5 Steps to a 5 AP Chemistry 2019

Electrochemistry ❮ 251

If the redox reaction is at equilibrium, E° = 0, the equilibrium constant may be cal-

culated by:

E

n

KK

0.0592V nE

logorlog

cell 0.0592V

°= = °cell

Let’s apply these relationships. Determine DG° and K for the following reaction:

Ni(s) 2Ag(aq)N+→++i(aq)Ag(s) ^2 +°Ecell=1.05V

Answer:

For this reaction, two electrons are transferred from the Ni to the Ag. Thus, n is 2 for

this reaction. The value of F (96,500 J/V mol) is given on the exam, so you will not need

to memorize it.

The first answer is:

∆°Gn=−FE°=cell −=2(96,500 J/Vmol)(1.05V) −×2.03 10 J/mol^5

The second answer is:

K

nE

log

0.0592V

2(1.05 V)

0.0592V

= cell 35.5

°

==

This gives a K of about 10^35 (actually K = 3 × 1035 ). In many cases, the approximate value

will be all you need for the AP exam.

Nernst Equation

Thus far, all of our calculations have been based on the standard cell potential or

standard half-cell 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:

=−











 =−











EE°° °

RT

nF

QE

n

ln Q

0.0592

cell cell cell logat25C

where R is the ideal gas constant, T is the Kelvin temperature, n is the number of elec-

trons 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 elec-

trochemical cell in which the same chemical species is used in both cell compartments,

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 calcula-

tion of the actual cell potential.

ENRICHMENT