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168 5 SIMPLEMIXTURES
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
2.0
4.0
6.0
ν
(ν
/[
EB
] o
ut
)/
(µ
M
−1
)
Figure 5.37
I5.8 �e dissolution of the protein according to the given equilibrium is described
by a solubility constant Ks
PXv(s)ÐÐ⇀↽ÐÐ Pv+(aq) + v X−(aq) Ks = aPavX
where the solubility constant is written in terms of the activities. Introducing
the activity coe�cients and molalities, b, gives
Ks = γv+1± bPbvX
At low tomoderate ionic strengths theDebye–Hückel limiting law, [5F.27–188],
log γ± = −A∣z−z+∣I1/2, is a reasonable approximation for the activity coe�-
cients.
Addition of a salt, such as (NH4)2SO4, causes I to increase, log γ± to become
more negative, and hence γ± to decrease. However, Ks is an equilibrium con-
stant and remains unchanged.�erefore, the molality of Pv+ increases and the
protein solubility increases proportionately.
�is e�ect is also explicable in terms of Le Chatelier’s principle. As the ionic
strength increases by the addition of an inert electrolyte such as (NH4)2SO4,
the ions of the protein that are in solution attract one another less strongly, so
that the equilibrium is shi�ed in the direction of increased solubility.
�e explanation of the salting out e�ect is somewhat more complicated and
can be related to the failure the Debye–Hückel limiting law at higher ionic
strengths. At high ionic strengths the Davies equation, [5F.30b–189], is a better
approximation
log γ± =
−A ∣z+z−∣ I1/2
1 + BI1/2
+ CI
At low concentrations of inert salt, I1/2 > I, the �rst term dominates, γ± de-
creases with increasing I, and salting in occurs; however, at high concentra-
tions, I > I1/2, the second term dominates, γ± increases with increasing I, and
salting out occurs. �e Le Chatelier’s principle explanation is that the water
molecules are tied up by ion-dipole interactions and become unavailable for
solvating the protein, thereby leading to decreased solubility.