Electrlyte Slutin Muhammad Abbas Ahmad Zaini PhD, CEng Centre f Lipids Engineering & Applied Research, UTM Tpic Outcmes Week Tpic Tpic Outcmes 6-7 Electrlyte Slutin The enthalpy, entrpy and Gibbs energy f In frmatin in slutin It is expected that students are able t: Define and determine activities and activity cefficient. Activities and activity cefficient The Debye-Hückel thery f electrlyte slutin Evaluate mean inic chemical ptential in electrlyte and its characteristic by Debye-Hückel limiting law. Chemical equilibrium in electrlyte slutin
Intrductin Slutins are hmgenus mixtures f 2 r mre pure substances In slutin, the slute is dispersed unifrmly thrughut the slvent. Inic slid disslving water Frmatin f Slutin Slvent mlecules attracted t surface ins. Each in is surrunded by slvent mlecules. Enthalpy ( H) changes with each interactin brken r frmed.
Ins are slvated (surrunded by slvent) If the slvent is water, the ins are hydrated The intermlecular frce here is in-diple Terminlgy Electrlyte cmpund that if disslved in water can t inized Electrlyte slutins slutin that can cnduct the electricity Inizatin prcess Prduce ve and ve in. Charge f the ins that cnduct the electricity frm 1 electrde t ther electrde
Slutin Strng electrlyte Electrlyte Weak electrlyte Slutin Nnelectrlyte Ideal & real slutins Neutral slutes Strng Electrlyte Prduce ins & cnduct electricity; underg the cmpletely inized. If its test by using electrlyte tester will prduce light lamp and there are gas bubble H 2 O NaCl(s) Na (aq) Cl (aq) H 2 O CaBr 2 (s) Ca 2 (aq) 2Br (aq) 100% ins
Weak Electrlyte Cnduct electricity by weak; underg half inized and prduce a few ins HF(g) H 2 O H 3 O (aq) F (aq) CH 3 COOH H CH3COO
Nn-electrlyte Slutins that can t cnduct electricity; d nt prduce ins Disslve as mlecules in slutin E.g. Glucse, urea & alchl H, S, G f in frmatin in slutin
Thermdynamics f Electrlyte The thermdynamics f electrlyte slutins is imprtant fr a large number f chemical systems Acid-base chemistry Bi-chemical prcesses Electrchemical reactins Materials that dissciate int psitively and negatively charged mbile slvated ins when disslved in an apprpriate slvent. Slvatin Shell 1/2 H 2 (g) 1/2 Cl 2 (g) H (aq) Cl (aq) H R -167.2 KJ/ml Energy flw int the system is needed t dissciate and inize hydrgen and chlrine Slvatin shell is essential in lwering the energy f the ins thus making the reactin spntaneus Mre energy is gained in the rerientatin f the diplar water mlecules arund the ins in the slvatin shell Reactin is exthermic Nte: H f fr a pure element in its standard state 0; A slvatin shell is a shell f any chemical species that acts as a slvent and surrunds a slute species
Heat f Reactin Standard state enthalpy in terms f frmatin enthalpies, H reh f,a( qc) H( l f)ah,qactin N cntributin f H 2 (g) & Cl 2 (g) (pure element) t H f Cannt be measured directly by calrimetric experiment Hw t btain the infrmatin f slvated catins and anins?? Nte: H f fr a pure element in its standard state 0 Thermdynamics Functins fr catins and anins Can be btained by making an apprpriate chice fr the zer f H f, G f and S m. GH,aq f Fr all T ( ) 0H,a( q ) ( ) TGH,aqSHand,aq f P ( ) f ( ) ( ) 0HGH f,aqtsh,aq0
H rxn, G rxn, S rxn 1/2 H 2 (g) 1/2 Cl 2 (g) H (aq) Cl (aq) Frm previus reactin, ( )aq,clhhfrxn ( )aq,clggfrxn ( ) ( ) ( ) g,cls1/2g,hs1/2aq,clss2m2mmrxn
