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Dear Physics Forum: Calculus problem (Physical Chemistry)

  1. Jun 30, 2013 #1
    1. The problem statement, all variables and given/known data

    In the electrochemists technique of cyclic voltammetry, the peak current, I, is a simple function of the scan rate, v, according to the Randles-Sevcik equation:

    2. Relevant equations

    I = 0.4463nFAc(nF / RT)^1/2 D^1/2 V^1/2

    Where n is the number of electrons transferred, F is the Faraday constant, D is the diffusion coefficient, and C the concentration of analyte. Write an expression to describe the gradient of a graph of I (as "y") against v (as "x") ie. dI/dV

    3. The attempt at a solution

    As a chemist, my maths isn't particularly strong, but I tried to answer the problem as best as possible. I treated the equation posted above as I = k*v^1/2, where k is treated as a constant and the answer I got was dI/dV = 1 ÷ 2*√v (assuming that constants when differentiated become zero).

    I would be delighted if a member could show me a thorough step by step procedure on how the answer should actually look if I'm incorrect in my logic.

    I appreciate your time and concern,

    Kindest Regards,

    Last edited: Jun 30, 2013
  2. jcsd
  3. Jun 30, 2013 #2


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    You started out with ##I = k v^{\frac 1 2}## so$$
    \frac{dI}{dv} =\frac k {2v^{\frac 1 2}}$$which is what I think you did. The constant just stays there as a multiple.
  4. Jun 30, 2013 #3
    Thank you very much mate. I thought that was correct and as usual I've over complicated it more than required.

    Appreciated fully.

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