Debye length setting when electrolyte containing bivalent ion

[Julyjing]

According to the Debye length formula, Debye length is related to concentration and valence of ion. May I ask if 1M H2SO4 electrolyte should be expressed as 2M monovalent cation and 1M bivalent anion?

[rhennig]

Dear Julyjing,

For multivalent electrolyte solutions, the Debye length is given by

\kappa\mathrm{D}^{-1} = \sqrt \frac{\epsilon k\mathrm{B} T}{e^2\sum_i{Z_i n_i^b}}

Where Z_i is the valence of the ions in the electrolyte and n_i^b there bulk concentrations. Based on this square root dependence you can determine how the Debye length changes with ionic concentration and their valence.

Best wishes, Richard

— Richard G. Hennig Professor, Materials Science and Engineering, University of Florida Associate Director, Quantum Theory Project, University of Florida Adjunct Professor, Materials Science and Engineering, Cornell University Email: rhennig@ufl.edumailto:rhennig@ufl.edu Web: http://hennig.mse.ufl.eduhttp://hennig.mse.ufl.edu/

On April 14, 2019 at 11:28:23 PM, Julyjing (notifications@github.commailto:notifications@github.com) wrote:

According to the Debye length formula, Debye length is related to concentration and valence of ion. May I ask if 1M H2SO4 electrolyte should be expressed as 2M monovalent cation and 1M bivalent anion?

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[xnmao]

Dear @rhennig,

I have a similar work. I tried to get the the Debye length 3.04 Å of 1M electrolyte following $ \kappa\mathrm{D}^{-1} = \sqrt \frac{\epsilon k\mathrm{B} T}{e^2\sum_i{Z_i n_i^b}} $

epsilon = 78.4
kB = 1.38e-23
T = 298.15
e = 1.60e-19
sumi_Zi_nib = 1*1 + 1*1

kappaD = 1 / (epsilon*kB*T/(e**2*sumi_Zi_nib))**0.5 # 3.9840061403095744e-10, not 3.04

What is wrong with that? Can you fix it? Thank you!

[ericfonseca95]

Hello Xnmao,

Here is the calculation worked out:

charge_electron = e = 1.6022 E-19 Coulombs T = 298.15 Kelvin K_b = 1.3802 E-23Joules / Kelvin epsilon_0 = 8.85 E-12 Farads/Meter epsilon_r = 78.4 epsilon = epsilon_0 epsilon_r = 6.94 E -10 Debye_Length (Gouy-Chapman theory) = [ (epsilon k_b T ) / ( 2 e^2 z^2 c_i0) ] ^ (1/2)

For a monovalent salt in water, z_i = 1, and c_i0 (bulk concentration of salt) = 1 Mol / Liter = 6.022 E+26 particles/m^3. Plugging in:

Debye_Length = [ (6.94 E -10 1.38 E-23 298 ) / (2 1.602 E-19 ^ 2 1.0^2 * 6.022 E +26)] ^ 1/2 Debye_Length = 3.04 E -10 Meters = 3.04 Angstroms

Hope this helps,

Eric Fonseca

[xnmao]

Cool. It works. Thank you for your help! @ericfonseca95