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I found a relationship online between the conductivity of electrolyte and current.

$$i = F \sum_i z_i N_i = F^2 \left( \sum_i z_i^2 u_i c_i \right)\nabla\phi = -\kappa\nabla\phi \qquad \kappa = F^2 \sum_i z_i^2 u_i c_i$$

This equation is hard for me to follow. I get what most of the variables mean and I am guessing that $\Delta\phi$ is the potential difference. However, I thought that the conductivity was also related to temperature, which I do not see in the equation.

It has been a struggle for me to find results on the internet to relate conductivity and current together. Can someone help me and tell me if this equation is right.

Also, this equation is true for dilute solutions, what will the equation be for concentrated solutions (solutions near $\pu{1 M}$)?

Also, how would you calculate the potential gradient?

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    $\begingroup$ As it stands, your question is a little broad and you are better served by breaking it up into multiple queries. That said, all your problems will be solved by visiting the Wikipedia page on Debye-Huckel theory, or others you might find with a search on those terms (pardon my lack of umlaut on the "u", apparently HTML and TeX are not working in this box). $\endgroup$ – Todd Minehardt Mar 24 '17 at 22:44
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    $\begingroup$ @Todd o.o Mathjax works in comments. $\endgroup$ – M.A.R. ಠ_ಠ Apr 12 '17 at 13:24

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