The description of my problem is as follows:

I will like to find out how can I obtain a mathematical equation which could give me a surface plot of the current output as a function of both concentration and time from an electrochemical cell which uses the following redox equation:

O2 + 2Pb -> 2PbO

I have the following information:

  1. Mass of Pb - 10g
  2. A fixed concentration of oxygen gas - 20.9% over volume of air in room

Assumptions made:

  1. Unlimited supply of oxygen
  2. The gas is supplied at constant room temperature and pressure (25 degree Celcius and 1 atm)

Tentatively, my plan was to use Farday's Law of Electrolysis (https://en.wikipedia.org/wiki/Faraday%27s_laws_of_electrolysis) to calculate the current which flows as a result of the transfer of electrons from the redox reaction. My hypothesis is:

  1. The magnitude of the current generated by the following reaction will be proportional to the rate of oxygen consumption.
  2. The magnitude of the current generated will decrease over time as the rate of reaction decrease (from the decrease in concentration of Pb).

My problem is that the plot I obtained shows me that the current vs time relationship is a reciprocal one under fixed concentration of oxygen gas. Hypothetical plot of current against time which does not agree with the experimental result This does not agree with the experimental results I obtained which shows that current output is steady and starts decreasing after a long period of time (a few months at least). Can someone help point out my the flaw in my argument? What should I do instead to obtain the plot I described?

  • 1
    $\begingroup$ It's a surface reaction - Pb isn't in solution, otherwise it could similar kinetics to what you've got. $\endgroup$ – Mithoron Aug 17 '17 at 14:02

In addition to the redox reactions the transport of material towards the electrodes also needs to be considered. This involves using Fick's equations for diffusion to calculate the concentration of species at distances away from the electrodes as reaction starts and reaches constant conditions. The steady state equations are of the form

$$ D_{ox} \frac{\partial C_{ox}}{\partial x}= k_cC_{ox}-k_aC_{rd} \\ D_{rd} \frac{\partial C_{rd}}{\partial x}= -k_cC_{ox}+k_aC_{rd}$$

These lead to the Cottrell equation for the limiting flux (current density) $j=-nFC^o_{ox}\sqrt{D_{ox}/\pi t}$. To get what you want you will probably need to consult some specialist text books on electrochemistry.

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  • $\begingroup$ The Cottrell equation still won't explain why the reaction produces a steady current for a period of time before decreasing. Also, experimental results show that the decrease in current approximates to a sigmoid function reflected at the y-axis, which is counter-intuitive to Cottrell's equation as it also gives an inverse relationship with time. May I know which part of the specialist textbook do you recommend me to go through? The book which I am using now is Electrochemical Methods_ Fundamentals and Applications by Bard and Faulkner $\endgroup$ – Christopher Aug 21 '17 at 7:22
  • $\begingroup$ You sound as though you understand this problem very well :) I have used 'Principles of Electrochemistry', Koryta, Dvorak & Kavan, publ Wiley. $\endgroup$ – porphyrin Aug 21 '17 at 11:15

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