1. Simple applications of conductivity measurements

2. Conductivity is a measurement of the ability of an aqueous solution to carry an electrical current. factors that determine the degree to which water will carry an electrical current. –the concentration or number of ions; –mobility of the ion; –oxidation state (valence) and; –temperature of the water. 1

3. Application of conductivity to determine water quality. 1.Determining mineralization: this is commonly called total dissolved solids. (TDS) information is used to determine the overall ionic effect in a water source. Certain physiological effects on plants and animals are often affected by the number of available ions in the water. 2.noting variation or changes in natural water and wastewaters quickly; 3.estimating the sample size necessary for other chemical analyses; and 4.determining amounts of chemical reagents or treatment chemicals to be added to a water sample. 2

4. Solubility product of a slightly soluble salt Solubility equilibrium is base on the assumption that solids dissolve in water to give the basic particles from which they are formed. Molecular solids dissolve to give individual aqueous molecules. 3

5. Ionic solids dissociate to give their respective positive and negative ions: 4

6. The ratio of the maximum amount of solute to the volume of solvent in which this solute can dissolve. –Generally expressed in two ways: grams of solute per 100 g of water moles of solute per Liter of solution 5

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8. A salt is considered soluble if it dissolves in water to give a solution with a concentration of at least 0.1 M at room temperature. A salt is considered insoluble if the concentration of an aqueous solution is less than 0.0001 M at room temperature. Salts with solubilities between 0.0001 M and 0.1 M are considered to be slightly soluble. 7

9. Salts that have extremely low solubilities dissociate in water according to the principles of equilibrium. For example, the reaction for the dissociation of the salt AgCl is: 8 The reverse reaction for the dissolving of the salt would be the precipitation of the ions to form a solid: The system has reached equilibrium when the rate at which AgCl dissolves is equal to the rate at which AgCl precipitates.

10. Ag/AgCl Electrodes

11. Ag/AgCl Fabrication

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13. Galvanic and electrolytic cells 12  Galvanic cell  reaction occurs spontaneously  converting chemical energy to electrical energy  primary cells, secondary cells, fuel cells  Electrolytic cell  imposition of an external voltage greater than the open-circuit potential of the cell  converting electrical energy to chemical energy  electrolytic synthesis, electroplating

14. Recap: Fundamentals of Electrochemistry Basic Concepts 2.)The first two reactions are known as “1/2 cell reactions”  Include electrons in their equation 3.) The net reaction is known as the total cell reaction  No free electrons in its equation 4.)In order for a redox reaction to occur, both reduction of one compound and oxidation of another must take place simultaneously  Total number of electrons is constant ½ cell reactions: Net Reaction:

15. Basic Concepts 5.)Electric Charge (q)  Measured in coulombs (C)  Charge of a single electron is 1.602x10 -19 C  Faraday constant (F) – 9.649x10 4 C is the charge of a mole of electrons 6.)Electric current  Quantity of charge flowing each second through a circuit - Ampere: unit of current (C/sec) Relation between charge and moles: Coulombs moles Recap: Fundamentals of Electrochemistry

16. Basic Concepts 7.)Electric Potential (E)  Measured in volts (V)  Work (energy) needed when moving an electric charge from one point to another - Measure of force pushing on electrons Relation between free energy, work and voltage: Joules Volts Coulombs Higher potential difference Higher potential difference requires more work to lift water (electrons) to higher trough Recap: Fundamentals of Electrochemistry

17. Fundamentals of Electrochemistry Basic Concepts 7.)Electric Potential (E)  Combining definition of electrical charge and potential Relation between free energy difference and electric potential difference: Describes the voltage that can be generated by a chemical reaction

18. Fundamentals of Electrochemistry Basic Concepts 8.)Ohm’s Law  Current ( I ) is directly proportional to the potential difference (voltage) across a circuit and inversely proportional to the resistance (R) - Ohms (  ) - units of resistance 9.)Power (P)  Work done per unit time - Units: joules per second J/sec or watts (W)

