1.1 1 Potential Difference between two metals in a cell without liquid junction 2 Potential difference between two metals in a cell with liquid junction 3 4 5 1.2 • t 6 7 8 9 10 2.Introduction to potentiomentry 2.1. Galvani potential and electrochemical potential Zero energy – charged particle in vacuum at infinite separation from a charged phase Basic concepts _ 1. Electrochemical potential - μ work done when a charged particle is transferred from infinite separation in vacuum to the interior of a charged phase 2. Chemical potential - μ work done when a charged particle is transferred from infinite separation in vacuum to the interior of a phase stripped from the charged surface layer 3. Inner potential ( Galvani potential ) - φ work done when a charged particle is transferred from infinite separation in vacuum across a surface shell which contains an excess charge and oriented dipoles 11 _ μμ=+e φ 12 The inner potential may be regarded as a sum of: 1) Potential created by the excess charge, the so called outer potential or Volta potential, denoted as Ψ. For a charge q on a sphere of radius a: q ψ = a 2. Potential created by oriented dipoles with dipole moment p referred to as surface potential, denoted as χ and equal to : χ =4πNp ε / Therefore the inner potential is equal to: φ =ψ +χ 13 Thermodynamic relationships In a charged system the inner potential φ is an additional independent variable of the total Gibbs free energy: G = f (p,T,nj,φ) Basic thermodynamic definitions: _ 1. μ = (/)dG dn i ipTnn,,ji≠ ,φ 2. μ = (/)dG dn iip,,Tnji≠n ,φ = 0 Equilibrium condition: two phases α and β are in thermodynamic equilibrium when: __α β μi= μ i 14 2.2 Electrochemical equilibria and electromotive force (emf) of a cell without liquid junction 2.2 2e Note that vertical bars in the scheme of the cell denote a phase boundary 15 The cell at equilibrium __ _ _ μμ+++=++2()2Cu μμμμμ− 2 2 2(Cu ') Zn2+ eClAg Zn AgCl e After rearrangement ⎛⎞__ ()(μμ2+−−−Zn 222 μAgCl − μμ Ag − ) =− 2()(')⎜⎟ μeeCu − μ Cu Zn Cl ⎝⎠ Electromotive force of the cell _ recall μ e =−μφe F ⎛⎞__ −−=2()(')2()(')2⎜⎟μμeeCu Cu F() φφ Cu −= Cu FE ⎝⎠ 16 Electromotive force of a cell ECuCu= φ()−φ (') or ()μμ2+−−−−Zn (222 μAgCl μμ Ag ) Zn − Cl = E 22FF 222μμμ−− ()μ 2+ − μZn ()AgCl Ag Cl− E = Zn E = 1 2F 2 2F However this separation is formal or conventional in reality: μ − μμμ+−22 =−Δ=GFE 2 ZnCl2 Zn Ag AgCl 17 Examples of electrochemical cells and their emf 1. Cu’│Ag│AgCl│Cl-, Zn2+│Zn│Cu ()μμ2+−−−−Zn (222 μAgCl μμ Ag ) E =−Zn Cl 22FF 2. Cu’│Ag│AgCl│Cl-, Mn2+│Mn│Cu ()μμ2+−−−−Mn (222 μAgCl μμ Ag ) E =−Mn Cl 22FF 3. Cu’│Ag│AgCl│Cl-, Sn4+,Sn2+ │Pt│Cu ()μμ42++−−−(222 μAgCl μμ Ag −) E =−Sn Sn Cl 22FF The second term in all three equations is the same hence we can write E= Etest − const 18 Reference electrode convention (222μμμAgCl−− Ag − ) Cl = 0 2F 1. Cu’│Ag│AgCl│Cl-, Zn2+│Zn│Cu (μ 2+ − μZn ) E = Zn 2F 2. Cu’│Ag│AgCl│Cl-, Mn2+│Mn│Cu (μμ2+ − Mn ) E = Mn 2F 3. Cu’│Ag│AgCl│Cl-, Sn4+,Sn│Pt│Cu (μμ42++− ) E = Sn Sn 