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Ref. No. [UMCES] CBL 2015-010
ACT VS15-03
pH SCALES
Four pH scales are commonly used to describe the acidity of an aqueous solution: (1) the
free hydrogen ion concentration scale, (2) the total hydrogen ion concentration scale, (3) an H
+
concentration scale termed the ‘seawater scale’ that is numerically quite similar to the total
hydrogen ion concentration scale, and a fourth pH scale that is expressed in terms of an ‘apparent
activity’. The relationship between the apparent activity scale and the other three scales is not
thermodynamically well defined.
The free hydrogen ion concentration scale is expressed as pH = -log[H
+
], where [H
+
]
indicates the concentration of a free hydrated hydrogen ion. The total scale (pH
T
) is written as
pH
T
= -log[H+]
T
where [H
+
]
T
≈ [H
+
] + [HSO
4
-
], and the seawater scale pH (pHsws) is written as
pHsws = -log[H
+
]
sws
where [H
+
]
sws
≈ [H
+
] + [HSO
4
-
] + [HF
o
].
The various pH scales are inter-related by the following equations:
a
H
= 10
-pH(NBS)
=
f
H
* [H
+
]/(1 mol/kg), and (1)
[H
+
] = [H
+
]
tot
/ (1 +
T
S/K
SO4
) = [H
+
]
sws
/ (1 +
T
S/K
HSO4
+
T
F/K
HF
) (2)
Where:
a
H
is an apparent activity,
f
H
is an apparent activity coefficient for the H
+
ion,
T
S and
T
F
are total concentrations of SO
4
2-
and fluoride ions in seawater, and K
HSO4
and K
HF
are HSO
4
-
and
HF
o
dissociation constants in seawater.
Because electrodes transferred between dilute buffers (e.g., NBS buffers) and
concentrated electrolytes (such as seawater) are subject to variations in the liquid junction
potentials of reference electrodes (an effect whose magnitude is generally specific to a particular
electrode), the
f
H
proportionality factor that relates the apparent activity scale to concentration
scales is, in part, influenced by factors that are not strictly thermodynamic. Consequently, use of
the apparent activity scale is generally discouraged for measurements in seawater.
Relationships between the different concentration scales depend on temperature, salinity,
and pressure. At 25°C, salinity 35, and 1 atm, relationships between seawater scale, total scale
and free scale pH (pH
sws
, pH
T
and pH) are given approximately as
pH minus pH
T
= 0.108 (4)
pH
T
minus pH
sws
= 0.008 (5)
pH
NBS
minus pH
sws
≈ 0.13 (6)
Equation (4) was derived using the K
SO4
characteristics given in DOE (1994). Alternative
descriptions of the HSO
4
-
dissociation equilibrium can produce significant variations in the offset
between total scale and free scale pH. Determinations of K
F
in seawater are sufficiently coherent
that deviations from the relationship given in eqn. (5) are quite small. The relationship between
pH
NBS
and pH
sws
(eqn. 6) is based on the discussion of Culberson (1981). It is important to note
that
f
H
, and therefore eqn. (6), is electrode-dependent. Measurements of
a
H
on the NBS scale are
expressed in terms of mol/kg-H
2
O, while the other scales express concentrations in terms of
mol/kg
(SW)
.
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