Electron transfer kinetics

Question 1

What is overpotential?

Answer 1

The potential difference between the reduction potential determined via thermodynamics and the reduction potential when observed experimentally.

Question 2

What is the nernst equation?

Answer 2

𝐸 = 𝐸𝑜 + (𝑅𝑇) / (𝑛𝐹) * ln[𝑂][𝑅]

Question 3

What is the Tafel relationship?

Answer 3

𝑖 = 𝑎*exp[𝜂/𝑏]
or
𝜂= 𝑎′+ 𝑏′log𝑖
where a , a’ , …. are constants

Question 4

The magnitude of the current flow of the electrode i, is given by?

Answer 4

i = A * F * j

A = area of electrode
F = faraday constant 96485
j = flux of reactant at reactant surface or quantity of material reacting at the electrode per second.
j = k[Reactant]

Question 5

the magnitude of the current flow of the electrode i is dependant on what?

Answer 5

1. The rate constant for the heterogeneous ET, k

2. Concentration of reactant at the electrode surface

Question 6

What is overpotential η defined as?

Answer 6

|η| = |E – E0|

Question 7

In an equilibrium, when E = E0, what happens when you apply more negative potential so that E < E0? and what happens when more positive potential is added so that E > E0? Which is more beneficial for the forward reaction and why?

Answer 7

When negative potential is added to the electrode, the energy of the fermi level will increase, causing the relative energy of the products to increase as they include the electron. When more positive potential is added, the energy of the fermi goes down as the electrons in the electrode has lower energy and the energy of the products is lowered.
Adding a positive potential is more beneficial because reducing the energy of the fermi level reduces the energy barrier of the reaction, making the formation of products more favourable

Question 8

In terms of electrode potentials what is ΔG?

Answer 8

ΔG = nF(E – E0)

Question 9

what is ΔGox‡(E0)?

Answer 9

ΔGox‡(E0) is the difference in free energy between the lowest point in free energy and the point where E = E0 or when E >/< E0.

Question 10

If ΔGox‡(E0) - ΔGox‡(E) is a fraction of F (E – E0) that can be quantified then what is ΔGox‡(E0) equal to?

Answer 10

if ΔGox‡(E0) - ΔGox‡(E) = (1 – α) F (E – E0) where 0 < α < 1,
then ΔGox‡(E) = ΔGox‡(E0) - (1 – α) F (E – E0)

Question 11

what is ΔGred‡(E) equal to?

Answer 11

ΔGred‡(E) = ΔGred‡(E0) + α F (E – E0)

Question 12

what are the rate constats of oxidation and reduction?

Answer 12

kox = k0 * exp ((1– α) F (E – E0)/RT)

kred = k0 * exp (α F (E – E0)/RT)

Question 13

what is the magnitude of the current for oxidation?

and what is the magnitude of the current for reduction?

Answer 13

𝑖𝑜𝑥 = 𝐴 𝐹 𝑘𝑜𝑥 [𝑅] = A F k0 [R] exp ((1– α) F (E – E0)/RT)
ired = 𝐴 𝐹 𝑘red [O] = A F k0 [O] exp (α F (E – E0)/RT)

Question 14

what is the total magnitude of current equal to?

Answer 14

𝑖= 𝑖𝑜𝑥 + 𝑖𝑟𝑒𝑑 = A F k0 [R] exp ((1– α) F (E – E0)/RT) -A F k0 [O] exp (α F (E – E0)/RT)

Question 15

What is the butler-volmer equation?

Answer 15

𝑖=𝐴 𝐹 𝑘𝑜 { [𝑅] exp [(1− 𝛼) 𝐹 𝜂/𝑅𝑇] − [𝑂] exp [ −𝛼 𝐹 𝜂/𝑅𝑇] }