CHPTER 6 / HRVEY. CHEMICL B. THERMODYNMICS ND C. MNUPULTING CONSTNTS D. CONSTNTS FOR CHEMICL RECTIONS 1. Precipitatin Reactins 2. cid-base Reactins 3. Cmplexatin Reactins 4. Oxidatin-Reductin Reactins E. LE CHÂTELIER'S PRINCIPLE F. LDDER DIGRMS G. SOLVING PROBLEMS H. BUFFER SOLUTIONS I. CTIVITY EFFECTS J. SUGGESTED PROBLEMS 6.1, 6.2, 6.4, 6.5, 6.7, 6.12, 6.14, 6.19 PPENDIX 3 ND 4 1
. Gulberg and Waage (1867) reactin is at equilibrium when the rates f the frward and reverse reactins are equal. It is a dynamic state. a bb cc dd rate f = rate r a b f f c d rate r = kr [ C] [ D] rate = k [ ] [ B] eq c d [ C] [ D] k f a b [ ] [ B] k r K = = The expressin btained is the crrect expressin fr the equilibrium cnstant, but the methd f derivatin has n general validity. Because, reactin rates depend n the mechanism f the reactin! Reactin rates depend n the number f clliding species (mlecularity) whereas the equilibrium cnstant expressin depends nly n the stichimetry f the reactin. e.g. S 2 O 2 8 3I 2 SO 2 4 I 3 Rate = k f [S 2 O 8 2 ] [I ] 2
Change in cncentratins f reactants and prducts as the reactin prceeds What can be predicted frm knwledge f the equilibrium cnstant? 1) the tendency f the reactin t ccur and in what directin 2) Nt whether it is fast enugh t be feasible in practice ** Even with a large K, a reactin may prceed frm right t left if sufficiently large cncentratins f prducts are initially present 3
B. THERMODYNMICS ND a bb cc dd chemical system evlves spntaneusly twards its lwest energy state. Energy f a chemical system changes during a chemical reactin. What determines the final psitin f a reactin? 1) Enthalpy 2) Entrpy and temperature G = H TS (1) t cnstant pressure and temperature G = H T S (2) G change in Gibbs free energy H change in enthalpy (net flw f energy as heat) S change in entrpy T temperature in Kelvins 4
H T S G Frward reactin Reverse reactin < 0 > 0 < 0 Spntaneus < 0 < 0, T S < H < 0 Spntaneus < 0 < 0, T S > H > 0 Spntaneus < 0 < 0, T S = H 0 > 0 < 0 >0 > 0 > 0, T S > H < 0 Spntaneus Spntaneus > 0 > 0, T S < H > 0 > 0 > 0, T S = H 0 Spntaneus 5
Gibbs free energy is a functin f cncentratins G = G RT ln Q (3) c d [ C] [ D] [ ] a [ B] b Q = (4) G change in Gibb's free energy under standard -state cnditins Standard-state cnditins 298 K 1M slute Pure slid Pure liquid 1 atm partial pressure t equilibrium G = 0 Therefre G = RT ln K (5) 6
Thermdynamic Equilibrium Cnstant versus Cncentratin Equilibrium Cnstant Fr very dilute/ ideal slutins (mm), in the absence f interactins between reactants, the equilibrium cnstant can be calculated using cncentratins. Equilibrium cnstant based n cncentratin is smetimes referred t as cncentratin equilibrium cnstant. C c [ C] [ D] eq d eq K = (6) a [ ] eq [ B] b eq Real thermdynamic equilibrium cnstant c d a C ad K = (7) a b a ab a [ ] = (8) a activity activity cefficient ph = lg a H Mlecular slutes have activity cefficients very near unity up t an inic strength f 0.1. ctivity cefficients f pure liquids and slids are equal t ne. 7
