Agriculture Reference
In-Depth Information
acidity of the solution is buffered. Electrical neutrality is maintained by the co- and
counter-diffusion of the other cations and anions present. Nye derives equations of
the transfer of protons through the soil as follows.
Consider the balance of acid, HS, between two imaginary planes of unit cross-
section at
x
and
x
+
δx
in the soil. The general reaction of the acids and bases
with the soil may be written
M
+
+
B
−
HB
+
MS
=
HS
+
(
2
.
26
)
where HB is an acid and B
−
its conjugate base. In unit time the increase in HS
will be the result of all reactions of this type and will equal the loss by reaction
of acids HB within the region. This loss must equal the sum of the fluxes of
all acids entering across the plane at
x
less those leaving across the plane at
x
+
δx
.IfM
+
and H
+
do not move in the solid phase, then by analogy with
Equations (2.5) and (2.18),
θ
L
f
L
D
LHB
∂
[HB]
∂x
∂
[HS]
∂t
∂
∂x
=
(
2
.
27
)
where
D
LHB
is the diffusion coefficient of HB in free solution, [HB] is the con-
centration of acid in solution and [HS] is the concentration of acid soil, i.e. of
proton donating groups as measured by the amount of strong base consumed by
unit volume of soil in raising the equilibrium pH to a standard pH. (Since only
differences in [HS] arise it is not necessary to define this pH.)
It is assumed that the impedance factor,
f
L
, is the same for all mobile acids
and bases. It is also assumed that the solid equilibrates rapidly with the adjacent
solution; in cases where it does not, terms for the rates of reaction can be added
to the equation.
The term
∂
[HB]
/∂x
in Equation (2.27) is expressed in terms of
∂
[HS]
/∂x
as
follows. The pH buffer power of each acid-base pair is defined as:
d[B
−
]
dpH
b
HB
=
(
2
.
28
)
However, because in general there is no net flux of component B, d[B
−
]
=
−
d[HB] and
d[HB]
dpH
b
HB
=−
(
2
.
29
)
Likewise the pH buffer power of the soil is
d[HS]
dpH
b
HS
=−
(
2
.
30
)
b
HS
is often fairly constant over a wide range of pH.
