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Electrochemical Potential, Work, and Energy. Potential, Work, and Energy Units Joule (J) = unit of energy, heat, or work (w) = kg • m 2 /s 2 Coulomb (C) = unit of electrical charge (q). 1 e - = 1.6 x 10 -19 C = electrical potential ( e )

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electrochemical potential work and energy
Electrochemical Potential, Work, and Energy
  • Potential, Work, and Energy
    • Units
      • Joule (J) = unit of energy, heat, or work (w) = kg•m2/s2
      • Coulomb (C) = unit of electrical charge (q). 1 e- = 1.6 x 10-19 C
      • = electrical potential (e)
      • 1 J of work is produced when 1 C of charge is transferred between two points differing by 1 V of electrical potential
      • Work flowing out of a system (Galvanic Cell) is taken to be negative work
      • Cell Potential is always positive
      • From last chapter, wmax = DG
slide2
Electrochemical Problems
    • When current flows, we always waste some of the energy as heat instead of work

w < wmax

    • We can, however, measure emax with a potentiometer, so we can find the hypothetical value of wmax
    • Example: eocell = 2.50 V 1.33 mole e- pass through the wire. eactual = 2.10 V
      • 1 Faraday (F) = the charge on 1 mole of electrons = 96,485 C

(6.022 x 1023 e-/mol)(1.6 x 10-19 C/e-) = 96,485 C/mol

      • w = -qe = -(1.33 mol e-)(96,485 C/mole e-)(2.10 J/C) = -2.69 x 105 J
      • wmax = -qemax = -(1.33 mol e-)(96,485 C/mole e-)(2.50 J/C) = -3.21 x 105 J
      • Efficiency = w/wmax = -2.69 x10-5 J/-3.21 x 105 J = 0.838 or 83.8%
    • Free Energy (DG)
      • q = nF where n = number of moles, F = 96,485 C/mole
      • DG = -nFe (assuming the maximum e)
      • Maximum cell potential is directly related to DG between reactants and products in the Galvanic Cell (This lets us directly measure DG)
slide3
Example: Calculate DGo for the reaction

Cu2+(aq) + Fe(s) Cu(s) + Fe2+(aq)

        • Half Reactions: Cu2+ + 2e- Cuoeo = 0.34 V

Feo Fe2+ + 2e- eo = 0.44 V

b) DGo = -nFeo = -(2 mol e-)(96,485 C/mol e-)(0.78 J/C) = -1.5 x 105 J

      • Example: Will 1 M HNO3 dissolve metallic gold to make 1 M Au3+?
        • Half Reaction: NO3- + 4H+ + 3e- NO + 2H2O eo = +0.96 V

Auo Au3+ + 3e-eo = -1.50 V

Au(s) + NO3-(aq) + 4H+(aq) Au3+(aq) + NO(g) + 2H2O(l) eocell = -0.54V

        • Since e is negative (DG = +) the reaction will not occur spontaneously
  • Cell Potential and Concentration
    • Concentration Cells
      • Up until now, concentration for all Galvanic solutions = 1 M (Gives eo)
      • What happens if we change these concentrations?

Eocell = +0.78 V

slide4
3) Le Chatelier’s Principle
    • Cu(s) + 2Ce4+(aq) Cu2+(aq) + 2Ce3+(aq) eocell = 1.36 V
    • Increase Ce4+ concentration, (e > eo)
    • Increase Cu2+ concentration, (e < eo)

d) Example

  • Concentration Cell = Galvanic Cell driven by the fact that concentrations of the same reactants are different on the two sides of the cell.
  • Example: Ag+ + e- Agoeo1/2 = +0.80 V
    • If both sides had [Ag+] = 1 M, then eocell = +0.80 V + (-0.80 V) = 0.00 V
    • If [Ag+]right = 1 M and [Ag+]left = 0.1 M then we should have a potential
      • Diffusion would try to equalize Ag+ on the right side and the left side

(Entropy favors even distribution, like gas particles in two chambers)

