Chemistry 232 Electrochemistry

A Schematic Galvanic Cell Galvanic cells – an electrochemical cell that drives electrons through an external circuit spontaneous redox reaction occurring inside cell. AnodeCathode e-e- Reducing Agent e-e- e-e- Oxidizing Agent Porous Disk

The Zinc/Copper galvanic cell. e-e V a(Zn 2+ ) = 1.00 e-e- e-e- AnodeCathode Porous Disk or Salt Bridge Zn(s) Cu(s) e-e- a(Cu 2+ ) = 1.00 The Zn/Cu Galvanic Cell Cu 2+ (aq) + 2 e -  Cu (s) (cathode, RHS) Zn 2+ (aq) + 2 e -  Zn (s) (anode, LHS)

Cell Reactions The difference in the RHS and the LHS reaction Cu 2+ (aq) + Zn (s)  Cu (s) + Zn 2+ (aq) For each half reaction, we can write the reaction quotient as follows Cu 2+ (aq) + 2 e -  Cu (s) Q = 1/ a(Cu 2+ ) Zn 2+ (aq) + 2 e -  Zn (s) Q = 1/ a(Zn 2+ ) Overall  Q cell = a(Zn 2+ ) / a(Cu 2+ )

Cell Diagrams A shorthand way of expressing what takes place in an electrochemical cell. For the above electrochemical cell. Pt Cu (s) Cu 2+ (aq) Zn 2+ (aq) Zn (s) Pt Note phase boundary liquid junction salt bridges

Another Example The cell reaction H 2 (g) + Cu 2+ (aq)  2 H + (aq) + Cu (s) Pt H 2 (g) H + (aq) Cu 2+ (aq) Cu (s) Pt Electrochemical cells a cell that has not reached equilibrium can do electrical work by driving electrons through an external wire.

Reversible Electrochemical Cells In order for us to make measurements on an electrochemical cell, it must be operating reversibly. Place an opposing source of potential in the external circuit Cell operates reversibly and at a constant composition. w e,max =  G

The Measurement of Cell Potentials Measure the potential of an electrochemical cell when the cell is at equilibrium, i.e., the state between the galvanic and the electrolytic cell. e-e- Reducing Agent e-e- e-e- Oxidizing Agent AnodeCathode Porous Disk Counter potential (load)

Derivation of the Nernst Equation Consider an electrochemical cell that approaches the equilibrium state by an infinitesimal amount d  Reminder

The Work in Transporting Charge The maximum work F = Faraday’s constant = e N A = C/mole For the passage d  electrons from the anode (LHS) to the cathode (RHS)

The Cell Potential The work to transport charge

Standard Cell Potentials From the reaction Gibbs energy We define

The Nernst Equation E  represents the standard cell potential, the potential of the cell when all cell components are under standard conditions. f (all gases) = 1 a (solutes) = 1 T = K P = 1.00 bar pressure

Cells at Equilibrium When the electrochemical cell has reached equilibrium K cell = the equilibrium constant for the cell reaction. Knowing the E° value for the cell, we can estimate the equilibrium constant for the cell reaction.

Equilibrium Constant Calculations from Cell Potentials Examine the following cell. Pt Sn 2+ (aq), Sn 4+ (aq) Fe 3+ (aq) Fe 2+ (aq) Pt Half-cell reactions. Sn 4+ (aq) + 2 e -  Sn 2+ (aq) E  (Sn 4+ /Sn 2+ ) = 0.15 V Fe 3+ (aq) + e -  Fe 2+ (aq)E  (Fe 3+ /Fe 2+ ) = V Cell Reaction Sn 2+ (aq) + 2 Fe 3+ (aq)  Sn 4+ (aq) + 2 Fe 2+ (aq) E  cell = ( V) = 0.62 V

Standard Reduction Potentials Standard reduction potentials are intensive properties. We cannot measure the potential of an individual half-cell! We assign a particular cell as being our reference cell Assign values to other electrodes on that basis.

a (H + ) = 1.00 H 2 (g) e-e- Pt gauze The Standard Hydrogen Electrode E o (H + /H 2 ) half-cell = V f{H 2 (g)} = 1.00

A Galvanic Cell With Zinc and the Standard Hydrogen Electrode. e-e- Zn 2+, SO 4 2- a (H + ) = 1.00 AnodeCathode Porous Disk or Salt Bridge Source of H + (e.g., HCl (aq), H 2 SO 4 (aq)) a(Zn 2+ ) = 1.00 H 2 (g) V e-e- Zn(s) Pt gauze

The Cell Equation for the Zinc- Standard Hydrogen Electrode. The cell reaction 2 H + (aq) + Zn (s)  H 2 (g) + Zn 2+ (aq) Pt Zn (s) Zn 2+ (aq),a=1 H + (aq), a=1 H 2 (g), f=1 Pt When we measure the potential of this cell E cell = E RHS - E LHS but E RHS = E  (H + /H 2 ) = V  E cell = E  (Zn 2+ /Zn) = V

The Spontaneous Direction of a Cell Reaction Examine the magnitude the of the standard cell potential! If the standard cell potential is positive, the  r G  is negative!

