17.4 The nernst equation  (Page 2/6)

Now that the connection has been made between the free energy and cell potentials, nonstandard concentrations follow. Recall that

where Q is the reaction quotient (see the chapter on equilibrium fundamentals). Converting to cell potentials:

This is the Nernst equation    . At standard temperature (298.15 K), it is possible to write the above equations as

If the temperature is not 273.15 K, it is necessary to recalculate the value of the constant. With the Nernst equation, it is possible to calculate the cell potential at nonstandard conditions. This adjustment is necessary because potentials determined under different conditions will have different values.

Finally, we will take a brief look at a special type of cell called a concentration cell    . In a concentration cell, the electrodes are the same material and the half-cells differ only in concentration. Since one or both compartments is not standard, the cell potentials will be unequal; therefore, there will be a potential difference, which can be determined with the aid of the Nernst equation.

Key concepts and summary

Electrical work ( w _ele ) is the negative of the product of the total charge ( Q ) and the cell potential ( E _cell ). The total charge can be calculated as the number of moles of electrons ( n ) times the Faraday constant ( F = 96,485 C/mol e ⁻ ). Electrical work is the maximum work that the system can produce and so is equal to the change in free energy. Thus, anything that can be done with or to a free energy change can also be done to or with a cell potential. The Nernst equation relates the cell potential at nonstandard conditions to the logarithm of the reaction quotient. Concentration cells exploit this relationship and produce a positive cell potential using half-cells that differ only in the concentration of their solutes.

Key equations

• $E_{\text{cell}}^{°}=\frac{RT}{nF}\text{ln}K$
• $E_{\text{cell}}^{°}=\frac{0.02\text{57 V}}{n}\text{ln}K=\frac{0.0\text{592 V}}{n}\text{log}K(\text{at 298.15}K)$
• $E_{\text{cell}}=E_{\text{cell}}^{°}-\frac{RT}{nF}\text{ln}Q\text{(Nernst equation)}$
• $E_{\text{cell}}=E_{\text{cell}}^{°}-\frac{0.02\text{57 V}}{n}\text{ln}Q=E_{\text{cell}}^{°}-\frac{0.05\text{92 V}}{n}\text{log}Q(\text{at 298.15}K)$
• Δ G = − nFE _cell
• $\text{Δ}{G}^{°}=\text{−}nF{E}_{\text{cell}}^{°}$
• $w_{\text{ele}}=w_{\text{max}}=\text{−}nF{E}_{\text{cell}}$

Chemistry end of chapter exercises