The Nernst Equation, formulated by German chemist Walther Nernst, is one of the most important equations in electrochemistry. Electrochemical reactions occur in electrochemical cells: closed loops consisting of two metallic conductors (electrodes) suspended in an aqueous solution called an electrolyte. Electrons are exchanged between the electrodes and the electrolyte. The Nernst Equation allows us to calculate useful information about the electrodes, discussed further below. Expect to find the results very stimulating.
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In simplest terms, the Nernst Equation relates the reduction potential of an electrochemical cell to the system’s electrode potential, temperature, and concentration of chemical species. The reduction potential refers to the tendency of electrons to be exchanged between electrolytes and electrodes in the cell.
The Reaction Quotient is the measurement of amounts of products relative to reactants in an electrochemical reaction. In deriving the Nernst Equation, the natural logarithm of the reaction quotient is multiplied by RT (the Universal gas constant x temperature). However, in order to complete the derivation, RT must be divided by another product (discussed below) so that the resulting reduction potential is in volts.
Faraday’s Constant is denoted as F in the Nernst Equation. This constant is the magnitude of electrical charge per mole of electrons. The product of RT, mentioned above, must be divided by the product of Faraday’s Constant and n, where n is the number of electrons transferred in the cell reaction. With these elements in place the Nernst Equation, in toto, is reproduced below:
E = Eo - (RT/nF)lnQ
Where E is the reduction potential
Eo is the electrode potential.
RT is the universal gas constant x temperature
nF is Faraday’s Constant x the number of electrons
lnQ is the natural logarithm of the reaction quotient.
THE GOLDMAN EQUATION
The Goldman Equation is a “Nernst-like” equation used in biochemistry. The Goldman Equation is specifically used in studying cell membranes. This equation determines the reverse potential across a cell’s membrane. Reverse potential is the difference in electron potential across a cell membrane at which no cells cross the cell membrane.
Closely related to the Nernst Equation, the Butler-Volmer Equation relates the electrode current density to the voltage difference between the electrodes and the electrolyte. When a reaction is at equilibrium, its Butler-Volmer Equation is transformed into the Nernst Equation.
Quizbowl is about learning, not rote memorization, so we encourage you to use this as a springboard for further reading rather than as an endpoint. Here are a few things to check out:
Visit this site for a concise explanation of the Nernst Equation and how it relates to the activities of a galvanic cell.
Walther Nernst contributed more than just his eponymous equation to the world of physical chemistry. Check out some of his other work!
To learn more about cell potentials in neurons, read this brief article.
Watch this video for a quick review of some key terms in electrochemistry:
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