## Very Lost

$E_{cell} = E_{cell}^{\circ}-\frac{RT}{nF}\ln Q$

JuliaPark2H
Posts: 19
Joined: Fri Sep 25, 2015 3:00 am

### Very Lost

Can someone summarize or explain in lay terms/easily understood how the Nernst equation works, real-life application wise AND what the equation symbolizes as it relates electric potential and concentration? :(

Chem_Mod
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### Re: Very Lost

We learned earlier that we can calculate a nonstandard Gibbs Free Energy through the equation $\Delta G=\Delta G^{o}+RTlnQ$. As we know that $\Delta G=-nFE$, we just made the substitution into the equation to arrive at the Nernst equation.

What the Nernst equation tells us is that at nonstandard conditions (i.e. the concentrations of both the reactant and products are not 1M), the cell potential will shift from the standard cell potential calculated from Ecathode-Eanode. As we can see in the equation, increasing the products (remember that $Q=\frac{[Products]}{[Reactants]}$) will increase the $RTlnQ$ term, resulting in the cell potential decreasing from the standard value. Similarly, increasing the reactant concentration decreases $RTlnQ$, resulting in the cell potential increasing from the standard potential.

We can frame the standard potentials in terms of Le Chatelier's principle. First consider this: voltage is analogous to electrical force. The higher the cell potential (measured in voltages) the more "force" there is to drive the reaction forward. Note that the cell potential is positive in this case. So when our Q increases due to product formation, according to Le Chatelier's principle, the system will react to form more reactant to bring the system back towards equilibrium. Looking at how an increase in Q affects the cell potential E, we see that the cell potential decreases as Q increases. This makes sense because now there is less "force" driving the reaction forward to produce the product as we would expect when considering Le Chatelier's principle under which we would say that the reaction is "less favored". Conceptually they are the same idea.

Real life examples are aplenty but what you should know is that the Nernst equation is going to be used in every biological process because of non standard conditions i.e. the concentrations of ions are not the same across a cell membrane. In neuroscience, the Nernst equation is used to determine the electric force of an ion gradient. Neurons have different concentrations of ions inside compared to outside. Take for example sodium which has a high concentration outside of the cell but low concentration inside at rest. We expect sodium to flow inward due to a concentration difference. However, we do not have a standard potential $E^{o}_{cell}$ because there is no redox reaction when sodium flows inward. However, because there is a concentration gradient, there is electrical force E which we can calculate by setting $E^{o}_{cell}$ to 0 (because Na+->Na+ is not a redox reaction). We consider the sodium inside sodium concentration to be the "product" because that is direction it will flow to due to the concentration gradient; consequently, we consider outside sodium to be the "reactant". Therefore we can setup an equation for the electrical force $E_{cell}=-\frac{RT}{ZF}ln\frac{[Sodium inside]}{[Sodium outside]}$. In neuroscience, we call the magnitude of this value to be the equilibrium potential or the electrical force needed to resist the force produced by the difference in concentration.

JuliaPark2H
Posts: 19
Joined: Fri Sep 25, 2015 3:00 am

### Re: Very Lost

I think I understand a lot more than when I posted this; thank you very much for the clear and extensive explanation!

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