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Ionic Solutions Structure of liquids Interactions in ionic solutions Ion-ion interactions Debye-Huckel theory.

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Presentation on theme: "Ionic Solutions Structure of liquids Interactions in ionic solutions Ion-ion interactions Debye-Huckel theory."— Presentation transcript:

1 Ionic Solutions Structure of liquids Interactions in ionic solutions Ion-ion interactions Debye-Huckel theory

2 How do we describe structure of liquids? Not random c.f. gas Not periodic c.f. solid Liquid are isotropic (same in all directions) Anisotropic  a property that is directionally dependent Structure of liquids

3 Let’s compare distribution functions Ideal Gas Radial distribution function g(r) completely featureless  equally likely to find a particle at any distance r from another particle Uncorrelated V. weak molecular attraction % Probability

4 g(r) Next nearest neighbour shell Nearest neighbour shell Solid Strong correlation between atoms even at large separations  lattice structure, fixed neighbours

5 Liquid Well-defined 1 st shell but broader than solid & less clear successive shells  short-range order Liquids form due to intermolecular potentials Broad Weak

6 Objective To find: Difficult to calculate from individual (microscopic) interactions using statistical mechanics techniques  Use macroscopic view of interactions Interactions in ionic molecules Interaction Potential  I,j  H,  G,  S average over molecules

7 3 classes of interactions: Solvent-solvent  H (H 2 O)= +44 kJmol -1 H-bonding Solvent-ion  H solv (K + Cl - )= -685 kJmol -1 Ion-ion  H solid (Na + Cl - )= -719 kJmol -1 Ionic solutions dissolve in polar solvents  strong solute-solvent interactions compensate for high lattice enthalpies and lost solvent-solvent interactions Na + Cl - solid solute H 2 O solvent Na + aq + Cl - aq solution strong interionic forces strong intermolecular forces strong solute-solvent interactions Net  G (KCl aq ) = -1.2 kJmol -1

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9 Energy between two ions carrying charge z 1 and z 2 separated by r is given by (from Coulomb’s Law): where  0 is the vacuum permittivity,  r is the relative permittivity or dielectric constant of the solvent This is the energy needed to move the ions to a distance r apart, starting from an infinite separation Ion-ion interactions

10 Like charge Opposite charge

11  r is extent to which a solvent reduces the energy of interaction between ions dissolved in it. Typical values at 25  C Value of  r correlates with the solvent polarity  explains why H 2 O excellent solvent C6H6C6H6 2 (C 2 H 5 ) 2 O4 Pyridine12 CH 3 OH33 CH 3 CN36 Me 2 SO47 H2OH2O78

12 Polar molecules possess a permanent dipole moment,   = q. r Dipole moment: 1.major source of solvation (hydration) energy 2.reduces ion-ion interactions in solution Source of polarisation: 1.molecular polarisability  : dipole induced by a field E  = . E r -q+q E Universal property but small  r (C 6 H 6 ) ~ 2

13 Electrolyte solutions are non-ideal due to long-range ion interactions Electrostatic interactions decrease with distance r only as versus for interactions between neutral species. Debye-Huckel theory Distance between ions / Å Interaction strength % Ions Neutrals

14 Electroneutrality of system (solute+solvent) means net charge around any ion is equal and opposite to its charge In ideal solutions this charge would be uniformly spread BUT Oppositely charged ions attract each other:  arrangement of ions in solution is not random  excess of counter-ions in vicinity (ion atmosphere) Time average - + -- -- -- -- Ionic atmosphere

15 Chemical potential of an ideal solution is:  A =   A + RT ln[A] For non-ideal (IONIC) solutions  A =   A + RT ln a A where a a =  A. [A] and a A is the activity of A,  A is the activity coefficient  A < 1 for dilute ionic solutions due to electrostatics Electrostatic interactions between an ion and its ionic atmosphere lower its chemical potential

16 The difference in  between 1.the charged solution 2.an ideal one without electrostatic interactions gives the energy of charging, w e  G = w e =  -  ideal = RTln   Neutral + Charges on wewe  G -ve if  < 1