19. Oxidation - Reduction Reactions Redox Terminology—REVIEW redox reaction -- electron transfer process e.g., 2 Na + Cl 2 --> 2 NaCl Overall process involves two Half Reactions: oxidation -- loss of electron(s) reduction -- gain of electron(s) e.g.Na --> Na + + e – (oxidation) Cl 2 + 2 e – --> 2 Cl – (reduction) Related terms: oxidizing agent = the substance that gets reduced (Cl 2 ) reducing agent = the substance that gets oxidized (Na) Oxidation and reduction always occur together so that there is no net loss or gain of electrons overall. OILRIG

20. Redox Reactions The transfer of electrons between species, meaning that one species is oxidized and one is reduced. The two processes will always occur together. When has a redox reaction occurred? –If there is a change in the oxidation state of any element in the reaction, a redox reaction has happened. –Remember that if something is oxidized, something else must be reduced! (and vice-versa) More examples: 2 Ca (s) + O 2(g) --> 2 CaO (s) 2 Al (s) + 3 Cl 2(g) --> 2 AlCl 3(s)

21. HALF-REACTION METHOD for balancing Redox Equations 1. Write unbalanced ionic equations for the two half-reactions. (Look at oxidation numbers in the “skeleton equation.”) 2. Balance atoms other than H and O. 3. Add appropriate number of electrons. 4. Balance O with H 2 O. 5. Balance H with H +. 6. If in acidic solution, then skip to step 7. If in basic solution, then add equal number of OH – to both sides to cancel all of the H +. 7. Multiply balanced half-reactions by appropriate coefficients so that the number of electrons are equal. 8. Rewrite the balanced half reactions. 9. Add the half-reactions together. 10. Cancel species that appear on both sides to get the balanced Net Ionic Equation. 11. If necessary, add spectator ions to get the balanced molecular equation. Check the Final Balance (atoms and charges)!

22. Example Problem Balance the following redox equation. Ce 4+ (aq) + Sn 2+ (aq) --> Ce 3+ (aq) + Sn 4+ (aq) The reaction can be separated into a reaction involving the substance being reduced; Ce 4+ (aq) + e – --> Ce 3+ (aq) And the substance being oxidized; Sn 2+ (aq) --> Sn 4+ (aq) + 2e – We can see that the equations don’t balance; you must multiply the top equation by two, then add them to get 2 Ce 4+ (aq) + Sn 2+ (aq) --> 2 Ce 3+ (aq) + Sn 4+ (aq)

23. Sample Problem The following redox reaction occurs in basic solution. Write complete, balanced equations for the individual half-reactions and the overall net ionic equation. MnO 4 – (aq) + N 2 H 4(aq) --> MnO 2(s) + NO (g) Oxidation Half Reaction: Reduction Half Reaction: Net Ionic Equation:

24. Sample Problem The following redox reaction occurs in basic solution. Write complete, balanced equations for the individual half-reactions and the overall net ionic equation. MnO 4 – (aq) + N 2 H 4(aq) --> MnO 2(s) + NO (g) Oxidation Half Reaction: 8 OH – (aq) + N 2 H 4(aq) --> 2 NO (g) + 6 H 2 O (l) + 8 e – Reduction Half Reaction: 3 e – + 2 H 2 O (l) + MnO 4 – (aq) --> MnO 2(s) + 4 OH – (aq) Net Ionic Equation: 3 N 2 H 4(aq) + 8 MnO 4 – (aq) --> 6 NO (g) + 8 MnO 2(s) + 2 H 2 O (l) + 8 OH – (aq)

25. Sample Problems Balance the following redox equations in acidic solution. Al (s) + I 2(s) --> AlI 3(s) KClO 3(aq) + HNO 2(aq) --> KCl (aq) + HNO 3(aq) Cl – (aq) + MnO 2(s) --> Mn 2+ (aq) + Cl 2(g) Balance the above redox equations in basic solution.

