The equilibrium constant and reaction quotient The response of equilibria to the conditions

1. CHAPTER 6: Chemical Equilibrium This chapter continues demonstration of applying the theory of thermodynamics, now to chemical equilibrium. The relationship between equilibrium constant (and reaction quotient) and Gibbs free energy and how the equilibrium constant is changed by reaction conditions (temperature, pressure, concentrations of reactants) are given precise theoretical foundation. Electrochemistry which is based on redox reactions and thermodynamics is chosen as another best example (in addition to heat engines) to showcase the power of thermodynamics. The equilibrium constant and reaction quotient The response of equilibria to the conditions Electrical chemical cells Electrode potentials

2. The Extent of Reaction, Reaction Gibbs Free Energy and Equilibrium The Extent of Reaction ξ Suppose an infinitesimal amount of A is changed into B, then When a finite amount of A is changed into B, then In general, Reaction Gibbs Free Energy Because The reaction Gibbs free energy is the difference between the chemical potentials of the products and reactants at current compositions of the reaction mixture. It changes over the course of a reaction before it reaches equilibrium (do not confuse it with standard Gibbs energies of formation ). At equilibrium:

3. Chemical equilibrium is reached when the reaction Gibbs free energy is zero Forward reaction spontaneous Reverse reaction spontaneous Equilibrium

4. Example: H2 + (1/2)O2 H2O spontaneous, exergonic Thermodynamically permitted reaction might be hindered by kinetics. A catalyst might be needed for a reasonable reaction rate for a spontaneous reaction. Above reaction needs initiation (ignition) or to be put in a fuel cell. not spontaneous, endergonic H2O H2 + (1/2)O2 To force it occur, at least 237 kJ/mol of work has to be done. A non-spontaneous reaction can be forced to occur. A spontaneous reaction can drive another non-spontaneous one.

5. Equilibrium and Equilibrium Constant Reaction quotient Perfect gases: If the partial pressures of the two gasses at equilibrium are equal (K =1), then and T has no effect. K > 1, the partial pressure of A is larger than that of B – the products are dominant at eq. K < 1, the partial pressure of B is larger than that of A – the reactants are dominant at eq. The forward reaction is spontaneous if Q < K, the reverse reaction is spontaneous if Q > K. These results apply to ALL chemical reactions, not just perfect gases. The standard Gibbs energy of the isomerization of pentane to 2-methylbutane t 298 K, the reaction CH3(CH2)3CH3 (g)  (CH3)2CHCH2CH3 (g), is -6.7 kJ/mol (estimated based on enthalpies of formation). Therefore, its equilibrium constant is

6. The Importance of Entropy in Chemical Reaction: A Simple but Important Example The presence of mixing entropy creates a minimum of reaction Gibbs free energy at the intermediate value of the extent of reaction (red dot) rather than at its maximum value (green dot). Rare are the cases when only products or reactants exist in a chemical reaction, owing to the fact that more reduction of Gibbs energy can be reached when an appropriate amount of mixing entropy is retained as compared to ‘pure products’ or ‘pure reactants’ cases.

7. The general case of a reaction Because activities are dimensionless, Q and K must be dimensionless.

8. which is thermodynamically exact and should be equal to At low pressures,

9. Degree of dissociation at equilibrium

10. Different equilibrium constants Because we have different forms of ‘concentrations’ hence activities, we have different forms of reaction quotient or equilibrium constant: For gas reactions:

11. The Importance of Entropy in Chemical Reaction: Why some endothermic reactions can occur or some exothermic reactions are hard We will show in chapter 15 (statistical mechanics that closely spaced energy levels correlate with a high entropy). Therefore, if the products have denser energy levels, the reaction entropy will be positive and can drive an endothermic reaction to K > 1.

12. Four major types of chemical reactions in terms of driving force • Both enthalpy and entropy promote forward reaction. • (2) Both enthalpy and entropy discourage forward reaction. • (3) Enthalpy promotes but entropy discourages forward reaction. • (4) Enthalpy discourages but entropy promotes forward reaction.

13. The responses of equilibria to the conditions At a given temperature, K is a constant independent of pressure, but it does not mean the equilibrium compositions are independent of pressure, but depend on how the pressure is applied. If the partial pressures of the reactants/products are not changed by increasing pressure (e.g., via filling in noble gas), K is not changed. If the system is compressed, then the compositions will be changed. When the gases are compressed, pa and pB are increased at the same rate, that is not enough to keep K constant. The mole fraction of B has to be decreased to keep K constant. Le Chatelier’s principle

14. Increasing the pressure must increaseKx by square to keep K constant. This means increasing pressure favors product. On the other hand, if the product is removed, the pressure must be reduced squarely by reducing the fraction of reactants.

15. The van’t Hoff equation Proof: Exothermic reactions: increasing temperature favors the reactants. Endothermic reactions: increasing temperature favors the products.

