Thermodynamics and Electrochemistry
1) Background info:
Cell Potential Electrical Work and Free Energy
emf = potential difference (V) =
cell potential= the negative sign means that work is done by the system.
Maximum work: Wmax = -qEmax
But to obtain work, electrons must flow, which causes friction. Inevitably, in any real spontaneous process, some energy is wasted.
The relationship between Gibbs free energy and Ecell
q = nF F= Faraday’s constant, 96485 Cmol-1
n = # mol of e-1
The change in free energy, DG, is equal to the maximum amount of work obtained by the process.
Wmax = DG
DG = -q Emax = -nFEmax
DG = -nFE
@ standard conditions: DGo = -nFEo
· The maximum cell potential is directly related to the free energy difference between the reactants and products in the cell.
· This provides the experimental means to obtain the value for the change in free energy, DG, for a reaction.
· The relationship between Gibbs fee energy and the E o cell is summarized by the expression above.
· This relationship also serves as a bridge between thermodynamics and electrochemistry.
2. Voltage and Spontaneity:
Where F = Faraday constant = 96500 J mol/V
96500 C/mole
n = number of moles of electrons transferred
Eo cell = standard reaction potential, V
Go = standard free energy, kJ/mol
K /Eocell
/ DGo /Conclusion
> 1 / Positive / Negative / Spontaneous cell reaction=1 / 0 / 0 / At equilibrium
< 1 / Negative / Positive / Non-spontaneous cell reaction. Reaction is spontaneous in the reverse direction
Example: Calculate the Gibb’s free energy for the following reaction:
Cu2+ Fe ------> Cu + Fe2+
Cu 2+ + 2e------à Cu Eo = +0.34V
Fe ----à Fe 2+ + 2e- Eo = 0.44V
------
Cu2+ Fe ------> Cu + Fe2+ Eo cell = 0.78 V
DGo = - (2mol e-)(9648 Cmol-1)(0.78 J/C)
D Go = -1.5 x 10 5J
- spontaneous since D Go is negative, and the Eo cell is positive.
3. Dependance of Cell Potential on Concentration.
Given the following cell: Cu/Cu2+//Ce4+/Ce3+
Cu(s) + 2 Ce4+(aq) ----- > Cu2+(aq) + 2 Ce3+(aq) Eocell=+1.36V
· if the concentration of [Ce4+], Le Chatelier’s principle says that the forward reaction is favoured. So the cell potential would increase.
Nerst Equation:
· equation used to calculate cell potential’s dependance on concentration for NON STANDARD CONDITIONS.
· Dependance of the cell potential on concentration results directly from the dependance of the free energy on concentration.
DG = DGo + RT lnQ
DG = -nFE, and DGo = -nFEo
-nFE = - nFEo + RT lnQ
Nerst Equation: E = Eo - lnQ
-R is the gas constant (8.314 J/K mol),
-T the Kelvin temperature,
-n the number of electrons transferred between the species,
-F the Faraday constant,
-Eocell is the voltage generated IF the conditions WERE standard,
-ln represents the natural logarithm
-and Q is the reaction quotient.
Note:
· At standard state, all concentrations are equal to 1, so E = Eo.
· At 25o C the equation above becomes: E = Eo - logQ
· As the concentration of the products increase, the voltage decreases.
· As the concentration of the reactants increases, the voltage increases.
Example Calculation
If the reaction below is carried out using solutions that are 5M Zn2+ and 0.3M Cu2+ at 298K, what is the actual cell voltage? Zn(s) + Cu2+(aq) è Cu(s) + Zn2+(aq)
Firstly, work out the Eocell assuming standard conditions. Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s)
Zn2+(aq) + 2e- çè Zn(s) Eo = -0.76V
Cu2+(aq) + 2e- çè Cu(s) Eo = +0.34V
Eocell = ER – EL = +0.34 - -0.76 = 1.1V
Then calculate Q. Since zinc and copper metals are solids, they are omitted from Q.
Q = [Zn2+]/[Cu2+] = 5/0.3 = 16.7
Two electrons are transferred between the zinc and copper, so n=2. Plug everything in
E = 1.1V - (0.0257/2) * ln (16.7) = 1.06V
Example Calculation 2 Fe3+ + Sn2+ ----- > 2 Fe2+ + Sn4+
In a galvanic cell, all the products have a concentration of 0.0355M and the reactants are 0.100M. What is the voltage at 25oC.
Eocell = - Eosn + EoFe
= -0.154V + 0.771V
= 0.617V
E=0.617V – (8.314)(298)/(2) (96485) ln (0.0355^2) (0.0355)/(0.100^2)(0.100)
E=0.657V
4. Voltage and equilibrium:
At equilibrium, E=0 and Q=K
E = Eo - lnQ 0 = Eo - lnK
Therefore, Eo = lnK
· This equation allows us to calculate the equilibrium constant for a redox reaction.
Electrochemistry and Thermodynamics Summary
Voltage and Spontaneity:
Nerst Equation: E = Eo - lnQ
Voltage and Equilibrium: Eo = lnK
K /Eocell
/ DGo /Conclusion
> 1 / Positive / Negative / Spontaneous cell reaction=1 / 0 / 0 / At equilibrium
< 1 / Negative / Positive / Non-spontaneous cell reaction. Reaction is spontaneous in the reverse direction