Electrochemistry

1. Electrochemistry

2. E1. Fundamental concepts Anelectrolyteis a substance which leads electric current in solution or in form of melt. Electrolytic dissociation: In solutions neutral molecules decompose to charged particles – ions: +: cation - : anion

3. The charge of one mol ion: z · e · NA = z · 1.602·10-19 C · 6.022·1023 mol-1= = z · 96485 C mol-1 NA : Avogadro constant; z: charge number. Faraday constant: F = 96485 C mol-1 Fundamental units Elementary charge:e = 1.602 · 10-19 C (The charge of anelectronis –1.602 · 10-19 C.) E.g. Ca2+ : z= +2 PO43- : z = -3

4. Fundamental concepts The Faraday constant is equal to the charge of one mole singly charged positive ions (e.g. Na+ or H+) Composition units used in electrochemistry Concentration: c [mol dm-3] (mol solute per dm3 solution, molarity) Molality: m [mol kg-1] (mol solute per kg solvent, Raoult concentration) Advantage of molality - more accurate - does not change with T

5. E2. Equilibrium in electrolytes Even very dilute solutions cannot be regarded ideal (because of the strong electrostatic interaction between ions). Still Kccan be frequently used as equilibrium constant (It is assumed here that the activity coefficients are independent of concentration, so K is taken constant).

6. Dissociation equilibrium C+: cation A-: anion CA = C+ + A- c0(1-a) c0·a c0·a c0 : initial concentrationa : degree of dissociation (E1)

7. The degree of dissociation(a) is the number of dissociated molecules per the number of all molecules (before dissociation). 0  a  1 adepends on concentration (it is higher in more dilute solutions).

8. Autoprotolitic equilibrium of water H2O+H2O = H3O+ +OH- (E2) Kw = a(H3O+)·a(OH-) The activity of wateris missing because it is in great excess, its concentration is practically constant, and can be merged into the equilibrium constantKw. At 220C: Kw 10-14 pH = -lg a(H3O+) (E3)

9. Ionization equilibrium of acids HA+H2O = H3O+ +A- Ionization constant: (E4) Its negative decimal logarithm is used: pKa = - lgKa (E5) Strong acids have small pKa .

10. Ionization equilibrium of bases B+H2O = BH+ +OH- Dissociation constant: (E6) (E7) pKb = - lgKb Ka is also frequently used for bases: BH+ +H2O = B + H3O+ (E8) (E9) Product of Ka and Kb: Ka·Kb = Kw

11. Standard chemical potentialactivity E3.Chemical potentials and activities in electrolytes The definition ofchemical potential: (E10) Its dependence on composition: (E11)

12. In dilute liquid solutions molality (as already mentioned m = mol solute per kg solvent) or concentration (molarity) (c = mol solute per dm3 solution) are used instead of mole fraction. The activitya is expressed as the product of a composition expressed quantity (m or c) and the corresponding activity coefficient (gmorgc,respectively)

13. Standard state: unit molality (or molarity) in case of infinitely diluted solution. So the standard state is a virtual state, result of extrapolation to infinitely diluted state. Since the cations and anions are always together in the solution, theindividual activitiesand therefore individual chemical potentials of the ionscannot be determined.

14. E.g. the chemical potentials in NaCl solution: That is Only the sum of the chemical potentials of the ions can be determined.

15. We can express the chemical pontentials as sum of their standards values andthe activity dependence(E11): The geometric mean of the activities of the two ions is calledmean activity:

16. Another example is CaCl2 solution: Introducing the mean activity The chemical potential

17. In general, if the electrolyte dissociates to nAanions and nC cations: (E12a) where zA and zC are the charges of anions and cations, respectively. The mean activity (E12b) wheren = nA + nC. The chemical potential: (E13)

18. gA, gC: activity coefficients mo: unit molality (1 mol kg-1), c0unit molarity The (dimensionless) activities can be expressed in the following way (examples): (E14) The mean activity using molalities: (E15)

19. Introducing the mean activity coefficient, g± and the mean molality m±: (E16) (E17) The mean activity: (E18)

20. Example: Calculation of the mean molality of 0.2 mol/kg Al2(SO4)3 solution.

21. E4. Debye-Hückel theory The electrolytes do not behave ideally even if the solution is dilute. The reason is the electrostatic interaction between ions. Debye and Hückel developed a theory in 1923, which explains the behaviour of dilute electrolytes. We discuss only the main points of this theory.

