Concise Physical Chemistry

c14 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

CONCENTRATION CELLS 225

or

E=E◦−

RT

nF

lnQ

which is theNernst equation. At 298 K,RTandFcan be combined to find

E=E◦−

0. 0257

n

lnQ

The meanings ofGandG◦enable us to better understandEandE◦.As

Gis the free energy change for any arbitrary equilibrium quotientQ,Erepresents

the potential obtained from a cell under these arbitrary conditions. If the reactants

and products are all in their standard states, the difference in free energy between

reactants and products isG◦. HenceE◦represents the potential of a cell in which

the reactants and products in the redox reaction are in their standard states and at unit

activity. This is just the cell potential from a table of standard half-cell potentials.

Knowing the concentrations of the constituents of any cell not at unit activity, one

can calculateE◦from the table and correct it to find the actual cell potential using

the Nernst equation. For example, if the activities in the electrode reaction are

Cu(s)+2Ag+(aq, 0 .01 m)→Cu^2 +(aq, 0 .1m)+Ag(s)

the equilibrium quotient isQ=Cu^2 +(aq, 0 .1m)/Ag+(aq, 0 .01 m)^2 = 0. 1 / 0. 012 =

1000. Thestandardcell potential isE◦= 0. 799 −(0.337)= 0 .462. Applying the
      Nernst equation withn=2, we obtain

E=E◦−

0. 0257

n

lnQ= 0. 462 − 0 .0128(6.908)= 0 .373 volts

Much of the older literature uses the logarithm to the base 10 in the Nernst equation.

Conversion from ln to log 10 requires multiplication of the lnQterm by 2.303 to yield

E=E◦−

0. 0257

n

lnQ=E◦−

2. 303 ( 0. 0257 )

n

logQ

= 0. 462 −

0. 0592

2

3 = 0 .343 volts

All of this assumes ideal behavior of course, as well as thata=mthroughout. We

should be skeptical. More about this later.

14.7 CONCENTRATION CELLS

The Nernst equation suggests that we can have an electrochemical cell with half-

cells that are identical in every way except for the concentrations of the ions in