2F Electrode potential – emf of a cell built up from a given test electrode and a reference electrode 19 Reference electrodes + H3O │H2│Pt Hydrogen electrode - Cl │Hg2Cl2│Hg Calomel electrode Cl-│AgCl│Ag Siver chloride electrode Electrode sign convention Write electrode reactions such that electrons flow through an external circuit from the reference to the test electrode e Reference electrode , Test electrode ΔG>0 E<0 ΔG<0 E>0 20 21 22 o (μ 2+ − μZn ) Eo = Zn 2F or o (μμOx− Re d ) Eo = nF 23 24 25 2.3 Conductance, transference numbers, mobility, flux and current Transference number When current flows through a cell a fraction t+ is carried by cations and a fraction t- by anions such that: tt+−+ = 1 or in general ∑ti =1 i ti is the transference or transport number Conductance Conductance of an electrolyte equal to the reciprocal or resistance is given by: 1 κ A L == Rl Where κ is the conductivity, A is the area and l is the length of a segment of electrolyte conducting current 26 Ionic mobility Ionic mobility ui is a limiting velocity of an ion in an electric field of unit field strength. Ionic mobility is measured in cm2 V-1 s-1 or (cm/s per V/m). It is related to the ionic conductivityκ by the formula: κ = F∑ zuCiii i The transference number of ion i is the contribution to conductivity made by that Ion divided by the total conductivity: κ zuC t ==i iii i κ ∑ zuCj jj j 27 28 Equivalent conductivity Defined by: κ Λ= Cz since and κ = F∑ zuCiii κiiii= FzuC i Λ =+F()uu+ − or Λ =+()λ+ λ− where λii= Fu is the equivalent conductivity of individual ion 29 In the case of a single electrolyte : λ t = i i Λ or ui ti = uu+ + − or zCiiiλ ti = ∑ zCj jjλ j 30 2.4 Electrochemical cell with a liquid junction potential ECuCuZnCu=−φ()φφφφαφφβφαφφβ (')() ={ − (')()()} +−{ Zn} +−+{ ()()} { ()Cu − ()} {φβ()−= φα ()} ELJ 31 Different ways to make the liquid junction potential 32 Boundary between two electrolyte solutions MA M+, A- 33 Liquid junction potential between two different solutions of the same electrolyte 34 Example: concentration cell 35 36 Henderson equation Activity coefficients independent of concentration and the liquid junction a continuous mixture of the two electrolytes 37 How to eliminate liquid junction potential? Consider the following interface uC−− uC AA AA−− t − = t = A A− uC− −−−+++++++ u C uC u C uC+++ u C uC u C A A Cl Cl K K M M AA− −−−++++ ClClKK M M uC+ uC>> uC + uC assume that CCKCl>> MA then Cl−− Cl K ++ K A −− A M ++ M in predominant fraction of the liquid – junction region: u u AM− ⎛⎞C A MM+ ⎛⎞C A t − = ⎜⎟ 0 and t + = ⎜⎟ 0 A uuC+ M uuC+ Cl−+ K ⎝⎠KCl Cl−+ K ⎝⎠KCl 38 Consequently: 11ββt Edt=− i μμμ=− dt− d LJ ∫∫∑ i ()K++ K Cl − Cl − Fzααi i F 1 To a good approximation ddμ ==μμ d and since KCl+−2 KCl tt≈ K + Cl− 11ββ1 Etdtdttd=−−=−−≈μμ μ0 LJ ∫∫()KKClCl++ − − ()KCl+ −KCl FFαα2 39 Elimination of the liquid junction potential by a salt bridge 40 2.5 Donnan equilibrium and Donnan potential( IUPAC definitions) 41 Donnan equilibrium and Donnan