22. Cations and anions are not distributed evenly in the solution.A selected anion is surrounded by more cations than anions and vica versa. Around a cation there is an excess of anions. Around an anion there is an excess of cations. The cloud of such ions has a spheric symmetry. It is calledionic atmosphere.

23. How does the cloud of ions of opposite charge influence the chemical potential? The interionic attractive forces reduces the energy of ions, the chemical potential is reduced, too. So the activity coefficient is less than 1. The result of a long derivation is a simple expression for the activity coefficient.

24. (E19) where I is the ionic strength. It depends on the molalities (or concentrations) of all the ions in the solution. (E20a) (E20b) The constant "A"depends on the permittivity (e, D=eE),density and temperature of the solvent. Its value is 0.509 in aqueous solutions at 25 oC.

25. 25oC, aqueous solution According to the equation E19 the logarithm of the mean activity coefficient is a linear function of the square root of the ionic strength. This law is valid in dilute solutions only. Therefore E19 is calledDebye-Hückel limiting law.

26. E5. The electrochemical potential The total differential of Gibbs free energy in an open system (material and energy exchange with the surroundings are allowed) at constant T and p: (E21) If dni mol neutral component is added to the solution, the change of Gibbs free energy is midni.

27. If ions are moved to a place where the electrical potential is F then electrical (non pV) work is done: Then the total differential of the Gibbs free energy is: (E22)

28. The partial derivative of the Gibbs function with respect to the amount of substance in the presence of ions: The flollowing quantity is calledelectrochemical potential: (E23)

29. If ions take part in the processes, the condition of equilibrium is expressed in terms of electrochemical potentials. Of course, for neutral atoms and molecules (zi=0) the electrochemical potential is equal to the chemical potential:

30. that is The condition of phase equilibrium is the equality of the electrochemical potential of the componentwhich is present in two phases. Chemical equilibrium: (E24a) (E24b) where n-s are the stochiometric coefficients, A-s are for the reactants, B-s are for the products.

31. Some practical applications of the electrochemical potential 1. Contactpotential Behaviour of electrons in metals. Their energies are different in different metals. Therefore their electrochemical potentials are also different. If two metals are brought into contact (welding, soldering), electrons flow from the metal where their electrochemical potential is higher to the metal where their electrochemical potential is lower.

32. As result the metal that gains net electrons, acquires negative charge, while the metal that loses net electrons, aquires positive charge. . Thus an electric potential difference DF occurs at the contact between the two metals. The condition of equilibrium is the equality of electrochemical potential for electrons in the two metals.

33. where a and b denotes the two metals. (E25) Substituting the expression E23 for E25, and considering that the charge of electron ze= -1, (E26) DF(E26) is called contact (electric) potential, it is proportional to the difference of the chemical potencials.

34. V copper 1 2 DF DF 1 2 constantan A useful application of the contact potential is the thermocouple. Here the contact potential can measured directly. Consider for example a copper-constantan (60 % Cu, 40 % Ni) thermo-couple (copper leadings join the voltmeter) copper copper

35. At the contact point of the two metals (1) the potential difference is DF1. If we want to measure this, we have to attach a voltmeter. The voltmeter have to have high internal resistance (high W/V value) for minimizing the electric current in the circuit. Since the source of the current in the circuit is only the internal contact potential DF2=-DF1

36. The contact potential depends on temperature (thermocouple!) If points 1 and 2 are of different temperature, the resultant voltage is not zero any more. It is the function of temperature difference:DU = f(Dt). Themocouples are used for temperature measurement. They always measure temperature difference between two points. Practically one of the two points have fixed temperature (cold point).

