Chrge, z,pm Atvty oeffent, N HP P z Ion Strength, M = z log ( ) / 305 Atvty oeffents of ll ons,. log x 0 x z 305 8
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