5 Steps to a 5 AP Chemistry

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

lated by:

Let’s apply these relationships. Determine ΔG°and Kfor the following reaction:

Answer:

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

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

memorize it.

The first answer is:

The second answer is:

This gives a Kof 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:

where Ris the ideal gas constant, Tis the Kelvin temperature, nis 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°cellallows 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 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 calcu-

lation 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,

EE

RT

nF

QE

cell cell cell n

=°−

⎛

⎝

⎜

⎞

⎠

⎟ =°−

⎛

⎝

⎜

⎞

⎠

ln ⎟

0 0592.

ll o gQat C 25°

log

.

(. )

.

K.

nE

=

°

cell ==

V

V

0 0592 V

2105

0 0592

35 5

ΔGnFE°=− ° =−cell 2 96 500(, J/V)(. ) .1 05V =− ×2 03 10^5 J

Ni s()+→+°= 21 Ag a q++()Ni^2 () ()a q Ag s E cell. 05 V

E

n

KK

nE

°= =

°

cell

V or cell

V

0 0592

0 0592

.

log log

.

Electrochemistry  249