Physical Chemistry , 1st ed.

The relationship between Eand the reaction quotient Qhas a practical use
in modern analytical chemistry. Consider the standard reduction reaction for
hydrogen:

2H^ (aq) 2e^ →H 2 (g)

Its defined E° is zero, but at nonstandard conditions of concentration,Efor
this half-reaction will be determined by the Nernst equation. We will have,
since E° is zero:

E



R

2 F

T

ln Q



R

2 F

T

ln 

(a

f

H

H

2

)^2

 

R

2 F

T

ln 

[H

pH

2

]^2



Assume we are working at standard pressure so that pH 2 1 bar. Further, using
the definition of pH 
log[H^ ] 
2.3^1  03 ln [H^ ] and the properties of loga-
rithms, we can rearrange the equation for Eusing these expressions and get

E

2.303 

R

F

T

pH (8.33)

At the common reference temperature of 25.0°C, the expression 2.303 (RT/F)
equals 0.05916 V. Equation 8.33 can be rewritten as

E

0.05916 pH volts (8.34)

Thus, the reduction potential of the hydrogen electrode is directly related to
the pH of the solution. What this means is that we can use the hydrogen elec-
trode, coupled with any other half-reaction, to determine the pH of a solution.
The voltage of the electrochemical cell that is made by the proper combination
of such half-cells is given by the combination of the two Evalues of the reac-
tions. Therefore,

E( 0.05916 V pH) E° (other half-reaction) (8.35)

where each term on the right has units of V. The value of “E° (other half-
reaction)” depends, of course, on what that reaction is as well as whether it is
an oxidation reaction or a reduction reaction. The point is that the voltage of
such cells can easily be measured and the pH of the solution determined us-
ing electrochemical means.
Because hydrogen electrodes are cumbersome, other electrodes are typically
used to measure pH. All of them use similar electrochemical principles and a
measurement of a voltage to determine the pH of a solution of interest. The
most well known is the glass pH electrode,Figure 8.7. A porous glass tube has
a certain buffer solution and a silver/silver chloride electrode. The Ag/AgCl
half-reaction is

AgCl (s) e^ →Ag (s) Cl^ E°0.22233 V

The buffer solution in the electrode is set so that E0 when the pH is about
7, and the electronics that monitor the voltage of the electrode can be adjusted
to calibrate the system so that E0 at pH 7.00 exactly. Such electrodes are
common in laboratories around the world.
The hydrogen ion is not special when it comes to electrochemical measure-
ment of this type. Virtually every ionic species can take part in oxidation-
reduction reactions, so the concentration of virtually any ion can be detected
with a similar electrode. These ion-specific electrodeshave some half-reaction
inside and, across a porous glass shell, set up an electrochemical cell whose
voltage can be measured and used to “back-calculate” the concentration of a

8.5 Nonstandard Potentials and Equilibrium Constants 223