17 The activity coefficient (deviation from ideality) depends upon the ionic strength of the solution: where c i is the concentration of ion i, and z i its charge. A general salt has the form: z  is charge on the anion/cation  gives stoichiometry sum includes all ions in solution Na + Cl - Na 2 + SO 4 2-

18 1.Calculate the ionic strength of a 0.2 M CaCl 2 solution 2.Calculate the ionic strength of a 0.2 M KCl solution cationanion I = Conc for 1:1 salt

19 Can now calculate activity (ion-ion interactions) where z  is the charge on the anion/cation, A depends on T and solvent and I the ionic strength. Assuming: 1.Only electrostatic interactions between hard-sphere ions (no ion-solvent) 2.Electrolyte is fully dissociated and no ion-pairs exist 3.Structureless solvent with uniform permittivity often formed in solvents of low polarity -+ Ion-pair Debye-Huckel Limiting Law ONLY VALID FOR VERY DILUTE SOLUTIONS

20 Electrochemistry Electrodes Electrochemical cells Electrode potentials Nernst Equation Electrode types

21 Electrodes Electroneutrality: Nature dislikes charge separation Consider immersing a Zn rod in water: small number of Zn atoms dissolve as Zn 2+ ions electrons left behind on rod Zn(s)  Zn e -

22 Build up of: –ve charge on rod +ve charge in solution rapidly inhibits this process  concentration of Zn 2+ ions v. low This prohibition is the Electroneutrality Principle -measure of work required to separate charges -non-spontaneous (  G > 0) Reaction can be enhanced by: 1.draining excess e - from rod 2.adding an e - acceptor to metal (e.g. H + ) ~ M  pure H 2 O acids attack metals

23 Later method is basis of electroplating: If place Zn rod in aqueous CuSO 4 instead of H 2 O Zinc metal quickly covered with black coating of finely-divided metallic copper. Simple oxidation-reduction process involving 2 e - from Zn to Cu Zn(s)  Zn e - Cu e -  Cu(s) Zn dissolution allowed as e - s removed from rod by copper ions and solution stays electrically neutral Net reaction:Zn(s) + Cu 2+  Zn 2+ + Cu(s) CuSO 4 1 hr

24 Electrochemistry is the study of reactions in which charged particles (ions/e - ) cross the interface between 2 phases of matter: a metallic phase - electrode a conductive solution - electrolyte This kind of reaction is known generally as an electrode process. Electrode processes at the surface of electrodes produce a slight charge imbalance between the electrode and electrolyte.  this produces an interfacial potential difference (can affect rate and extent of chemical reactions)

25 These interfacial potential differences (  ) are small (a few volts) BUT occur over extremely short distances. Electrodes immersed in solution have a thin, stable layer of water molecules and ions attached to their surface. Small voltages produce v. large potential gradient: 1 volt over 100 Å = 10 8 V cm -1 huge potential gradient ~ Å  +

26 ASIDE Interfacial potential difference  - arises from changes in chemical+electrical environments  =  metal -  solution = E (V) Zn Metal core Sea of e -  metal  solution Zn 2+ SO 4 2- Hydrated Free ion Anion interaction

27 Since electron-transfer reactions occur near electrode surfaces we cannot channel e - s through an instrument to measure this voltage BUT If have 2 metal-solution interfaces can easily measure potential difference between them - this arrangement is called an electrochemical (galvanic) cell. Typical cell consists of 2 metal electrodes e.g. Zn and Cu, each immersed in a salt solution of the corresponding metal 2 solutions are connected by a tube with a porous barrier (salt bridge) - this prevents rapid mixing but allows ions to diffuse through. OxidationReduction

28 A special notation is used to describe electrochemical cells: Vertical bars indicate phase boundaries Double vertical bar in the middle denotes salt bridge Each electrode/solution pair is called a half-cell Cell reaction written so: Oxidation occurs at left-hand electrode Reduction occurs at right hand electrode Independent of actual location of 2 electrodes on bench! Electrochemical cells

29 Conventions Anode is where oxidation occurs Cathode is where reduction occurs If electrons flow from left  right electrodes spontaneously  potential of the RIGHT electrode > LEFT electrode Electrochemical cell potential = Right - Left E cell = E right – E left E cell +ve if spontaneous -ve requires external drive Thermodynamics

