The Effect of Concentration on Cell Potential

So far, we ve considered cells with all components in their standard states. But most cells don t start at those conditions, and even if they did, the concentrations change after a few moments of operation. Moreover, in all practical voltaic cells, such as batteries, reactant concentrations are far from standard-state values. Clearly, we must be able to determine Ecc h the cell potential under nonstandard conditions. 

To do so, let s derive an expression for the relation between cell potential and concentration based on the relation between free energy and concentration. Recall from Chapter 20 (Equation 20.13) that AG equals AG° (the free energy change when the system moves from standard-state concentrations to equilibrium) plus RT In Q (the free energy change when the system moves from nonstandard-state to standard-state concentrations)  

Dividing both sides by -nF, we obtain the Nernst equation, developed by the German chemist Walther Hermann Nernst in 1889  

The Nernst equation says that a cell potential under any conditions depends on the potential at standard-state concentrations and a term for the potential at nonstandard-state concentrations. How do changes in Q affect cell potential From Equation 21.9, we see that 

As before, to obtain a simplified form of the Nernst equation for use in cal- 

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In Chapter 20, we discussed the relationship of useful work, free energy, and the equilibrium constant. In this section, we examine this relationship in the context of electrochemical cells and see the effect of concentration on cell potential. 

The Nernst equation, expressing the effect of concentration on cell potential... 

The Nernst equation has also been introduced in Chapter 20 to give a quantitative explanation of the effect of concentration on the value of electrode potential for a given half-cell. 

We will now look at the effects of Ej on thermodynamic calculations, and then decide on the various methods that can be used to minimize them. One of the most common reasons for performing a calculation with an electrochemical cell is to determine the concentration or activity of an ion. In order to carry out such a calculation, we would first construct a cell, and then, knowing the potential of the reference electrode, we would determine the half-cell potential, i.e. the electrode potential E of interest, and then apply the Nemst equation. 

The effects of digitalis on the electrical properties of the heart are a mixture of direct and autonomic actions. Direct actions on the membranes of cardiac cells follow a well-defined progression an early, brief prolongation of the action potential, followed by shortening (especially the plateau phase). The decrease in action potential duration is probably the result of increased potassium conductance that is caused by increased intracellular calcium (see Chapter 14). All these effects can be observed at therapeutic concentrations in the absence of overt toxicity (Table 13-2). 

Shen and Crain [13] tested the effects of biphalin on naive and chronic morphine-treated dorsal root ganglion (DRG) neurons in cell culture. At low (pM-nM) concentrations, most mu, delta, or kappa opioid peptides as well as morphine and other opioid alkaloids elicit dose-dependent excitatory prolongation of the calcium-dependent component of the action potential duration (APD) of many mouse sensory DRG neurons. In contrast, application of the same opioids at higher (pM) concentrations results in inhibitory shortening of the APD [14]. Biphalin at a low concentration elicits only dose-... 

In real cells, multiple transmembrane pumps and channels maintain and regulate the transmembrane potential. Furthermore, those processes are at best only in a quasi-steady state, not truly at equilibrium. Thus, electrophoresis of an ionic solute across a membrane may be a passive equilibrative diffusion process in itself, but is effectively an active and concentra-tive process when the cell is considered as a whole. Other factors that influence transport across membranes include pH gradients, differences in binding, and coupled reactions that convert the transported substrate into another chemical form. In each case, transport is governed by the concentration of free and permeable substrate available in each compartment. The effect of pH on transport will depend on whether the permeant species is the protonated form (e.g., acids) or the unprotonated form (e.g., bases), on the pfQ of the compound, and on the pH in each compartment. The effects can be predicted with reference to the Henderson-Hasselbach equation (Equation 14.2), which states that the ratio of acid and base forms changes by a factor of 10 for each unit change in either pH or pfCt ... 

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