ctivity cefficients f inic slutes Fr inic slutes the extended Debye-Huckel equatin is used t calculate the activity cefficient lg 2 0.51 z = 1 3.3 α µ µ (9) at 25 C, µ 0. 1 1 2 µ = c i z i (10) 2 i z charge f the in α effective diameter f the hydrated in in nanmeters µ inic strength f the slutin It is handy t recgnize the fllwing Type f inic cmpund Inic strength B C 2 B 2 3 C 2 B 2 4 C 3 B 3 6 C 8
Relatinship between cncentratin equilibrium cnstant and thermdynamic equilibrium cnstant K = K C c C a d D b B lg K = lg K C lg c C a d D b B pk C = pk lg c C a d D b B pkc = pk c lg C d lg D a lg b lg B pk C = pk 2 2 z C z 0.51 µ ( D z z c d a b B )( ) α α α α 1 3.3 µ C D 2 2 B Measure K C at different inic strength and extraplate t zer t btain K. 9
C. MNUPULTING CONSTNTS C.1 Reverse reactin's equilibrium cnstant 1 K 2 = K1 C.2 Overall equilibrium cnstant Ni 2 NH 3 Ni(NH 3 ) 2 Ni(NH 3 ) 2 NH 3 Ni(NH 3 ) 2 2 Ni(NH 3 ) 2 2 Ni(NH 3 ) 3 2 K verall = K1K2K3K 4 NH 3 Ni(NH 3 ) 3 2 NH 3 Ni(NH 3 ) 4 2 If reactins ( B) = reactin C, the equilibrium cnstant f reactin C (Kc) is equal t the prduct f the equilibrium cnstants fr reactin and B. C.3 Equilibrium Cnstants are used fr: Calculatin f cncentratins f chemical species at equilibrium under cnditins where the same infrmatin might be difficult t measure r is unbtainable by direct experiment. Predictin f cnditins that will lead t desired results 10
D. CONSTNTS FOR CHEMICL RECTIONS D.1 PRECIPITTION RECTIONS Metathesis reactin gno 3 NaCl gcl( s) NaNO3 g ( aq) NO3 ( aq) Na ( aq) Cl ( aq) gcl( s) Na ( aq) NO3 ( aq) Net inic equatin g ( aq) Cl ( aq) gcl( s) Slubility prduct : K sp gcl( s) g ( aq) Cl ( aq) K sp = [ g ][ Cl ] = 10 1.8 10 pk sp = 9. 74 11
D.2 CID-BSE RECTIONS D.2.1 Brønsted and Lwry definitin cid: prtn dnr Base: prtn acceptr D.2.2 Strng and weak acids and bases Strng acids and bases are cmpletely dissciated in water HCl, HNO 3, HCLO 4, HI, First prtn f H 2 SO 4 NaOH, KOH Weak acids and weak bases Weak acids and weak bases are weak electrlytes, they are partially dissciated in water. CH 3 COOH H 2 O CH 3 COO - H 3 O Cnjugated base f the acid CH 3 COO - H 2 O CH 3 COOH OH - NH 3 H 2 O NH 4 OH - NH 4 H2 O NH 3 H 3 O Cnjugated acid f the base 12
D.2.3 cid and base dissciatin cnstants [ CH 3COO ][ H3O ] K a = [ CH 3COOH ] K b [ CH3COOH ][ OH ] = [ CH3COO ] K a Kb = [ H3 O ][ OH ] = K w 13
D.2.4 Dissciatin f water H 2 O(l) H 2 O(l) H 3 O (aq) OH - (aq) Water is amphiprtic 14 K w = 1.0000 10 at 24 C [ K OH ] = w [ H3 O ] ph poh = pk w =14 pk a pkb = pk w =14 D.2.5 Other amphiprtic species HCO 3 - H 2 O H 2 CO 3 (aq) OH - (aq) HCO 3 - (aq) H 2 O(l) CO 3-2 (aq) H 3 O (aq) D.2.6 Plyprtic acids H 2 CO 3 H 3 PO 4 H 2 C 2 O 4 14
H 2 CO 3 (aq) H 2 O(l) HCO 3 - (aq) H 3 O (aq) HCO 3 - (aq) H 2 O(l) CO 3-2 (aq) H 3 O (aq) [ HCO3 ][ H3O ] 7 K a 1 = = 4.45 10 [ H 2CO3] pk a1 = 6.352 K a 2 [ CO 3 ][ H3O ] 11 = 4.69 [ HCO3 ] 2 = 10 pk a2 =10.329 K f K f K a1 a2 a3 15