      • Electrons would flow from left to right to even out [Ag+]
      • A very small voltage would be generated
      • Example
slide6
The Nernst Equation
    • Derivation
      • DG = DGo + RTlnQ = -nFe
      • DGo = -nFeo
      • -nFe = -nFeo + RTlnQ
    • At 25 oC, this simplifies to
    • Example: 2Al(s) + 3Mn2+(aq) 2Al3+(aq) + 3Mn(s) eocell = 0.48 V
      • Oxidation: 2Al(s) 2Al3+(aq) + 6e-
      • Reduction: 3Mn2+(aq) + 6e- 3Mn(s)
      • [Mn2+] = 0.5 M, [Al3+] = 1.5 M
      • Q = [Al3+]2 / [Mn2+]3 = (1.5)2 / (0.5)3 = 18
      • As the reaction proceeds, ecell 0 (Q K) = Dead Battery!
      • Calculating K:
slide8

VO2+ + 2H+ + e- VO2+ + H2O eo = 1.00 V

Zn2+ + 2e- Zn eo = -0.76 V

Find Ecell

      • Example: [VO2+] = 2M, [H+] = 0.5M, [VO2+] = 0.01M, [Zn2+] = 0.1M
  • Ion-Selective Electrodes
    • Cell potential depends on concentration of an ion
    • pH meter
      • Standard electrode of known potential
      • Glass electrode filled with known [HCl] whose potential changes based on external [H+]
      • Potentiometer measures the potential difference
    • You can make similar Na+, K+, or NH4+, Cl-, F-, etc…selective electrodes
      • Glass “senses” the presence of H+ in open sites (pH meter)
      • Change the type of glass for sensing other ions

Line Notation for a typical pH electrode:

Ag | AgCl | Cl- || H+ outside | H+ inside, Cl- | AgCl | Ag

Outer ref elec.

sample

Known H+

Inner ref elec.

H+ sensing glass membrane

slide9
Batteries
    • Battery Basics
      • Battery = galvanic cells used as a portable source of electrical potential
      • Batteries are a source of direct current only; not suitable for providing alternating current like permanent outlets do
    • Lead Storage Batteries
      • Highly rechargeable, durable batteries that can operate between –30 and 120 oF
      • Lead anode, Lead oxide cathode, Sulfuric Acid electrolyte

Anode: Pb + H2SO4 PbSO4 + H+ + 2e-

Cathode: PbO2 + HSO4- + 3H+ + 2e- PbSO4 + 2H2O

Cell: Pb(s) + PbO2(s) + 2H+(aq) + 2HSO4-(aq) 2PbSO4(s) + 2H2O eo = 2.0V

          • For cars: 6 of these cells in series with grid electrodes provides 12 V (2 V each)
          • Sulfuric Acid is consumed; so density of the acid drops over its life
          • Water is also consumed; can “top off” the battery with water. New Ca/Pb electrodes no longer use up water (sealed batteries)
          • Alternator recharges battery by forcing current in opposite direction
          • Physical Damage, not chemical depletion, usually “kills” the battery
slide10
Other Batteries
    • Dry Cell Batteries = calculators, watches, etc…
      • Acid Version: Zn anode, C cathode, MnO2/NH4Cl/C paste as electrolyte 1.5V

Anode: Zn Zn2+ + 2e-

Cathode: 2NH4+ + 2MnO2 + 2e- Mn2O3 + 2NH3 + H2O

      • Alkaline Version has KOH or NaOH as electrolyte

Anode: Zn + 2OH- ZnO + H2O + 2e-

Cathode: 2MnO2 + H2O + 2e- Mn2O3 + 2OH-

        • Rechargable Nickel—Cadmium Batteries

Anode: Cd + 2OH- Cd(OH)2 + 2e-

Cathode: NiO2 + 2H2O + 2e- Ni(OH)2 + 2OH-

d) Nickel-Metal Hydride (NiMH) Batteries

Anode: M∙H + OH- M + H2O + e-

Cathode: NiO2 + 2H2O + 2e- Ni(OH)2 + 2OH-

e) Lithium Ion Batteries: flow of Li+ inside battery matched by e- in wire

slide11
Fuel cells = galvanic cell with continuous source of reactants
    • The Hydrogen—Oxygen Fuel Cell is used for NASA spaceflights
    • The reactant gases can be stored as liquids in tanks
      • Anode: 2H2 + 4OH- 4H2O + 4e-e1/2 = 0.83V
      • Cathode: 4e- + O2 + 2H2O 4OH-e1/2 = 1.20V
      • Overall: 2H2(g) + O2(g) + catalyst 2H2O(l) eo = 2.03V
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