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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: scientizscht on 25/06/2020 12:43:59

Title: How to calculate the mass transport on an electrode?
Post by: scientizscht on 25/06/2020 12:43:59
Hello

I want to calculate the mass transport via diffusion for an electrode.

This is the current density that can be achieved if diffusion replenishes the concentration of a solute that reacts on an electrode.

Can you describe the inputs that I need and the steps to calculate it?

I know the concentration of the solute in the solution and we can assume that this is stable.

I am struggling to apply Fick's law as I am not sure about the dφ/dx.

Thanks!
Title: Re: How to calculate the mass transport on an electrode?
Post by: Bored chemist on 25/06/2020 14:39:00
The basics are here
https://en.wikipedia.org/wiki/Debye%E2%80%93H%C3%BCckel_theory

Good luck
Title: Re: How to calculate the mass transport on an electrode?
Post by: scientizscht on 25/06/2020 19:03:04
That's interesting thanks.

If I want to calculate only the Fickian diffusion, how do I calculate the dφ/dx ?

Is the dφ basically the [substatrate] - 0 ?
And is the dx the diffusion layer thickness which is mentioned in the literature to be 0.01cm?

Thanks!
Title: Re: How to calculate the mass transport on an electrode?
Post by: Bored chemist on 25/06/2020 19:45:23
Do you understand calculus?
https://en.wikipedia.org/wiki/Calculus
Title: Re: How to calculate the mass transport on an electrode?
Post by: scientizscht on 25/06/2020 23:11:52
It seems to work for both dx and Δx !
Title: Re: How to calculate the mass transport on an electrode?
Post by: evan_au on 25/06/2020 23:27:34
Quote from: scientizscht
It seems to work for both dx and Δx !
Newton in England and Liebniz in Germany both developed calculus about the same time.
This set off a big argument about who had really invented it first,
- Δx was the way Newton wrote it.
- dx was the way Libniz wrote it

They both worked, because they are two different notations for the same concept: an infinitesimally small step.
Title: Re: How to calculate the mass transport on an electrode?
Post by: Bored chemist on 26/06/2020 18:05:34
Quote from: scientizscht on 25/06/2020 23:11:52
It seems to work for both dx and Δx !
What does?
Title: Re: How to calculate the mass transport on an electrode?
Post by: scientizscht on 26/06/2020 20:00:16
Quote from: Bored chemist on 26/06/2020 18:05:34
Quote from: scientizscht on 25/06/2020 23:11:52
It seems to work for both dx and Δx !
What does?

If you go to https://www.sciencedirect.com/topics/engineering/diffusion-layer and scroll to the "Table 13.4. id and δ Under Various Fluid Dynamic Conditions" you will see:

Electrolysis with no convections: 6A/m2
Thickness of diffusion layer: 4.75mm

These values are based on the following conditions:
0.3 mol/L CuSO4 solution, diffusivity is 10^−9 m2/s

If you take Fick's Law by using dφ = 0.3M and dx = 4.75mm, you get:
J = 10^-4cm2/s * 3x10-4mol/cm3 / 0.475cm
J = 60A/m2

I think they made a mistake in diffusivity, it should be maximum 10^-10m2/s as this is the case for most small ions.

So you get from Fick's Law the 6A/m2.

If we use the impingement rate formula you suggested, we would get 276kA/cm2!