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COPYRIGHT
Prof. Beyenbach
Mammalian Physiology BIOAP 4580
2011
THE NERNST EQUATION
CONCENTRATION DIFFERENCES TO VOLTAGES
1) How a concentration difference can generate a voltage.
Under certain conditions, a
concentration difference can give rise to a voltage difference.
Under other conditions, a
voltage can give rise to a concentration difference (electrophoresis, electroplating).
The
chemical potential ∆[
] giving rise to an electrical potential ∆V is considered first in these
pages (where V is voltage).
a) A concentration difference can give rise to a voltage.
Consider the condition depicted in
Fig. 1.
Compartments 1 and 2 are separated by a membrane that is selectively permeable
to K
+
which means that the membrane is permeable to K
+
only. Since the K
+
concentration in compartment 1 is greater than in compartment 2, K
+
will want to diffuse
into compartment 2.
Fig. 1.
Diffusion of K
+
across a K
+
selective membrane.
The membrane is K
+

selective because it allows the passage of K
+
only.
The passage of Cl

is prohibited.
Cl

is “reflected” back.
Note that the diffusion of K
+
from compartment 1 to 2 moves
charge across the membrane, generating a voltage, but only at the surface of the
membrane.
Since the diffusion of K
+
carries positive electrical charge, the membrane surface facing
compartment 2 gains positive charge, and the membrane surface facing compartment 1
loses positive charge.
As a result a voltage difference is generated across the membrane,
positive on the surface of the membrane facing compartment 2, and negative on the
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surface of the membrane facing compartment 1.
The voltage thus developed opposes the
further diffusion of K
+
into compartment 2.
Eventually, the chemical force driving K
+
from compartment 1 to 2, i.e. the ∆[
] is equal to the electrical potential, ∆V, holding K
+
back.
At this point, K
+
is at electrochemical equilibrium; there is no net movement of K
+
across the membrane.
This equilibrium situation is described and quantified by the
Nernst equation which equates a voltage with a concentration difference.
(eq. 1)
where R is the gas constant 8.3 joules/
Kmole (or 2.0 cal/
Kmole), T is the temperature
in
K, z is the valence of the ion (no units), and F is the Faraday constant (96,485.3
coul/mole, or 23.1 kcal/Vmole, or 96.5 kjoules/ Vmole).
The important point is that in
the case of a K
+
selective membrane, the K
+
concentration difference is equivalent to a
voltage – i.e. no more than the conversion of one force into another force.
For the particular case depicted in Fig. 1, equation 1 yields
(eq. 2)
Accordingly, a 6fold concentration difference of a monovalent cation is equivalent to an
electrical force of 47.8 mV provided the membrane (barrier) is as exclusively
permselective to K
+
as the membrane shown in Fig. 1.
Since this voltage occurs under
the unique condition of ideal permselectivity to one ionic species only (Fig. 1), and since
a true equilibrium occurs between concentration and voltage, this type of voltage bears
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 Spring '11
 BEYENBACH,K.
 Electric charge, EQ, Concentration difference

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