Biomedical Engineering Reference
In-Depth Information
where
ΔΦ
hc
,0
is the half-cell potential under standard conditions (25
°
C and 1 atm)
and
represents activity (i.e., ideal thermodynamic concentrations of oxidized and
reduced states). In dilute solutions, activity is nearly equal to concentration. How-
ever, activity is smaller than concentration in concentrated solutions due to inter-
molecular effects. Often the reduced state is a metal in which case
α
α
M
is a constant
equaling to 1. It is more convenient to consider concentrations rather than activi-
ties. These parameters are related by the activity coefficient,
γ
,
αγ
=
C
Ox
Ox
Ox
The Nernst equation is therefore rewritten as
C
RT
nF
'
ΔΦ
= ΔΦ
+
ln
Ox
(9.2)
hc
hc
,0
C
Red
where
ΔΦ′
hc
,0
is the formal potential and is related to the standard potential by the
equation:
γ
γ
RT
nF
'
ΔΦ
= ΔΦ
+
ln
Ox
hc
,0
hc
,0
Red
Equation (9.2) relates the concentration of the electrolyte to the electrical po-
tential. One could calculate the unknown concentration of the electrolyte know-
ing the potential. However, half cell potentials cannot be measured because the
connection between the electrolyte and one terminal of the potential measuring
device cannot be completed. Hence, the potential difference is measured between
the half-cell potential of the electrode and a second electrode called the reference
electrode. The reference electrode refers to an electrode that provides a particular
reference voltage for measurements recorded from the working electrode. The half-
cell potential of the normal hydrogen electrode (NHE) is used as the reference elec-
trode. NHE consisting of a platinum wire dipped into hydrochloric acid (1.18M
corresponding to unit activity of H
) solution and acts as the electrode over which
hydrogen gas (1 atm pressure at 25°C) is bubbled. The reaction is represented as
+
+
−
Hg
2
()
↔+
2
Haq
( ) 2
e
The two electrodes are connected internally by means of an electrically (Figure
9.3) conducting bridge (called a salt bridge) and externally to a voltmeter. When
the reference electrode potential is incorporated, the net potential of the cell is
ΔΦ
= ΔΦ
− ΔΦ
− ΔΦ
cell
hc
ref
LJ
ΔΦ
LJ
is the liquid junction potential. One aspect that is often overlooked is
the variation of the reference electrode potential with temperature. For example,
the half-cell potential of the silver/silver chloride at 25°C is
where
+
0.222V versus NHE.