30 Problem How do we find absolute values for individual half-cells? (E R and E L ) Can only ever measure difference between 2 electrodes ? 2 nd electrode

31 Can measure half-cell potentials relative to that of other half cells. Adopt a reference electrode (half-cell) whose potential is arbitrarily defined as zero. Measure potentials of various other electrodes against reference Standard Electrode Potentials Salt bridge Also electrodes but:  (KCl) tiny Cancels anyway! E = (E R + E KCl ) – (E L + E KCl ) = E R - E L

32 Standard Hydrogen Electrode (SHE) Use under standard conditions: 1 bar 298 K Unit activity (dilute solns)

33 Carry out series of measurements for various M x+ /M systems Construct table arranging these half-cell reactions in order of their potentials. Convention: Write half-cell reactions as reductions (so M x+ /M on RIGHT) e.g. Zn e  Zn(s)  Standard Electrode Potential E  = E  M2+/M - E  H+/H2 set = 0 (SEP)

34 SEP clearly related to spontaneity of process In practice H 2 electrode rarely used in routine measurements: Difficult to prepare; Pt surface has to be specially treated Need H 2 gas  cumbersome and hazardous Activity (Electromotive) Series Disfavoured Favoured

35 Want stable reference: Concentration of ionic species involved must be constant. Simplest method uses an electrode reaction involving saturated soln. of an insoluble salt of the ion e.g. silver-silver chloride electrode Ag | AgCl(s) | Cl - || AgCl(s) + e -  Ag(s) + Cl - Coating made using Ag rod in an electrolytic cell containing HCl - Ag+ ions combined with Cl - ions at the silver surface Silver-Silver Chloride Electrode (SHE)

36 Given the E  values for two half reactions, you can easily predict the voltage of the corresponding combined cell: SEP of the reduction half-cell minus SEP of the oxidation half-cell Example 1: Construct a Zn/Cu electrochemical cell & state cell reaction Zn(s) | Zn 2+ || Cu 2+ | Cu(s)or Cu(s) | Cu 2+ || Zn 2+ | Zn(s) Cell reaction Zn(s) + Cu 2+  Zn 2+ + Cu(s) orZn 2+ + Cu(s)  Zn + Cu 2+ E cell = E  Cu2+/Cu - E  Zn2+/Zn E cell = E  Zn2+/Zn - E  Cu2+/Cu (-0.76) Prediction of cell potentials E cell = E right – E left

37 Example 2: Find the standard potential of the cell and the direction of e - flow Ag(s) | AgCl(s) | Cl - || Cu 2+ | Cu(s) Half-cell reactions: AgCl(s) + e -  Ag(s) + Cl - Cu e -  Cu(s) Net cell reaction: 2Ag(s) + 2Cl - + Cu 2+  AgCl(s) + Cu(s) E cell = E  Cu2+/Cu - E  Cl-/AgCl = (+0.337) – (+0.222) = V Since E cell is +ve reaction is spontaneous e - flow Ag  Cu Written as reductions

38 Thermodynamics: Nernst equation Charge imbalance at electrode surfaces produces an interfacial potential difference  - reflects different electrochemical energies in electrode vs soln. Electrochemical potential of species A defined as: Recall:  A =  A + z A F  A chemicalelectrical F = Faradays constant amount of charge carried by 1 mole of electrons 1 F = Coulombs  =  + RT ln[A] AA 

39 Example: Fe 3+ + e - (metal)  Fe 2+ (  Fe3+ + 3F  solution ) + (  e- - F  metal ) = (  Fe2+ + 2F  solution ) Recall for ANY reaction at equilibrium Fe 2+ Fe 3+ X-X- Total  reactants = Total  products Rearrange  F(  metal -  solution ) =  Fe3+ +  e- -  Fe2+  F  =  Fe3+ +  e- -  Fe2+  =  + RT ln[Fe 3+ ] Fe 3+   =  + RT ln[Fe 2+ ] Fe 2+   Fe3+  e-  Fe2+ where  = (  Fe3+ +  e- -  Fe2+ ) 

