# Relationship of ionic strength and solubility

### Mineral Solubility and Saturation Index

Why does adding an inert salt to a low solubility omarcafini.info activity is a result of ionic strength As ionic strength increases in a solution, ion. At the isoelectric point, protein have no net charges and therefore will be less soluble. Why does increasing ionic strength result in an increase. Read 14 answers by scientists with 9 recommendations from their colleagues to the question asked by Yakoub Ladjal E. on Apr 29,

This is due to the reversed triple hydration of the positively charged halogen atom in addition to the expected hydration of the negatively charged oxygen atoms [ ]; thus preventing any clathrate cage-like hydration. The Hofmeister series has been rewritten to show the main variations [ ] and has been investigated in polar non-aqueous solutions [ ]. These differences may be due to the ionic concentration used, the sensitivity of the methods to the scale of potential structural changes in the bulk water, the difficulty in separating coexisting but opposite effects that is, chaotropic and kosmotropicsee laterthe precise meaning of 'bulk' water, and the importance of the presence of surfaces in stabilizing effects [ ].

In particular, effects of salts at lower concentrations may be smothered in many studies by the relatively large amount of unaffected 'bulk' water present whereas at high concentrations there may be insufficient water to show any specific effects properly.

### Hofmeister series

Some techniques do pick up the more extensive clustering effects expected; for example, Fourier transform infrared studies show four well-defined hydration spheres around a proton with an additional outer hydration layer and more loosely bound water molecules further out [ ].

Water in the hydration shell has been shown to be vibrationally decoupled from its neighbors [ ]. The effect of ions has been successfully approximated by the equivalent osmotic pressure [ ] and by the equivalent effect on water activity 4 molal NaCl is equivalent to 0. Ions that have the greatest such effect exhibiting weaker interactions with water than water itself are known as structure-breakers or chaotropeswhereas ions having the opposite effect are known as structure-makers or kosmotropes exhibiting strong interactions with water molecules.

Strongly hydrated ions considerably increase the difference between the hydrogen-bond donating capacity and the hydrogen-bond accepting capacity of the linked water molecules resulting in the breakdown of the tetrahedral network.

Anions hydrate more strongly than cations for the same ionic radius as water hydrogen atoms can approach about 0. Anions are also thought more likely to promote the salting-out of amphiphiles. Although we put forward the surface charge density as being the important determinant of Hofmeister effects as does [ ], others state it is the polarizability that is important [ ]. However, a comprehensive study has shown the dominant role of charge density but no correlation of polarizability with thermal effects on either of an acidic or basic protein [ ].

Small ions are strongly hydratedwith small or negative entropies of hydration, creating local order and higher local density. Small cations do not bind directly to polar surfaces but small anions, which have lower surface charge density than the cations, may bind through ion-pairing [ ]. These amide-backbone binding sites for weakly hydrated anions are the most significant locations for the salting-in of uncharged polypeptides.

They may additionally be pushed on by strong water-water interactions and certainly induce a change in the surface hydration and interfacial aqueous clustering [ ]. Such large ions possess low surface charge density e. This relationship is entirely based on classical thermodynamics and entails the validity of Cohn's equation Cohn,which restricts the development to the region of phase diagrams wherein an increase of the salt concentration results in a decrease in protein solubility i.

This situation is the most important one from the point of view of industrial applications. The methodology developed is applied to the modeling of aqueous solutions of lysozyme and ovalbumin.

It was shown that, for the modeling of the solid-liquid equilibrium of proteins, it is important to consider all protein ionization states in the thermodynamic description. The same hypothesis is made here: As observed by Moretti et al.

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- Ionic strength
- Solubility

Using the molality scale, the chemical potential of a given compound j in solution can be expressed as: The summation in this equation is carried out over all solutes.