rxn41rxn1.2kjmlexample: NaCl NaCl (s) Na (aq) Cl (aq) H H HCl f1 3.90,aqHNa, ( ) f ( ) f( ) 67.2kJml1240.1kJml1 ( ) ( )1aqHNaCl,skJm l1 Values f G f and S m can be determined in similar manner Nte: H f, cnventinal frmatin enthalpies; G f, cnventinal Gibbs energies frmatin; S, cnventinal frmatin entrpies Nte H f, G f & S m fr ins are defined relative t H (aq) H f ve; Frmatin f the slvated in is mre exthermic than the frmatin f H (aq) Multiply charged ins and smaller ins mre exthermic because strnger electrstatic attractin with water in the slvatin shell Entrpy decreases as the hydratin shell is frmed because water mlecules are cnverted t relatively immbile mlecules Larger charge-size-rati than H (aq). E.g. Mg 2( aq), Zn 2( aq), PO 3 4 (aq) Slvatin shell is mre tightly bund
Example 1 Calculate H reactin, S reactin and G reactin fr the reactin AgNO 3 (aq) KCl(aq) AgCl(s) KNO 3 (aq) Check Yur Understanding Calculate H reactin, S reactin and G reactin fr the reactin Ba(NO3) 2 (aq) 2KCl(aq) BaCl 2 (s) 2KNO 3 (aq)
Thermdynamics f In Frmatin & Slvatin Earlier, H f, G f & S m cannt be determined fr an individual in in a calrimetric experiment. Nw, the thermdynamic functins assciated with individual ins can be calculated with reasnable level cnfidence using a thermdynamic mdel. Allws H f, G f & S m values t be cnverted t abslute values fr individual ins. Example: Individual Cntributin t G f ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1rxn22slvatinrxnslvatinrxn1rxn1rxn1rxn21rxn2131.2kJmlGaqClaqHg1/2Clg1/2Haq,HGGaqHgHaq,ClGGaqClgCl349kJmlGgClegCl1312kJmlGegHgH105.7kJmlGgClg1/2Cl203.3kJmlGgHg1/2H Dissciatin Frmatin f ins Analyze the frmatin f H (aq) & Cl (aq) The change in the Gibbs energy fr verall prcess, ( ) ( ) 1slvatinslvatinrxn1272kJmlaq,HGaq,ClGG
HaqvanPathway 1/2 H 2 (g) 1/2 Cl 2 H (aq) Cl (aq) G rxn G G 1 rxnsl27 tin2kj131.2kj / ml Cl,aqG ( ) sl( ml)1 vati, Play imprtant rle in the determinatin f the Gibbs energies f in frmatin Can be estimated using Brn mdel Determinatin f G slvatinεw nnexp, rev assciated with slvatin can be calculated, G fr the prcess is knwn. Cnsider, neutral atm A gains the charge q, first in a vacuum and then in a unifrm dielectric medium. G slvatin f an in with a charge q W rev (A(g) A q (aq)) slvatin rev. prcess (A(g) A q (g)) vacuum Electrical ptential arund sphere, φ 4'rπQCharge Q Radius r Nte: W nn-exp, rev, nn-expansin wrk fr a reversible prcess
14Q'dqWrk The wrk in charging a neutral sphere in vacuum t the charge q QQ 00' 4εr εr 00Q8εrπ 2wπ π Q'dq'0The wrk f the same prcess in a Qwslventr 8εε2π 0rPermittivity f free space Relative permittivity (dielectric cnst.) f the slvent Brn Mdel ( G slvatin) Fr an in f charge Q ze, G slvatin Charge number f the in z2e2n1ga 1 slvatin 8εr ε π 0r radius Avgadr s cnst. Because ε r >1, G slvatin < 0 Slvatin is spntaneus prcess Relative permittivity (dielectric cnst.) f the slvent Nte: Values fr ε r fr number f slvents, Table 10.2 (App. A, Data Tables)
2iiBrn Mdel (Fr Water) G slvatin < 0 is strngly negative fr small, highly charged ins in media f high relative permittivity. Fr water at 25 C, G slvatinz r 6.86104( 1) kjm lref.: Atkins, P., Paula, J. D. (2006). Physical Chemistry. 8 th ed. W.H Freeman and Cmpany. N. Y. Example 2 Calculate G slvatin in an aqueus slutin fr Cl (aq) using the Brn mdel. The radius f the Cl in is 1.81 10 10 m.