40 In general, Thermodynamics states: since,  = E (V) Nernst Equation -nF

41 Proof: Maximum amount of work, w, is given by w = -VQ where V is emf,Q charge flowing. Q = nF for 1 mole of cell reaction Since dG = dw(T, P constant ) and when E +ve Spontaneous

42 What does it all mean?! Often need to describe non-standard conditions M 2+ (aq) + 2e -  M (s) If [M 2+ (aq) ] is increased, the equilibrium shifts to the right (i.e. more e - are absorbed from the electrode )  Actual value of E M2+/M is more positive than E  M2+/M Nernst Equation: quantifies this relationship where = RT/F

43 The effect of n: Consider the reaction Mn(s) | Mn 2+ (aq) || Fe 3+ (aq) | Fe 2+ (aq) First write down the two half-cell reactions. Mn e -  Mn(s) E  = V Fe 3+ + e -  Fe 2+ E  = V Cell reaction: 2Fe 3+ + Mn  Fe 2+ + Mn 2+  E  cell = (-1.182) = 1.95 V Even though Mn reaction involves 2 e - and the iron only 1 e - !! Hence ½ Mn 2+ + e -  ½Mn (s) E  = V Mn e -  Mn(s) E  = V

44 Care must be taken when making comparisons -  G terms are truly additive - convert to  G if unsure How can this be true?! Consider, So if n doubles:  G  doubles as expected  twice as much work to transfer 2 e - but E  remains the same 2+

45 Calculating how far reactions go? Since And We can combine the two equations such that We can therefore determine E Θ values from K and vice versa Consider our first reaction. Zn (s) + Cu 2+ (aq)  Zn 2+ (aq) + Cu (s) E Θ cell = V E Θ cell = = ln K Hence, ln K = 85.6 or K = 1.62 x n The reaction therefore goes to completion.

46 More importantly, electrochemistry allows the measurement of very large or very small values of K. Manganate (VI) ions are unstable with respect to disproportionation into Mn(VII) and Mn(II) in acidic solution. 5 HMnO 4 2- (aq) + 3 H + (aq)  4 MnO 4- (aq) + Mn 2+ (aq) + 4 H 2 O (l) This reaction can be expressed as: HMnO 4 2- (aq) + 7 H + (aq) + 4 e -  Mn 2+ (aq) + 4 H 2 O (l) E Θ = V 4 MnO 4 2- (aq) + 4 H + (aq) + 4 e -  4 HMnO 4- (aq) E Θ = V Overall E = 0.73 V, hence K = since n = 4. High concentrations of MnO 4 2- cannot be achieved in acidic solution.

47 Calculation of an unknown electrode potential from two others using  G. Given: (a)E  (Pu 3+ /Pu) = V (b) E  (Pu 4+ /Pu 3+ ) = 0.98 V find E  (Pu 4+ /Pu) = ? First write out the half reactions and express in terms of  G  (a)Pu e -  Pu (s) E  = -2.03;  G  = +6.09F (b)Pu 4+ + e -  Pu 3+ E  = +0.98;  G  = -0.98F (c)Pu e -  Pu (s)  G  = -4FE  Construct a suitable thermodynamic cycle  G  c =  G  a +  G  b  G  c = +6.09F – 0.98F = 5.11F = - 4FE   -4FE  = 5.11 E  (Pu 4+ /Pu) = V

48 Summary Ionic solids require polar solvents to overcome high lattice energies Even in ionic solutions electrostatic interactions between ions cause strong deviations from ideal neutral solutions Deviations increases with ion concentrations/charge Electrochemical potential of ions differs from neutral (solid) phase Interfacial potential difference drives electrochemical reactions (ion reactivity described by electromotive series) Interfacial potential related to Gibbs free energy for e - transfer Electrochemical reactions subject to  G>0

49 Electrochemistry Key Equations Chemical Potentials  A =   A + RT ln[A] IDEAL  A =   A + RT ln a A NON-IDEAL a a =  A. [A] activity  A < 1 for dilute solutions activity coefficient Ionic Strength z i = charge on each ion c i = conc. of each ion Electrochemical Cell Potential E cell = E right – E left E cell +ve spontaneous -ve non-spontaneous Gibbs Free Energy Nernst Equation Q = reaction quotient  equilibrium constant


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