potential 42 2.6 Selectively permeable membranes C+ C+(p) C+(q) C1 Cx C C 2 C-(p) - 1 C-(q) 2 pqx Δ=φφ(2)(1)(2)()()() − φ ={ φ − φqqpp} +{ φ − φ} +{ φ ()(1) − φ} Δφ =ΔφφφDL(2) +ΔJD +Δ (1) 43 or AgBr 44 45 46 S1 S2 K + + + + H (s1) + Napp(p) = H (p) + Na (s1) + + + + H (s2) + Na (q) = H (q) + Na (s2) 57 A B A B 48 49 valinomicine 50 51 52 2.8. Membrane potential – overview ) 53 54 } 55 56 2.8 57 58 59 60 Review 1. Solid state membrane ( AgCl pelet) ΔφLJ = 0 2. Membrane with dissolved ion exchanger ΔφLJ = 0 3. Membrane with a fixed ion exchanger ΔφLJ ≠ 0 61 General expression for the membrane potential ⎧ zi ⎫ RT ⎪ pot z j ⎪ EMM=Δφ =ln ⎨aKa iijj + ⎬ Fz i ⎩⎭⎪ ⎪ 62 2 ICz= 0.5∑ ii i Ci 63 t 64 2.9 Quantitative analysis – Standard addition method Standard addition method: 1) Use an excess of an “inert electrolyte” (0.15M NaCl in Ca2+ analysis) to keep the ionic strength constant (γ = constant). 2) Take the measurement of the unknown: RT EE10=+ ln CAγ FzA 3) Spike unknown with a standard solution ( volume Vs, , concentration Cs ) RT ⎛⎞CVA Ass+ CV EE21=+Δ=+ EE 0 ln ⎜⎟γ FzAAs⎝⎠ V+ V 4) Calculate the difference E21− EE=Δ RT ⎛⎞CV+ CV zFA Δ E CV+ CV Δ=E ln ⎜⎟A Ass or 10 2.3RT = A Ass Fz C() V+ V AAAs⎝⎠ CVA ()As+ V and after rearrangement Cs CA = zFA Δ E⎛⎞VV 102.3RT 1+−A A ⎜⎟ 65 ⎝⎠VVs s 66 67 ISE – sources of errors 68 2.11 Biosensors 69 b) Tissue electrode E/mV -log C(glutamine) 70 c) Bacterial electrode 71 d) Chemically modified field effect transistor pn-junction 72 Field effect transistor 73 Chemically modified field effect transistor 74 3. Introduction to electrometric methods 3.1 Structure of the metal interface neutrality condition σ M =−(σσid + ) interface – two capacitors in series 111 =+ CCCid σ OHP- outer Helmholtz plane; distance of the closest approach of solvated ions IHP – inner Helmholtz plane; plane in which specifically adsorbed ions are located Diffuse layer – layer within which ionic cloud screening the charge on the metal is located 75 Capacity of an Au electrode adsorbed anions 60 50 Nonadsorbing electrolyte 40 2 30 F/cm μ C 20 10 adsorbed neural organic molecules 0 -1.2 -0.8 -0.4 0.0 0.4 E V vs. Ag/AgCl 76 Capacity of an electrode changes with potential – the changes reflect changes in the Coverage by specifically adsorbed ions or molecules σ M = fE(,)Γ ⎛⎞∂∂σσMM ⎛⎞ ddσ M = ⎜⎟Ed+Γ ⎜⎟ ⎝⎠∂∂E Γ ⎝⎠ΓE dσσMM⎛⎞⎛⎞∂∂ σ MdΓ C ==⎜⎟⎜⎟ + dE⎝⎠⎝⎠∂∂Γ E Γ E dE } true capacity pseudo capacity 77 Potential drop across the metal solution interface no specific adsorption specific adsorption of anions 78 3.2 Electrochemical cell in the presence of a current flowing through the cell Two electrode cell 79 when potential E is applied from an external source current flows through the cell From Ohm’s Law: E i = Z ZZZ= ie++ ZRe f + Z ext Zi – impedance of the indicator electrode Ze – impedance of the electrolyte ZRef – impedance of the reference electrode Zext – impedance of the external circuits 80 In an electrochemical experiment Ze, ZRef, Zext must be eliminated a.