37. 2. Electrode reaction Behaviour of a metal dips into a solution containing ions of this metal. What happens in this case? Let copper dips into CuSO4 solution. The following equilibrium sets in: Cu2+(solution) + 2e-(metal) = Cu The condition for equilibrium is (E27) That is

38. For the neutral copper atoms the chemical potential, for the charged particles (copper ions and electrons) the electrochemical potentials are used. Substituting for E27 the expression of the electrochemical potential (E23) : (E28)

39. Rearrange the equation E28 so that the electrical potential difference is on the left hand side (E29) We cannot measure this electrical potential difference, because for that we have to dip another metal in the solution and the voltage of all the circuit can only be measured.

40. E6.Electrochemical cells Consider the following redoxreaction: CuSO4 + Zn = ZnSO4 + Cu Cu2+ + Zn = Zn2+ + Cu In this reaction Cu2+ions are reduced and Zn atoms are oxidized.

41. Two steps: Cu2+ + 2 e- = Cureduction Zn = Zn2+ + 2 e-oxidation In an electrochemical cell the oxidation and reduction are separated in space: reduction means electron gain, oxidation means electron loss. Galvanic cell: production of electrical energy from chemical energy. Electrolytic cell: electrical energy is used to bring about chemical changes. (E.g. production of chlorine from sodium chloride)

42. The following slide shows a Daniell cell. On the left hand side it works as a Galvanic cell, and produces electric current (spontanous process). On the right hand side we use an external power source to reverse the process. In that case the cell works as an electolytic cell. Cathodes and anodes are electrodes. Observe the change of anodic and cathodic functions comparing the galvanic and electrolytic cells!

43. flow of electrons flow of electrons y y y y ^^^^ anode cathode anode cathode Å y Zn Cu Zn Cu y Å ZnSO CuSO ZnSO CuSO 4 4 4 4 Galvanic cell Electrolytic cell Daniell cell resistor Cathodes and anodes are electrodes.

44. Galvanic cellElectrolytic cell Zn Zn2+ + 2 e- Zn2+ + 2 e- Zn Cu2+ + 2 e- Cu Cu  Cu2+ + 2 e-  1.1 V Oxidation on anodes, reduction on cathodes. The potential difference of a cell in equilibrium conditions is called electromotive force (emf).The electromotive force E of the cell can be measured as the limiting value of the electric potential difference DF, i.e. as the current through the cell goes to zero. (E30) E = DF(I=0)

45. Simple measurement of emf: - the emf is compensated by a measurable and changable voltage source. If the G meter measures zero, the two tensions are equal.

46. Cell diagram (description of the cell): ZnZn2+ (aq.)  Cu2+ (aq)  Cu Phase borders are denoted by vertical lines. Two vertical lines are used for the liquid junction. Usually a salt bridge is used to prevent the liquids from mixing(KNO3/H2O colloid in agar-agar, a sea kelp).

47. The electromotive force is the sum of the potential differences on the phase boundaries. If the external leads are made of copper: CuZn - contact potential Zn Zn2+ - between solution and metal Zn2+ Cu2+ - between two solutions Cu2+Cu - between metal and solution

48. Cu I Zn2F [(Zn) - left(Cu)] = 2e (Zn) - 2e (Cu) Zn I Zn2+2F [(sol) - (Zn)] = Zn - Zn2+ - 2e(Zn) Zn2+ICu2+diffusion potential (ediff , neglected,equation E40, section E8) Cu2+ I Cu 2F [right(Cu) - (sol)] = 2e (Cu) + Cu2+ -Cu Summing up: 2F [right(Cu) - left(Cu)] = Zn + Cu2+ - Cu – Zn2+ 2F E = - r (= -rG)

49. In general: (E31) Left hand side of E31: Gibbs free energy change for the reaction. (It depends on the concentration of participants) Right hand side of E31: Electrical work done by the system.

50. Sign dependence of the emf (E) Positive E - The reaction goes spontaneosly from left to right according to reaction equation. (DrG < 0) Negative E - The reaction goes spontaneosly in the opposite direction. (DrG > 0) E = 0 - Chemical equilibrium. (DrG = 0)