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Equilibrium Electrochemistry

Equilibrium Electrochemistry. Subtopics. Half-Reactions and Electrodes Varieties of Cells The Cell Potential Standard Potentials Applications of Standard Potentials Impact on Biochemistry: Energy Conversion in Biological Cells. Equilibrium Electrochemistry.

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Equilibrium Electrochemistry

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  1. Equilibrium Electrochemistry ERT 108 Physical Chemistry Semester II Sidang2010/2011

  2. Subtopics • Half-Reactions and Electrodes • Varieties of Cells • The Cell Potential • Standard Potentials • Applications of Standard Potentials • Impact on Biochemistry: Energy Conversion in Biological Cells ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  3. Equilibrium Electrochemistry • An electrochemical cell consists: • two electrodes (or metallic conductors) • an electrolyte (an ionic conductor – may be a solution, a liquid or a solid). • An electrode & its electrolyte comprise an electrode compartment. • two electrodes may share the same compartment • if the electrodes are different, the two compartments may be joined by a salt bridge [a tube containing a concentrated electrolyte solution (potassium chloride in agar jelly)] that completes the electrical circuit & enables the cell to function. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  4. Equilibrium Electrochemistry • A galvanic cell is an electrochemical cell that produces electricity as a result of the spontaneous reaction occurring inside it. • A electrolytic cell is an electrochemical cells in which a non-spontaneous reaction is driven by an external source of current. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  5. Half-Reactions and electrodes • Oxidation – the removal of electrons from a species. • Reduction – the addition of electrons to a species. • Redox reaction – transfer of electrons from one species to another. • Reducing agent (reductant) – the electron donor. • Oxidizing agent (oxidant) – the electron acceptor. • Any redox reaction (or even not redox reaction) may be expressed as the difference of two reduction half-reactions. • Half-reactions – conceptual reactions showing the gain of electrons. • the reduced & oxidized species in half-reaction form a redox couple. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  6. Example 1 • Express the following reactions in terms of reduction half-reactions. • The dissolution of silver chloride in water: (Note: it is not a redox reaction.) • The formation of H2O from H2 and O2 in acidic solution. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  7. Reaction quotient, Q • Useful to express the composition of an electrode compartment in terms of the reaction quotient, Q for the half reaction. • The reaction quotient, Q has the form Q= activities of products/activities of reactants with each species raised to the power given by its stoichiometric coefficient. • Q is defined as ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  8. Consider the reaction 2A + 3B  C + 2D, in which case vA= -2, vB= -3, vC= +1 and vD= +2. the reaction quotient is then • Example: The reaction quotient for the reduction of O2 to H2O in acid solution O2(g) + 4H+ (aq) + 4e-  2H2O (l) is The approximations used in 2nd step ate that the activity of water is 1 (because the solution is dilute) and the oxygen behaves as perfect gas, so aO2≈pO2/p. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  9. Half-Reactions and electrodes • Anode: • the electrode at which the oxidation occurs. (-): removal of e-. • Cathode: • the electrode at which the reduction occurs. (+): addition of e-. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  10. Half-Reactions and electrodes ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  11. Varieties of cells • In an electrolyte concentration cell- the electrode compartments are identical except for the concentrations of electrolytes. • In an electrode concentration cell- the electrodes themselves have different conc, either because they are gas electrodes operating at different pressures or because they are amalgams (sol in mercury) with different concs. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  12. Varieties of Cells • Daniel cell: • the redox couple at one electrode is Cu2+/Cu and at the other is Zn2+/Zn. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  13. Liquid junction potentials • Liquid junction potentials (Elj): • an additional source of potential difference across the interface of the two electrolytes. • E.g. In the Daniel cell (i) two different electrolyte solutions are in contact, (ii) different concentration of hydrochloric acid- At the junction, the mobile H+ ions diffuse into the more dilute solution. The bulkier Cl- ions follow, but initially do so more slowly- results in a potential difference at the junction. The potential then settles down to a value such that, after brief initial period, the ions diffuse at the same rates. • The contribution of the liquid junction to the potential can be reduced by joining the electrolyte compartments through a salt bridge. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  14. Liquid junction potentials Galvanic cell with liquid junction. Galvanic cell without liquid junction. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  15. Notation • Phase boundaries are denoted by a vertical bar. • A liquid junction is denoted by • Interface is denoted by a double vertical line ||. For which It is assumed that the junction potential has been eliminated • Fig 1: • Zn (s)|ZnSO4 (aq) CuSO4 (aq) |Cu (s) • Fig 2: • Zn (s)|ZnSO4 (aq)||CuSO4 (aq) |Cu (s) Fig 1 Fig 2 ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  16. The cell potential • The cell reaction corresponding to a cell diagram: 1st : write the right hand half-reaction as a reduction (cathode) (Assumption: spontaneous reaction). 2nd : subtract from it the left-hand reduction half- reaction. (By implication, the electrode is the site of oxidation) In the cell: Zn(s)|ZnSO4(aq)||CuSO4(aq)|Cu(s) Right-hand electrode: Cu2+(aq)+2e- Cu(s) Left-hand electrode: Zn2+(aq)+2e- Zn(s) Overall cell reaction: Cu2+(aq)+ Zn(s) Cu(s) +Zn2+(aq) ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  17. The Nernst equation • A cell in which the overall cell reaction has not reached chemical equilibrium can do electrical work as the reaction drives electrons through an external circuit. • the work that a given transfer of electrons can accomplish depends on the potential difference between the two electrodes. • This potential differences is called the cell potential and is measured in volts, V (1 V = 1 JC-1 s). • A cell in which the overall reaction is at equilibrium can do no work, & then the cell potential is zero. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  18. The Nernst equation • When expressed in terms of a cell potential, the spontaneous direction of change can be expressed in terms of the cell emf. • the reaction is spontaneous when E>0. • the reverse reaction is spontaneous when E<0. • when the cell reaction is at equilibrium, the cell potential is zero. Note: The potential difference is called the electromotive force (emf), E ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  19. The resulting potential difference is call cell potential, Ecell. The relation between the reaction Gibbs energy and the cell potential is: -vFEcell = rG F is Faraday’s constant, F = eNA v is the stoichiometric coefficient of electrons in half-reactions. • By knowing the reaction Gibbs energy at a specified composition- we can state the cell potential at that composition. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  20. The Nernst equation • The Nernst equation relates the cell’s potential (E) to the activities ai of the substances in the cell’s chemical reaction & to the standard cell potential of the cell (E Ѳ)(the cell’s chemical reaction). • where F = Faraday constant, F=eNA v = the stoichiometric coefficient of the electron in the half-reactions. Q = the reaction (or activity) quotient , ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  21. The Nernst equation • A practical form of the Nernst equation is • because at 250c, ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  22. Cells at equilibrium • Suppose the reaction has reached equilibrium; then Q = K (K= the equilibrium constant of the cell reaction). • A chemical reaction at equilibrium cannot do work, & hence it generates zero potential difference between the electrodes of a galvanic cell. • Setting E=0, Q=K: • the Nernst equation: ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  23. Example 2 • Three different galvanic cells have standard cell potential (EѲ) of 0.01, 0.1 and 1.0V, respectively, at 250C. • Calculate the equilibrium constants (K) of the reactions that occur in these cells assuming the charge number (v) for each reaction is unity. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  24. Standard Electrode Potentials • A galvanic cell is a combination of two electrodes, & each one can be considered as making a characteristics contributions to the overall cell potential. • although it is not possible to measure the contribution of a single electrode, we can define the potential of one of the electrodes as zero & then assign values to others on that basis. • the specially selected electrode is the standard hydrogen electrode (SHE): Pt(s)|H2(g)|H+(aq), EѲ=0 (at all temperatures). ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  25. Standard Potentials • To achieve the standard conditions, the activity of the hydrogen ions must be 1 (pH=0) & the P of the hydrogen gas must be 1 bar. • The standard potential (EѲ) of another couple is then assigned by constructing a cell in which it is the right-hand electrode & the standard hydrogen electrode (SHE) is the left-hand electrode. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  26. The procedure for measuring a standard potential can be illustrated by considering a specific case, the silver chloride electrode: • ½ H2(g) + AgCl(s)  HCl(aq) + Ag(s) • Ecell = E(AgCl/Ag, Cl-) – E(SHE) = E(AgCl/Ag,Cl-) • For which the Nernst equation is • We shall set aH2 = 1 from now on, and for simplicity write the standard potential of the AgCl/Ag, Cl- electrode as E, then ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  27. The activities can be expressed in terms of the molality b of HCl (aq) through aH+ = b/b and aCl- = b/b, so: • Where for simplicity, b/b is replaced by b. this expression rearranges to ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  28. The Debye-Huckel limiting law • Theory to calculate activity coefficients of electrolyte solutions • Activities rather than conc are needed in many chemical calculations because solutions that contain ionic solutes do not behave ideally even at very low conc. • Debye-Huckel limiting law: • Where A= 0.509 for an aqueous solution at 25oC and I is the dimentionless ionic strength of the solution: • zi- charge no of ion i (+ve for cations and –ve for anions) • bi- molality ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  29. Standard Potentials ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  30. Example 3 • Consider the following galvanic cell: • What is: • the cell reaction? • the standard potential of the cell? • The equilibrium constant? > Table 9.1 ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  31. Application of standard potentials • The more positive E0 is, the greater the tendency for the substance to be reduced – e.g. Fluorine, F2 • Li + is the weakest oxidizing agent because it is the most difficult species to reduce – it has the most negative E0. • Under standard-state conditions, any species on the left of a given half-cell reaction will react spontaneously with a species that appears on the right of any half-cell reaction ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  32. Application of standard potentials • In the Daniel cells: Cu2+(aq)+2e- Cu(s) E0=0.34V Zn2+(aq)+2e- Zn(s) E0= - 0.76V • Zn spontaneously reduces Cu2+ to form Zn2+ and Cu. • Standard potential of a cell, Ecell Ecell = E(right)- E(left) ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  33. Impact on Biochemistry: Energy Conversion in Biological Cells. • The whole of life’s activities depends on the coupling of exergonic & endergonic reactions, for the oxidation of food drives other reactions forward. • In biological cells, the energy released by the oxidation of foods is stored in adenosine triphosphate (ATP). • the essence of the action of ATP is its ability to lose its terminal phosphate group by hydrolysis & to form adenosine diphosphate (ADP). where Pi denotes an inorganic phosphate group e.g. H2SO4. ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  34. Impact on Biochemistry: Energy Conversion in Biological Cells. • Examples: • Glycolysis – the oxidation of glucose to CO2 and H2O by O2 (the breakdown of foods is coupled to the formation of ATP in the cell). • Glycolysis is the main source of energy during anaerobic metabolism, a form of metabolism in which inhaled O2 does not play a role. • The citric acid cycle & oxidative phosphorylationare the main mechanisms for the extraction of energy from carbohydrates during aerobic metabolism (in which inhaled O2 does play a role). ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  35. Answer (Example 1) • The two reduction half-reactions: The redox couples are AgCl/Ag, Cl-& Ag+/Ag. • The two reduction half-reactions: The redox couples are H+/H2 & O2,H+/H2O ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  36. Answer (Example 2) • For EѲ = 0.01V, = 1.476 • For EѲ = 0.1V, K = 49.0 • For EѲ = 1.0V, K = 8.02 x 1016 ERT 108 Physical Chemistry Semester II Sidang 2010/2011

  37. Answer (Example 3) (a) & (b) Right-hand electrode: Cu2+(aq)+2e- Cu(s) E0=0.34V Left-hand electrode: Zn2+(aq)+2e- Zn(s) E0= - 0.76V Overall cell reaction:Cu2+(aq)+ Zn(s) Cu(s) +Zn2+(aq) E0 = 0.34 – (-0.76) V E0 = 1.10 V (c) The equilibrium constant: K = 1.80 x 1037 ERT 108 Physical Chemistry Semester II Sidang 2010/2011

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