26. Sample Problems Balance the following redox equations in acidic solution. Al (s) + I 2(s) --> AlI 3(s) 2 Al (s) + 3 I 2(s) --> 2 AlI 3(s) KClO 3(aq) + HNO 2(aq) --> KCl (aq) + HNO 3(aq) KClO 3(aq) + 3 HNO 2(aq) --> KCl (aq) + 3 HNO 3(aq) Cl – (aq) + MnO 2(s) --> Mn 2+ (aq) + Cl 2(g) 4H + (aq) + 2 Cl – (aq) + MnO 2(s) --> Cl 2(g) + Mn 2+ (aq) + 2 H 2 O (l) Balance the above redox equations in basic solution. –First doesn’t change. –Second: use NO 2 – and NO 3 – rather than the acids. –Third: Add 4 OH- to each side, 2 H 2 O (l) + 2 Cl – (aq) + MnO 2(s) --> Cl 2(g) + Mn 2+ (aq) + 4 OH – (aq)

27. Electrochemistry Terminology Electrochemical Cell -- a device that converts electrical energy into chemical energy or vice versa Two Types: Electrolytic cell Converts electrical energy into chemical energy Electricity is used to drive a non-spontaneous reaction Galvanic (or voltaic) cell Converts chemical energy into electricity (a battery!) A spontaneous reaction produces electricity Conduction: Metals: metallic (electronic) conduction -- free movement of electrons Solutions: electrolytic (ionic) conduction (or molten salts)-- free movement of ions

28. Galvanic/Voltaic Cells In spontaneous oxidation-reduction (redox) reactions, electrons are transferred and energy is released.

29. Galvanic/Voltaic Cells We can use that energy to do work if we make the electrons flow through an external device. We call such a setup a voltaic cell.

30. A typical cell looks like this. The oxidation occurs at the anode. The reduction occurs at the cathode. Galvanic/Voltaic Cells

31. Once even one electron flows from the anode to the cathode, the charges in each beaker would not be balanced and the flow of electrons would stop. Galvanic/Voltaic Cells

32. Therefore, we use a salt bridge, usually a U-shaped tube that contains a salt solution, to keep the charges balanced. –Cations move toward the cathode. –Anions move toward the anode. Galvanic/Voltaic Cells

33. Electrochemical Conventions Charges on the electrodes Galvanic cell: (+) cathode ~ reduction (–) anode ~ oxidation Electrolytic cell: (+) anode ~ oxidation (–) cathode ~ reduction Cell Notation -- summary of cell description e.g. Cu (s) | Cu 2+ (aq) || Ag + (aq) | Ag (s) anode cathode

34. Cell Potential Cell potential ~ Eº cell (an electromotive force, emf) Units of Eº cell are volts: 1 volt = 1 joule/coulomb Eº cell is a measure of the relative spontaneity of a cell reaction Positive (+) Eº cell --> spontaneous reaction Eº cell depends on: –Nature of reactants –Temperature -- superscript º means 25 ºC –Concentrations -- superscript º means all conc are at 1.00 M and gases are at 1.00 atm but, Eº cell is independent of amounts of reactants

35. Standard Cell Potential Standard Reduction PotentialsEº (volts) F 2(g) + 2 e – --> 2 F – (aq) + 2.87 Ag + (aq) + e – --> Ag (s) + 0.80 Cu 2+ (aq) + 2 e – --> Cu (s) + 0.34 2 H + (aq) + 2 e – --> H 2(g) 0.00 Zn 2+ (aq) + 2 e – --> Zn (s) – 0.76 Li + (aq) + e – --> Li (s) – 3.05 Ease of Reduction ~ increases with Eº e.g. F 2 is easiest to reduce, Li + is the hardest Standard Cell Potential ~ Eº cell can be determined from standard reduction potentials: Eº cell = Eº red – Eº oxid = [reduction potential of substance reduced] – [reduction potential of substance oxidized]

36. Standard Potential Example Problem Is the following a galvanic or an electrolytic cell? Write the balanced cell reaction and calculate Eº cell. Zn (s) | Zn 2+ (aq) || Cu 2+ (aq) | Cu (s) Cathode: Cu 2+ + 2 e – --> Cu Eº = 0.34 V Anode: Zn --> Zn 2+ + 2 e – Eº = – 0.76 V Cell rxn: Zn (s) + Cu 2+ (aq) --> Zn 2+ (aq) + Cu (s) Eº cell = Eº red – Eº ox = 0.34 V – (– 0.76 V) = + 1.10 V ∴ galvanic.

