Nernst Equation for AP Chemistry

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By — McGraw-Hill Professional
Updated on Feb 9, 2011

Practice problems for these concepts can be found at:

Thus far, all of our calculations have been based on the standard cell potential or standard halfcell potentials—that is, the standard state conditions that were defined previously. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. The actual cell potential, Ecell, can be calculated by the use of the Nernst equation:

where R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday's constant, and Q is the reaction quotient discussed in the Equilibrium chapter. The second form, involving log Q, is the more useful form. If one knows the cell reaction, the concentrations of ions, and E ° cell, then the actual cell potential can be calculated. Another useful application of the Nernst equation is in calculating the concentration of one of the reactants from cell-potential measurements. Knowing the actual cell potential and E °cell allows calculation of Q, the reaction quotient. Knowing Q and all but one of the concentrations allows the calculation of the unknown concentration. Another application of the Nernst equation is in concentration cells. A concentration cell is an electrochemical cell in which the same chemical species is used in both cell co partments, but differing in concentration. Because the half-reactions are the same, E ° cell = 0.00 V. Simply substituting the appropriate concentrations into the reaction quotient allows calculation of the actual cell potential.

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E ° values, and then apply the Nernst equation. If E cell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell), or that the reaction is written backwards if it supposed to be a galvanic cell. If it is supposed to be a galvanic cell, all you need to do is to reverse the overall reaction and change the sign on Ecell to positive. The other method involves using the Nernst equation with the individual half-reactions, then combining them depending on whether or not it is a galvanic cell. The only disadvantage to the second method is that you must use the Nernst equation twice. Either method should lead you to the correct answer.

Let's practice. Calculate the potential of a half-cell containing 0.10 M K2Cr2O7(aq), 0.20 M Cr3+(aq), and 1.0 × 10–4 M H+(aq).


The following half-reaction is given on the AP Exam

Practice problems for these concepts can be found at:

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