kjm4v6.86using the Brn Equatin T see hw clsely the Brn equatin reprduces the experimental data, we calculate the difference in the values f G f fr Cl and I in water, fr which ε r 78.54 at 25 C, given their radii as 181 pm and 220 pm (Table 20.3*), respectively, is G sl ( ) s( ) ( lv 18 2 )16 11120ClGI7kJml 10 l1 This estimated difference is in gd agreement with the experimental difference, which is 61 kj ml 1. *Ref.: Atkins, P., Paula, J. D. (2006). Physical Chemistry. 8 th ed. W.H Freeman and Cmpany. N. Y. Activities & activity cefficient fr electrlyte slutin
Thermdynamics f Ins in Slutins μμrtln caγ cdeviatins f electrlyte slutin frm ideal behavir ccur at mlalities as lw as 0.01 mle/kg Thermdynamic prperties f inic species in slutin?apreviusly, fr the H (aq) in, we define H f 0 kj/mle at all T S m 0 J/(K mle) at all T G f 0 kj/mle at all T Activities & Activity Cefficient Activity & activity cefficient f cmpnent f real slutin is Nt Valid fr electrlyte slutins. Slute-slute interactins are dminated by lng range electrstatic frces present between ins in electrlyte slutins NaClH( ) OlNC( ) aa( q) l ( )as2 NaCl cmpletely dissciated Slute-slute interactins are electrstatic in nature Activity & activity cefficient must be frmulated differently fr electrlytes t include the Culmb interactins amng ins. q
Activities in Electrlyte Slutins Cnsider 1 mle f an electrlyte dissciating int ν catins & ν - anins, Gibbs energy f the slutin, Nte: subscript, catin;, anin slutesluteslventslventμnμng In general dissciates cmpletely, vvba( ) μvμvnμnμnμnμngsluteslventslventslventslventv, v- are stichimetric cefficients f the catins & anins, prduced upn dissciatin f the electrlyte Mean Inic Chemical Ptential Since, v v v μvμvμslutefr a strng electrlyte Mean inic chemical ptential μ fr the slutevμvμvvμμslute Next task is t relate the chemical ptentials f the slute & its individual ins t the activities f these species.
μmean Inic Activity Define the activities, μμr TlnaFr the individuals ins μμrtlna μμ slu tevv μμμrtlna vμ v Fr the ideal dilute slutin μμrtlna Nte: The standard chemical ptentials f the ins (μ & μ ) are based n Henry s law standard state Relatinship between a & a μe saaμlut μ RTlna vμrtlnaarvv( ) 1 ( ) This gives us the relatinship between the electrlyte activity & the mean activity av Mean inic activity a is related t the individual in activities by,vaaa/vvvva
a/vcacheck Yur Understanding vμv vμμ Express µ in terms f µ and µ fr a) NaCl, b) MgBr 2, c) Li 3 PO 4, and d) Ca(NO 3 ) 2. Assume cmplete dissciatin. avv( ) 1 a Express a in terms f a and a fr a) Li 2 CO 3, b) CaCl 2, c) Na 3 PO 4 and d) K 4 Fe(CN) 6. Assume cmplete dissciatin. Inic Activity avv( ) 1 a /vaγ cif the inic activities are references t the cncentratin units f mlality, mm v m aγmaγm mm v m Activity is unitless, the mlality must be referenced t a standard state cnc. m 1 ml kg 1 In this standard state, Henry s law (valid in the limit m 0), is beyed up t a cnc. f m 1 mlal.
Activities in Electrlyte Slutins vvvaaa γmma γmma vvvvvγγmmmma Relatinship between a, m & γ γmmaγmmavvv r Thus, the mean inic activity is related t the mean inic activity cefficient & mean inic mlality, Simplify, ( ) mvvmmmm1/vvvvvv ( ) 1/vvvvvvγγγγγγ Mean inic mlality, m Mean inic activity cefficient, γ ccγa
μsluμsluluchemical Ptential Expressin μμsμrtlna vμrtlna tete mvμrtlnvvvrtlnvrtlnγ vv [ ( )] m v avvγv m m Nrmal standard state (usually taken t be Henry s law standard state) Obtained frm the chemical frmula fr the slute This can be factred int 2 parts temμvrtln vrtlnγ m The ideal part (assciated with γ 1) Deviatins frm ideal behavir (γ can be btained thrugh exp. r measurement n electrchemical cells r theretical mdel)
Check Yur Understanding Express γ in terms f γ and γ fr a) SrSO 4, b) MgBr 2, c) K 3 PO 4, and d) Ca(NO 3 ) 2. Assume cmplete dissciatin. γ γvv( ) 1 γ /vexample 3 Calculate the value f m in 5.0 x 10 4 mlal slutins f a) KCl, b) Ca(NO 3 ) 2, and c) ZnSO 4. Assume cmplete dissciatin. Calculate the mean inic mlality & mean inic activity f a 0.150m Ca(NO 3 ) 2 slutin fr which the mean inic activity cefficient is 0.165. Calculate the mean inic activity f a 0.0150m K 2 SO 4 slutin fr which the mean activity cefficient is 0.465. (Ans: 0.0111)
The Debye- Hückel Thery Estimates f Activity Cefficients amγ m Deviatins frm ideal slutin behavir ccur at much lwer cncentratin fr electrlytes Lng-range electrstatic Culmb interactin is mre dminant (interactin between the ins) Cannt be neglected (even fr very dilute slutins f electrlytes) Allw theretical estimatin f the mean activity cefficients f an electrlyte. Each has a limited range f applicability.