37. Another Example Problem Given the standard reduction potentials: O 2(g) + 4 H + (aq) + 4 e – --> 2 H 2 O (l) Eº = 1.23 V Cl 2(g) + 2 e – --> 2 Cl – (aq) Eº = 1.36 V Write a balanced equation and calculate Eº cell for a galvanic cell based on these half reactions. Sketch the galvanic cell. “galvanic” implies a positive value for Eº cell so, Cl 2 /Cl – should be the reduction half reaction, since 1.36 – 1.23 = + 0.13 V ∴ reverse the O 2 half reaction and make it the oxidation Multiply the Cl 2 reaction by 2, to make e – ’s cancel, hence: 2 Cl 2(g) + 2 H 2 O (l) --> 4 Cl – (aq) + O 2(g) + 4 H + (aq) Note: When a half-reaction is multiplied by a coefficient, the Eº IS NOT MULTIPLIED by the coefficient.

38. Galvanic Cells 1.)Galvanic or Voltaic cell  Spontaneous chemical reaction to generate electricity - One reagent oxidized the other reduced - two reagents cannot be in contact  Electrons flow from reducing agent to oxidizing agent - Flow through external circuit to go from one reagent to the other Net Reaction: Reduction: Oxidation: AgCl(s) is reduced to Ag(s) Ag deposited on electrode and Cl - goes into solution Electrons travel from Cd electrode to Ag electrode Cd(s) is oxidized to Cd 2+ Cd 2+ goes into solution

39. Galvanic Cells 1.)Galvanic or Voltaic cell  Example: Calculate the voltage for the following chemical reaction  G = -150kJ/mol of Cd Solution: n – number of moles of electrons

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41. Galvanic Cells 2.)Cell Potentials vs.  G  Reaction is spontaneous if it does not require external energy

42. Galvanic Cells 3.)Electrodes Cathode: electrode where reduction takes place Anode: electrode where oxidation takes place

43. Galvanic Cells 4.)Salt Bridge  Connects & separates two half-cell reactions  Prevents charge build-up and allows counter-ion migration Two half-cell reactions Salt Bridge  Contains electrolytes not involved in redox reaction.  K + (and Cd 2+ ) moves to cathode with e - through salt bridge (counter balances –charge build-up  NO 3 - moves to anode (counter balances +charge build-up)  Completes circuit

44. Zn|ZnSO 4 ( a ZN 2+ = 0.0100)||CuSO 4 ( a Cu 2+ = 0.0100)|Cu anode Phase boundary Electrode/solution interface Solution in contact with anode & its concentration Solution in contact with cathode & its concentration 2 liquid junctions due to salt bridge cathode Galvanic Cells 5.)Short-Hand Notation  Representation of Cells: by convention start with anode on left

45. Ag + + e - » Ag(s)E o = +0.799V Standard Hydrogen Electrode (S.H.E) Hydrogen gas is bubbled over a Pt electrode Pt(s)|H 2 (g)( a H 2 = 1)|H + (aq) (a H + = 1) || Standard Potentials 1.) Predict voltage observed when two half-cells are connected  Standard reduction potential (E o ) the measured potential of a half-cell reduction reaction relative to a standard oxidation reaction - Potential arbitrary set to 0 for standard electrode - Potential of cell = Potential of ½ reaction  Potentials measured at standard conditions - All concentrations (or activities) = 1M - 25 o C, 1 atm pressure

46. Standard Potentials 1.) Predict voltage observed when two half-cells are connected As E o increases, the more favorable the reaction and the more easily the compound is reduced (better oxidizing agent). Reactions always written as reduction Appendix H contains a more extensive list

47. Standard Potentials 2.) When combining two ½ cell reaction together to get a complete net reaction, the total cell potential (E cell ) is given by: Where:E + = the reduction potential for the ½ cell reaction at the positive electrode E + = electrode where reduction occurs (cathode) E - = the reduction potential for the ½ cell reaction at the negative electrode E - = electrode where oxidation occurs (anode) Electrons always flow towards more positive potential Place values on number line to determine the potential difference

48. Nernst Equation 1.) Reduction Potential under Non-standard Conditions  E determined using Nernst Equation  Concentrations not-equal to 1M aA + ne - » bB E o For the given reaction: The ½ cell reduction potential is given by: Where:E = actual ½ cell reduction potential E o = standard ½ cell reduction potential n = number of electrons in reaction T = temperature (K) R = ideal gas law constant (8.314J/(K-mol) F = Faraday’s constant (9.649x10 4 C/mol) A = activity of A or B at 25 o C

