Mass conservation and elemental fractionation - Geochemistry: An Introduction - page 23

2. What is the chemical composition of a sediment for which the composition and
abundance of the clay and quartz fragments are known?
3. A certain percentage of olivine of known composition precipitates from a basalt lava.
What is the composition of the residual melt?

All three questions draw on the same principle: the whole is the sum of its parts. The ele-
ments of the river downstream are a combination of all of the upstream elements; the rock
combines all of the elements present in the minerals; the parent basalt can be reconstructed
by reincorporating the olivine in the residual lava. This principle is perfectly applicable,
provided simply that all the components forming the aggregate system have been identified
for certain. It is applicable whether the initial components have lost their physical identity
during mixing (case 1) or whether their identity has been preserved, as in sand (case 2).
Let us try to determine the silicon content of the sediment in Question 2. We have a mass
M sed of sediment composed exclusively of M clay kilograms of clay and M qz kilograms of
quartz. The concentration of silicon in the clay fraction is C Si

clay , that of the quartz fraction

C Si

qz , and that of the total sediment C Si

sed . The applicable conservation equations are first that

of the total mass of material:

M sed = M clay +

M qz (2.1)

and that of silicon:

M sed C Si M clay C Si M qz C Si

sed = clay +

(2.2)

qz

Dividing (2.2) by ( 2.1) yields:
C Si

clay + 1

f clay C Si

f clay C Si

sed =

− (2.3)

qz

where the weight fraction, M sed , of the clay component is shown. Notice

that the conservation of mass has been written in the trivial form f clay +

f clay = M clay /

f qz = 1. A similar

expression may be obtained for each element, e.g. for aluminum:
C Al

clay + 1

f clay C Al

f clay C Al

sed =

− (2.4)

qz

Subtracting the concentration of each corresponding element in the quartz from both sides
of (2.3) and (2.4) and dividing one by the other gives a single equation no longer dependent
on f clay . This indicates that in a C Al

sed diagram ( Fig. 2.1 ) , the silicon and aluminum
concentrations of sediments obtained by varying the proportion of quartz and clay form
a straight line (mixing line) through the points representing the compositions of the two
components. A mixture like this with linear properties is said to be conservative.
More generally, we are interested in a component j of mass M j and an element i whose
concentration in the component j is C i j . Here, i might refer to silicon and j to,say,the
clay content of the sediment. The properties of the entire system, here the sediment, can be
denoted by index 0, and the conservation equations can be written in the form:

sed , C Si

f j = 1 (2.5)

j

C 0 = f j C j (2.6)

j