Bulk concentration and concentration gradient

[Soti]

I have a membrane with a eutectic carbonate mixture and there is also OH- in the melt.
I want to calculate the conductivity of the OH- using the diffusivity of OH- and the bulk concentration.
How can I calculate the bulk concentration if I know that there is a concentration gradient of OH- and the concentration at the 2 surfaces?

 

[Zefram]

To calculate the bulk concentration of OH- in the eutectic carbonate mixture, you will need to know the concentration gradient of OH- and the concentration at the two surfaces. This information can be obtained through experimental measurements or by using mathematical models.

Once you have the concentration gradient and the surface concentrations, you can use Fick's first law of diffusion to calculate the diffusivity of OH-. This law states that the flux of a substance is proportional to its concentration gradient and the diffusivity of the substance.

Next, you will need to use the Nernst-Planck equation, which takes into account the effects of electrochemical potential, to calculate the conductivity of OH-. This equation is given by σ = D * N * q * μ, where σ is the conductivity, D is the diffusivity, N is the number of ions, q is the charge of the ion, and μ is the mobility of the ion.

To calculate the bulk concentration of OH-, you can rearrange the Nernst-Planck equation to solve for N, which is the number of ions. Then, use the formula for molar concentration (c = n/V) to calculate the bulk concentration, where n is the number of moles and V is the volume of the mixture.

It is important to note that the bulk concentration of OH- may not be constant throughout the mixture, as it can be affected by factors such as temperature and pressure. Therefore, it is recommended to take multiple measurements at different points in the mixture and calculate an average bulk concentration.

In summary, to calculate the bulk concentration of OH- in a eutectic carbonate mixture, you will need to measure the concentration gradient and surface concentrations, use Fick's law and the Nernst-Planck equation, and take into account any variations in temperature and pressure.