L06 Con to Volt 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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1/11 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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2/11 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/ K-mole (or 2.0 cal/ K-mole), 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/V-mole, or 96.5 kjoules/ V-mole). 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 6-fold 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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L06 Con to Volt 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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