March 28, 2017

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for the current density equation (I) , solve for dV/dx when I = 0
I = - [ uz2F[C] dV/dx + uzRT d[C]/dx]

According to your equation.

dV/dx= uzRT/uz2[C] d[C]/dx

I am uncertain what your symbols mean.

It's supposed to be the current density equation I think??
My teacher also gave the form:
I = -(ƒÊ(z^2)F(C))(dv/dt)+ (UZRT d(C)/dx))

C is concentration.
z valence
F Faraday constant
U I am not sure of
R is gas constant
T is temp

and he wanted us to set I to 0 and solve.

also, he wanted us to show how
RT/zF ln (C)out/(C)in ends up to be
58millivolts log10 (C)out/(C)in
with constants:

deg K = absolute T = deg C + 273.16
1 cal = 4.2 Joules
1V = 1Joule/Coulomb
F = Faradaysf Constant (96,480 Coulombs/mol)
R = Gas Constant (1.987 cal / mol degK)
e = elementary electrical charge = 1.602x10-19 C
Avogadrofs Number 6.02x1023 molecules/mole

I am really confused about the ln and log10 and how to get 58

dV/dx= uzRT/uz2[C] d[C]/dx
integrate with respect to x to get
v= uzRT/uz2 ln(C)

μ is mobility of ions in solution in units of cm2v-1s-1

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