Geoscience Reference
In-Depth Information
the process. Let
be the concentration of active sites capable of hosting the adsorbing
species per unit area of the solid surface. To the first order, the rate of desorption
R
des
is
proportional to the proportion of the occupied sites:
σ
R
des
=
k
des
θσ
(5.25)
where
k
des
is the rate constant. Likewise, the rate of adsorption
R
ads
is proportional to the
proportion of free sites and to the pressure of species
i
:
R
ads
=
k
ads
(
1
−
θ) σ
P
i
(5.26)
At equilibrium, these two rates are equal and we get:
1
θ
k
des
k
ads
P
i
=
1
+
(5.27)
which is the famous Langmuir “isotherm,” a name by which it is implied that both the
rate constants and pressure are temperature dependent. The parameter
is the ratio of the
volume
V
of adsorbed material to the volume
V
0
corresponding to a continuous single
layer and therefore:
θ
1
V
=
1
V
0
+
k
des
k
ads
V
0
P
i
(5.28)
By plotting the inverse of the volume
V
of species adsorbed as a function of 1
P
i
, the zero
intercept gives the volume
V
0
of the monolayer. Dividing
V
0
by the footprint (cross-section)
of the adsorbed species gives us the surface area of the solid. For adsorption in liquids, pres-
sures should be replaced by concentrations. An equivalent isotherm exists that accounts for
multilayer coverage and is known by the initials BET of its discoverers (Brunauer, Emmett,
and Teller). Isotherms are routinely used to determine the “surface area” of various solids
of geochemical interest: if for crystalline silicates, such as quartz or feldspars, the adsorp-
tion recovers values similar to those inferred from their geometry, the enormous surface
area obtained for iron hydroxides (600 m
2
g
−
1
) attests to the fact that the surface of these
solids is made of a myriad of nanoscale embayments and protrusions, which make them
the prime scavengers of the sea.
/
Exercises
1. Which of these properties are conservative: total energy, kinetic energy, tempera-
ture, velocity, moles of iron content, moles of ferric iron, concentration of iron, pH,
alkalinity?
2. At a given locality at the bottom of the ocean, the rate of sedimentation is 10 mm ky
−
1
.
The density of the surface sediment is 2.0 g cm
−
3
and its phosphorus content is 0.65
wt%. What is the sedimentary (advection) flux of phosphorus in kg P m
−
2
My
−
1
?
3. Explain why, during exhumation of mountain ranges, minerals should be treated as
“Lagrangian” bodies.
