Calculation of ion flux across potential barrier

[a b]

Hello!
As far as I know, the Eyring equation is used to calculate the speed of a reaction:

$$k=\frac{{k}_{b}}{h} {e}^{\frac{-\Delta G}{RT}}$$

In my course the teacher used this formula to calculate the flux of a species of ions across a barrier of potential, but I didn't understand very much.

Let's suppose that I have two aqueous solutions of the same species of ions (just 1 species) connected by a ion channel where the potential barrier is, and that I know:

The shape of the barrier of electrochemical potential (for example a gaussian curve or two gaussian curves side by side (but maybe these are two barriers));

The width of the barrier in space, that is the length of the ion channel;

Its peak value,and the values at the borders with the ionic solutions;

The concentrations of the ions in each side of the barrier;


Can you explain me how to calculate the ion flux, briefly, but explaining the steps you do?
Thank you

 

[jbsteele]

very much!The Eyring equation can be used to calculate the rate of transport across the barrier. To do this, you'll need to calculate the activation energy for the reaction. This involves subtracting the peak value of the potential barrier from the values at either side of the barrier, and then multiplying by the width of the barrier. Once you have the activation energy, you can use the Eyring equation to calculate the rate of transport across the barrier:k = \frac{{k}_{b}}{h} {e}^{\frac{-\Delta G}{RT}} where k is the rate of transport, k_b is the Boltzmann constant, h is the Planck constant, e is the base of natural logarithms, Delta G is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This calculation will give you the rate of transport (i.e. flux) across the barrier.