Agriculture Reference
In-Depth Information
Consider a two-phase system with components AY and BY in which some of
the BY(s) becomes dissolved in AY(s): BY is the solute and AY the solvent. If
the resulting solid solution is homogeneous, that is, it contains no concentration
gradient, the equilibrium distribution of A and B between the liquid and solid is
AY ( s ) + B + = BY ( s ) + A +
( 3 . 48 )
and the equilibrium constant is
(BY(s)) ( A + )
(AY(s)) ( B + ) =
X BY f BY ( A + )
X AY f AY ( B + ) =
K SP ( AY )
K SP ( BY ) = K
( 3 . 49 )
where the ratio of the activities of the solids is replaced by the ratio of the mole
fractions [ X AY = n AY /(n AY + n BY ) and X BY = n BY /(n AY + n BY ) ] multiplied by
activity coefficients, and K SP ( AY ) and K SP ( BY ) are the solubility products of pure
AY and BY. Pure AY and BY are the 'end members' of the solid solution series.
This equation shows that the dissolution of BY in solid AY is a function of:
(a) the ratio of the solubility products of AY and BY ( K );
(b) the solution composition with respect to A + and B + ;
(c) a solid solution factor equal to the ratio of the activity coefficients of the
solid solution components (f AY /f BY ) .
Assuming as a first approximation f AY /f BY = 1 (an ideal solid solution) and
that the activity ratio of the species in solution can be replaced by the concen-
tration ratio, then
X AY = K [B + ]
X BY
( 3 . 50 )
[A + ]
As an example, consider a solid solution of 5% ZnCO 3 in MgCO 3 (95%) in
equilibrium with Mg 2 + , Zn 2 + and [CO 3 2 ]
10 5 M (realistic conditions for
=
many submerged soils). We have
10 7 . 46
10 10 . 0
K SP ( MgCO 3 )
K =
K SP ( ZnCO 3 ) =
=
347
Assuming the solubility of MgCO 3 is little altered, then [Mg 2 + ]
10 3 M
=
3 . 47
×
and from Equation (3.49)
[Zn 2 + ] = [Mg 2 + ] 1
K
X ZnCO 3
X MgCO 3 = 5 . 26 × 10 7 M
This compares with [Zn 2 + ] = 10 5 M for equilibrium with pure ZnCO 3 .
If K is very large or small, the solid solution cannot be homogeneous because
A or B will be selectively scavenged from the liquid as the solid precipitates. In
this case A or B will be occluded within the solid and will only be desorbed back
into solution very slowly. This mechanism provides a means by which toxic or
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