Dear Physics Forum: Calculus problem (Physical Chemistry)

[Luke Attigan]

Homework Statement

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:

Homework 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

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,

Luke.

 

[LCKurtz]

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.

 

[Luke Attigan]

Thank you very much mate. I thought that was correct and as usual I've over complicated it more than required.

Appreciated fully.

L.