Considering that protein molecules in different ionization states constitute different species, but that the second virial coefficient is independent of the ionization state, one gets for the neutral molecules in solution: Taking the partial derivative of the above expression in relation to the salt molality in the liquid phase, and considering that the temperature is constant: Substituting Equation 4 into Equation 3 and performing some algebraic manipulation, it can be shown that: Along the solubility curve, the chemical potential of the protein in the solid phase is constant, as it does not depend on the liquid phase composition.

Nonetheless, there is evidence that there may be solid phase transitions along the solubility curves Watanabe et al. Hence, the criterion for solid-liquid phase equilibrium is: Equation 5 can thus be written as: This equation is a theoretical relationship connecting the osmotic second virial coefficient, the protein solubility in the liquid phase and the salt molality in the liquid phase.

It can be used if one previously establishes how the reference chemical potential varies with salt molality and how to calculate the fraction of electrically neutral protein molecules. Cohn's Equation The so-called Cohn's equation Cohn, is an empirical equation that correlates the protein solubility and the salt molality in the salting-out region.

### Ionic strength - Wikipedia

Due to its remarkable ability to describe several systems with few parameters, this equation has gained much notoriety and is extensively used to model protein solubility data in the study of unit operations based on protein precipitation.

It can be written as Cohn, It should be noted that, theoretically, the value of Ks does not depend on the solution pH. If Cohn's equation is valid, the partial derivative of the natural logarithm of the protein solubility in relation to the salt molality, which appears in Equation 8can be written simply as: This explanation can also be used to elucidate the variation of the reference chemical potential in Equation 8as will be seen in the next section.

The last term of Equation 11 is due to the change in the free volume. When only the salt concentration in the liquid phase changes and there is no significant change in the interactions between the protein molecule and the salt ionsone can assume that the energy of the transfer process is affected only by changes in and.

## 5.8: Ionic Activity

Since the other terms are kept unchanged with the variation of the salt concentration, it is sufficient to evaluate these two terms. Thus, one can write: On the other hand, assuming a reference state at a certain salt molality m1, and another reference state with an equilibrium salt molality m2, the difference between the chemical potential of these states is equal to the difference between the chemical potentials for transfer: Hence, one can write: In the salting-out region, the salt molalities are sufficiently high to consider the following approximation, valid for the partial derivative of in relation to the salt molality through Equation From Equation 12one can write: Therefore, the variation of the reference chemical potential of the protein molecule in the liquid phase in relation to the salt molality is given by: Proposed Model Substituting Equations 10 and 19 into Equation 8one can write: This equation is a general one that relates the osmotic second virial coefficient Bthe protein solubility S and the salt molality msalt in the salting-out region.

Although the description of this fraction is not trivial, given that it depends upon salt ions, it can be assumed that, in the salting-out region, it is approximately constant. Alternatively, substituting for the value of the partial derivative of the solubility S using Equation 10 results in: Integrating both equations between an appropriate reference state identified by the asterisk and the actual condition results in: Equation 25 is an expression that relates the protein solubility to the osmotic second virial coefficient at different salt concentrations.

Equation 26 states that the relation between the natural logarithm of the osmotic second virial coefficient and the equilibrium salt molality is linear and its angular coefficient is the salting-out constant defined by Cohn's equation, Equation 9. Therefore, the application of Equation 25 and 26 will be restricted to data for lysozyme and ovalbumin, the only two proteins for which both kinds of data can be found in the literature.

## Biochemistry 601

Figure 1 shows the results of the application of Equation 9or Cohn's equation, to lysozyme solubility data obtained by Watanabe et al. For this system, the value of Ks is 0. Equation 26 was applied to a set of experimental data published by Curtis et al. In that work, values of the osmotic second virial coefficient at different values of sodium chloride molality were presented for solutions containing native lysozyme and the mutant lysozyme DF, in which residue is changed from aspartic acid symbol D to phenylalanine symbol F.

The values of the osmotic second virial coefficient were measured by light scattering.

**PCE103 Effect of ionic strength on solubility - Salting in and salting out**