D.3 COMPLEXTION RECTIONS D.3.1 Definitins G.N. Lewis definitin f acids and bases cid: electrn pair acceptr Base: electrn pair dnr in the frmatin f a cvalent bnd. Cmplexatin generally refers t reactins where a ligand (a Lewis base) dnates an electrn pair t a metal in (a Lewis acid) t frm a cvalent bnd between. D.3.2 Frmatin cnstants (K f ) and dissciatin cnstants (K d ) Stepwise frmatin cnstants ( K i ) Cumulative r verall frmatin cnstants ( β ) β i = K 1 K 2 K3... K i i 16
D.4 OXIDTION-REDUCTION RECTIONS D.4.1 Definitins Reactin in which electrns are transferred frm ne reactant t anther. The reducing reagent is xidized (xidatin state increases) The xidizing reagent is reduced (xidatin state decreases) 5 C 2 O -2 4 (aq) 2 MnO - 4 (aq) 16 H (aq) 10 CO 2 (g) 2 Mn 2 8H 2 O(l) Oxalate is xidized [xidatin state f C changes frm 3 t 4] Permanganate is reduced (xidatin state f manganese changes frm 7 t 2) Oxalate is the reducing agent Permaganate is the xidizing agent 17
D.4.2 Equilibrium Cnstant fr Redx reactins? Because electrchemical ptentials are easily measured fr redx reactins, they are cnveniently used t express equilibrium and t calculate equilibrium cnstants. Free energy fr mving a charge under the influence f a ptential E is given by: G = E Q (1) Q = nf (2) G = nfe (3) n number f mles f electrns per mle f reatant F Faraday's cnstant (96,485 C.ml 1 ) Negative sign???? G = nfe (4) G = G RT ln Q (5) Substituting (3) and (4) in (5), yields (6) nfe = nfe RT ln Q (6) Divide (6) by (nf) RT E = E ln Q (7) nf 1 1 R = 8.31451JK ml T = 298.15 ln Q = 2.30258lgQ RT 2.30258 = 0.05916V = 59.16mV F 18
E 0.05916 = E lgq (8) n Standard-State Electrchemical Ptential fr the Reactin ( E ) t equlibrium E = 0, therefre E RT = lg K (9) nf Therefre, if the standard-state ptential f a reactin is knwn, the equilibrium cnstant f the reactin can be calculated. Standard-state ptentials fr chemical reactin can be calculated using available standard state-ptentials f the xidatin and reductin halfreactins. E reac = E red E x E red standard-state reductin ptential f the reduced reactant E x standard-state reductin ptential f the xidized reactant 19
What are Standard-State Reductin Ptentials? (ppendix 3D) Standard-state reductin ptential f chemical species relative t the reductin ptential f the hydrnium in, which by cnventin is set t 0.000 V. They express the tendency f chemical species t be reduced relative t the hydrnium in. 2 H 3 O (aq) 2 e - 2 H 2 O(l) H 2 (g) E H O / 3 H 2 = 0.000V If E > 0.000, species has a greater tendency t be reduced than H Strng xidizing agents have large psitive E (dixygen, permanganate) If E < 0, species has lesser tendency t be reduced than hydrgen and a greater tendency t be xidized. Strng reducing agents have large negative E (Zinc, Sdium) 2H ( aq) 2e H 2 ( g) E = 0. 000V 2 Zn 2e Zn( s) E = 0. 763V O2 ( g) 4H 4e 2H 2O E = 1. 229V 3 2 Fe e Fe E = 0. 771V I3 2e 3I E = 0. 536V 20
Calculate the equilibrium cnstant f the fllwing reactin 3 2 2Fe 3I 2Fe I3 1) Standard-State reactin ptential 2) Equilibrium cnstant 21