17. Measuring a reaction enthalpy

18. The value of K at different temperatures

19. Electrochemical Cell • A device in which an electric current is either produced by a spontaneous chemical reaction or is used to bring about a nonspontaneous reaction. A galvanic cell is an electrochemical cell in which a spontaneous chemical reaction is used to generate an electric current.

23. In an electrochemical cell, a reaction takes place in two separate regions. Oxidation occurs at one electrode, and the electrons released travel through the external circuit to the other electrode, where they cause reduction. The site of oxidation is called the anode, and the site of reduction is called the cathode. negative positive

24. Any two objects that have different (first) ionization energies may function as a cell. - 1.234 + - 0.02 +

25. When a bar of zinc is placed in a beaker of copper(II) sulfate solution, copper is deposited on the zinc and the blue copper (II) ions are gradually replaced by colorless zinc ions. (b) The residue in the beaker is copper metal. No more copper ions can be seen in solution.

26. The reaction shown in Fig. 18.3 takes place all over the surface of the zinc as electrons are transferred to the Cu2 ions in solution.

27. The Daniell cell consists of copper and zinc electrodes dipping into solutions of copper(II) sulfate and zinc sulfate, respectively. The two solutions make contact through the porous pot, which allows ions to pass through to complete the electrical circuit.

28. Electrodes and Cell Diagram

29. This cell is typical of galvanic cells used in the laboratory. The two electrodes are connected by an external circuit and a salt bridge. The latter completes the electrical circuit within the cell.

30. The cell potential is measured with an electronic voltmeter, a device that draws negligible current so that the composition of the cell does not change during the measurement. The display shows a positive value when the  terminal of the meter is connected to the cathode of the galvanic cell.

31. E = 1.1 V Cell Potential

32. The cell potential • An indication of the electron-pulling and –pushing power of the cell reactions; cell reactions at equilibrium generate zero potential.

33. Electrons produced by oxidation leave a galvanic cell at the anode (), travel through the external circuit, and reenter the cell at the cathode (), where they cause reduction. The circuit is completed inside the cell by migration of ions through the salt bridge. A salt bridge is unnecessary when the two electrodes share a common electrolyte. positive negative

34. This schematic picture of a galvanic cell indicates the identities of the anode and cathode, displays the oxidation and reduction half-reactions, and shows the direction of electron flow.

35. Describing a galvanic cell and identifying the cell reaction (KCl gel)

36. Exercise: Describing a galvanic cell and identifying the cell reaction(Assume platinum electrode is used)

37. The cell potential can be thought of as being the difference of the two reduction potentials produced by the two electrodes. The cell potential is positive if the cathode has a higher potential than the anode. Cell potential and electrode potential

38. Redox couple

39. Cell Potential, Electrical Work, and Free Energy Work • Work is never the maximum possible if any current is flowing. • In any real, spontaneous process some energy is always wasted – the actual work realized is always less than the calculated maximum.

41. Nernst Equation Relation between free energy difference and electric potential difference: The change of free energy is equal to the work done by moving 1 mole of charges (νe-) from anode to cathode.

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

44. Example: Calculating G for a Cell Reaction • Using the data in previous Table, calculate G for the reaction Cu2+(aq)+ Fe(s)Cu(s)+ Fe2+(aq) Is this reaction spontaneous? • The half-reactions are • We can calculate Gfrom the equation G

45. Example: Calculating G for a Cell Reaction • Since two electrons are transferred per atom in the reaction, 2 moles of electrons are required per mole of reactants andproducts. Thus n = 2 mol e-, F = 96,485 C/mol e-, and = 0.78 V = 0.78 J/C. Therefore, • The process is spontaneous, as indicated by both the negative sign of G and the positive sign of

46. The relation between the standard potential of a reaction (reactants, purple; products, yellow) and the equilibrium constant. For a (half) reaction (Mn+ + ne- M), the higher the reduction potential (the more negative ΔGo), the more easily it proceeds.

47. Dependence of Cell Potential on Concentration A Concentration Cell

48. Dependence of Cell Potential on Concentration Nernst Equation • The relationship between cell potential and concentrations of cell components • At 25°C: aA + νe-bB At equilibrium (E=0, Q=K):

49. Dependence of Cell Potential on Concentration EXERCISE! A concentration cell is constructed using two nickel electrodes with Ni2+ concentrations of 1.0 M and 1.00 × 10-4M in the two half-cells. Calculate the potential of this cell at 25°C. 0.118 V

50. Dependence of Cell Potential on Concentration CONCEPT CHECK! You make a galvanic cell at 25°C containing: • A nickel electrode in 1.0 M Ni2+(aq) • A silver electrode in 1.0 M Ag+(aq) Sketch this cell, labeling the anode and cathode, showing the direction of the electron flow, and calculate the cell potential. 1.03 V