How to find forward and backward reaction rate constant for electrolysis reaction?

Question

Giving values of charge Q recorded at different time, how do we find the rate constant of C+ne <->D knowing initial concentration of C and D?

Answer 1

The charge of the electron is 1.602x10^-19 C. You can convert this to the amount of charge per mole of electrons:

 

(1.602x10^-19 C/e-) x [(6.022x10^23 e-)/(1 mole e-)] = 96500 C/mole e-

 

this last value is known as Faraday's constant, symbolized by F. Now, using the hypothetical equation you've given and the charge Q, the amount of reactant D formed will be:

 

moles D = Q x [(1 mole e-)/(96500 C)] x [(1 mole D)/(n moles e-)]

 

or

 

D = Q/nF

 

and

 

[D] = Q/nFV

 

where V is the volume of the solution and [D] is the concentration of D.

 

d[D]/dt = (1/nFV)(dQ/dt) = I/nFV, where I is the current.

 

Since C and D have the same stoichiometry, d[D]/dt = - d[C]/dt. Also, assuming a first order rate on this reaction then the rate of disappearance of C is given by:

 

d[C]/dt = -k[C]

 

thus,

 

k[C] = I/nFV

 

and

 

k = I/nFV[C]

 

If you know the current input and the number of stoichiometric electrons you can calculate this rate constant using the equation above. However, if all you are given is the charge as a function of time, then you need to integrate the above equation:

 

dQ = nFVk[C]dt

 

or

 

Q2-Q1 = nFVk[C](t2-t1)

 

thus,

 

k = (Q2-Q1)/{nFV[C](t2-t1)}

 

Notice that (Q2-Q1)/(t2-t1) is simply the slope function Q or the current I, as we had shown before.