49. E o and the Equilibrium Constant 1.) A Galvanic Cell Produces Electricity because the Cell Reaction is NOT at Equilibrium  Concentration in two cells change with current  Concentration will continue to change until Equilibrium is reached - E = 0V at equilibrium - Battery is “dead” aA + ne - » cC E + o dD + ne - » bB E - o Consider the following ½ cell reactions: Cell potential in terms of Nernst Equation is: Simplify:

50. E o and the Equilibrium Constant 1.) A Galvanic Cell Produces Electricity because the Cell Reaction is NOT at Equilibrium Since E o =E + o - E - o : At equilibrium E cell =0: Definition of equilibrium constant at 25 o C

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52. Cells as Chemical Probes 1.) Two Types of Equilibrium in Galvanic Cells  Equilibrium between the two half-cells  Equilibrium within each half-cell If a Galvanic Cell has a nonzero voltage then the net cell reaction is not at equilibrium For a potential to exist, electrons must flow from one cell to the other which requires the reaction to proceed  not at equilibrium. Conversely, a chemical reaction within a ½ cell will reach and remain at equilibrium.

53. Biochemists Use E o ´ 1.) Redox Potentials Containing Acids or Bases are pH Dependent  Standard potential  all concentrations = 1 M  pH=0 for [H + ] = 1M 2.) pH Inside of a Plant or Animal Cell is ~ 7  Standard potentials at pH =0 not appropriate for biological systems - Reduction or oxidation strength may be reversed at pH 0 compared to pH 7 Metabolic Pathways

54. Biochemists Use E o ´ 3.) Formal Potential  Reduction potential that applies under a specified set of conditions  Formal potential at pH 7 is E o ´ Need to express concentrations as function of K a and [H + ]. Cannot use formal concentrations! E o ´ (V)

55. Applying different voltage to a Galvanic cell and the corresponding chemical reactions 54  When the voltage applied by the external power supply, E appl, is 0.64 V, i= 0.  When E appl is made larger (i.e., E appl >0.64 V, such that the cadmium electrode is made even more negative with respect to the SCE, the cell behaves as an electrolytic cell.

56. Relationship between the current and the reaction rate 55  An electrode process is a heterogeneous reaction occurring only at the electrode- electrolyte interface.  Since electrode reactions are heterogeneous, their reaction rates are described in units of mol/s per unit area. (j is the current density)

57. Ideal polarizable electrode and ideal nonpolarizable electrode 56  An ideal polarized electrode shows a very large change in potential upon the passage of a small current.  Ideal polarizability is characterized by a horizontal region of an i-E curve  Ideal nonpolarizable electrode is an electrode whose potential does not change upon passage of current.  Nonpolarizability is characterized by a vertical region on an i-E curve. i E i E

58. Pathway of a general electrode reaction 57  When a steady-state current is obtained, the rates of all reaction steps in a series are the same. The magnitude of this current is often limited by the inherent sluggishness of one or more reactions called rate determining steps.

59. Processes in an electrode reaction represented as resistances 58  Each value of current density, j, is driven by a certain overpotential, which can be viewed as a sum of terms associated with the different reaction steps: η mt, η ct, η rxn, etc.  The electrode reaction can then be represented by a resistance, R, composed of a series of resistances representing the various steps: R m, R ct, etc.

60. Applying different voltage to a Galvanic cell and the corresponding chemical reactions 59  When the voltage applied by the external power supply, E appl, is 0.64 V, i= 0.  When E appl is made larger (i.e., E appl >0.64 V, such that the cadmium electrode is made even more negative with respect to the SCE, the cell behaves as an electrolytic cell.

61. Distribution of the applied voltage 60  The extra applied voltage -0.80 V is distributed in two parts.  The potential of the Cd electrode, E cd, must shift to a new value, e.g. -0.70 V vs. SCE.  The remainder of the applied voltage, -0.10 V, represents the ohmic drop required to drive the ionic flow in the solution.  SCE is nonpolarizable at the extant current level and does not change its potential.  The ohmic potential drop in the solution should not be regarded as a form of overpotential, because it is characteristic of the bulk solution and not of the electrode reaction.