The Debye-Hückel Limiting Law This valid fr small cncentratins (up t 0.010 mlal*) Izz0.5092lgγ ( ) ( ) 2ii2ii2ii2iizmzm21zvzv2mIIzz1.173lnγ r The Debye-Hückel Extended Law (reliably estimate the activity cefficients up t a cnc. f 0.10 mle/kg*. B 1.00 (kg/mle) 1/2 IB1Izz0.510lgγ *Ref: http://peple.stfx.ca/gmarang/chem232 0.1 0.06 The Davies Equatin Can reliably estimate the activity cefficients up t a cncentratin f 1.00 mle/kg*. *Ref: http://peple.stfx.ca/gmarang/chem232 mi0.30mi1mizz0.510lgγ1/21/2an empirical mdificatin f Debye-Hückel limiting law fr high cncentratin
Ilnγ173zICheck Yur Understanding m2v2 ( ii ii ) 2zvzIExample 4 Calculate inic strength, I fr 0.05 mlal Na 2 SO 4. m2v2 ( ii ii ) 2zvz 1. z Using the Debye-Hückel limiting law, calculate the f γ in 5. 0 10 3 m f slutins f a) KCl (Ans: 0.92) b) Ca(NO 3 ) 2 c) ZnSO 4 (Ans: 0.52) Assume cmplete dissciatin
Equilibrium Cnstant fr Electrlyte Slutin Equilibrium cnstant in terms f activities K e( qv) ji ithe activity f a species relative t its mlarity Activity cefficient f species i i acaγiiactivities rather than cncentratin must be taken int accunt t accurately mdel chemical equilibrium Cnsider the range f inic strengths fr which the Debye-Hückel limiting law is valid cthe Aut-inizatin f Water Water aut-inizes (self-dissciates) t a small extent 2H 2 O(l) H 3 O (aq) OH - (aq) H 2 O(l) H (aq) OH - (aq) These are bth equivalent definitins f the autinizatin reactin. Water is amphteric. Nte: Amphteric, can act as either an acid r a base
()()OHK(()())()The Aut-inizatin Equilibrium The activity equilibrium cnstant, aha 3 HOaHO222we knw a(h 2 O) is 1.00, r ahoaaohkw a(h) a(oh-) In prduct cnst. fr water, K w, is the prduct f the activities f the H and OH - ins in pure water at a temperature f 298.15 K K w a(h ) a(oh - ) 1.0x10-14 at 298K Slubility Prduct Cnstant The equilibrium cnstant in terms f mlarities fr inic salts is usually given the symbl K sp Nte: sp, slubility prduct
Example: Dissciatin MgF 2 Cnsider ( ) ( ) ( )aq2faqmgsmgf22 The activity f the pure slid can be set equal t 1,932FMg2FMgsp106.4γccccaaK22 Frm the stichimetry f the verall equatin, Mg2F2ccFcandγ?? Iteratin Slve fr c F, Giving c Mg2 Calculate inic strength Recalculate γ Final γ & c Mg2 1 γ ( ) mzmz21i22assume 932FMg2FMgsp106.4γcaccaaK22 Cnverge Izz0.5092lgγ
Tutrial Calculate the slubility f BaSO 4 (K sp 1.08 10 10 ) (a) in pure H 2 O and (b) in an aqueus slutin with I 0.0010 ml kg 1. At 25 C, the equilibrium cnstant fr the dissciatin f acetic acid, K a, is 1.75 10 5. Using the Debye-Hückel limiting law, calculate the degree f dissciatin in 0.100m and 1.00m slutins. Cmpare these values with what yu wuld btain if the inic interactins had been ignred.