The Composition Dependence of the Cell Potential Nonstandard cell potential (E cell ) will be a function of the activities of the species in the cell reaction. u To calculate E cell, we must know the cell reaction and the value of Q cell.

Example For the following system Pt H 2 (g) H + (aq) Cu 2+ (aq) Cu (s) Pt u Calculate the value of the cell potential when the f (H 2 ) = 0.50, a(Cu 2+ ) = 0.20, and a(H + ) = 0.40.

Concentration Cells Electrolyte concentration cell the electrodes are identical; they simply differ in the concentration of electrolyte in the half- cells.

Concentration Cells (II) Electrode concentration cells the electrodes themselves have different compositions. This may be due to. Different fugacities of gases involved in electrode reactions (e.g., The H + (aq)/H 2 (g) electrode). Different compositions of metal amalgams in electrode materials.

Applications of Electrochemistry Measurement of activities and activity coefficients. Electrochemical series. Equilibrium constants and thermodynamic functions of cell reactions

Obtaining Standard Cell Potentials Look at the following cell Pt H 2 (g) HCl (aq) AgCl (s) Ag (s) Pt E  cell = E  (AgCl/Ag) - E  (H + /H 2 ) = E  (AgCl/Ag)

E  cell Values and Activity Coefficients In dilute solution, using the DHLL Plot LHS vs. m 1/2 Once E  cell is known, we can obtain experimental estimates of the mean activity coefficients.

The Calculation of Standard Cell Potentials

Electrochemical Series Look at the following series of reactions Cu 2+ (aq) + 2 e -  Cu (s) E  (Cu 2+ /Cu) = V Zn 2+ (aq) + 2 e -  Zn (s) E  (Zn 2+ /Zn) = V Zn has a thermodynamic tendency to reduce Cu 2+ (aq) Pb 2+ (aq) + 2 e -  Pb (s) E  (Pb 2+ /Pb) = V Fe 2+ (aq) + 2 e -  Fe (s) E  (-Fe 2+ /Fe) = V Fe has a thermodynamic tendency to reduce Pb 2+ (aq)

Thermodynamic Information Note  And

Entropy Changes To obtain the entropy change for the cell reaction

Enthalpy Changes To obtain the enthalpy change for the cell reaction

The Liquid Junction Potential Examine the following electrochemical cell Activity difference of the HCl between compartment 1 and compartment 2 There should be a transport of matter from one cell compartment to the other!

A Concentration Cell e-e- a (Cl - ) = LeftRight Porous Disk or Salt Bridge a(Cl - ) = V e-e- Ag(s)

The Development of Liquid Junction Potentials The cell compartments are identical except for the activities of the electrolyte solutions. HCl (a  1 ) HCl (a  2 ) Ag/AgCl electrode

Note that we now have the migration of both cations and anions through the liquid junction. Cl - Ag/AgCl electrode H +

After a period of time Ag/AgCl electrode

Choose the lower compartment as our LHS electrode. Ag AgCl Cl - (aq) a 1 Cl - (aq), a 2 AgCl (s) Ag (s) Note: liquid junction u For the passage of one mole of charge through the cell -F E cell =  G J

The Cell Reactions For the LHS and RHS electrodes AgCl (s) + e -  Ag (s) + Cl - (a 1 ) LHS AgCl (s) + e -  Ag (s) + Cl - (a 2 ) RHS Net change Cl - (a 1 )  Cl - (a 2 ) Note that the charge at the interface is transported by the anions and cations in the cell reaction!

The Transport Numbers How is the charge carried at the interface of the cells? t + moles of charge carried by the H + (cation). t - moles of charge carried by the Cl - (anion). Passage of one mole of “+” charge through the interface requires the passage of t + moles of H + (aq) from the LHS  RHS, and the passage of t - mole of Cl - charge from the RHS  LHS.

At the boundary t + H + (a 1 ) + t - Cl - (a 2 )  t + H + (a 2 ) + t - Cl - (a 1 ) For the entire cell Cl - (a 1 ) t + H + (a 1 ) + t - Cl - (a 2 )  Cl - (a 2 ) t + H + (a 2 ) + t - Cl - (a 1 ) The cell reaction involves the transport of t + moles of HCl from the LHS to the RHs of the cell.

The Gibbs Energy Changes For the above cell reaction, we can write the Gibbs energy expressions as follows

Cells With Transference Note a(H + ) a (Cl - ) = {a  (HCl)} 2 Note that the cell potential with transference, E wt is determined as follows

Cells without Transference What if we were able to set up a cell so that the transport at the interface did not contribute to the overall  G? The potential of this cell would be the cell potential without transference, E wot. Cl - (a 1 )  Cl - (a 2 )

The Liquid Junction Potential The liquid junction potential is the difference in the cell potentials with and without transference!

L.J. Potentials Depend on Transport Numbers What is the following were true? t +  t -  0.5  E LJ would be very small and would only make a small contribution to the overall cell potential !

L.J. Potentials Depend on Transport Numbers E LJ a potential problem any time we measure the cell potential whose electrodes have different electrolytes How does the salt bridge help? e.g., for species with t +  t -  0.5, the E LJ values are small and are readily established!