Gurney co-sphere

In Passynski s theory, the basic assumption is that the compressibility of water sufficiently bound to an ion to travel with it is zero. Onori thought this assumption questionable and decided to test it. He used more concentrated solutions (1-4 mol dm ) than had been used by earlier workers because he wanted to find the concentration at which there was the beginning of an overlap of the primary solvation spheres (alternatively called Gurney co-spheres) of the ion and its attached primary sheath of solvent molecules. 

For an NaCl solution, calculate the concentration at which the so-called Gurney co-sphere is reached. (Hint For 1 1 electrolyte, the average separation 1 (in A) = 9.40c where c is the concentration in mol dm ". Assume the Gurney co-sphere is two water molecules beyond the ions periphery.) (Xu)... 

Draw a diagram representing the Gurney co-sphere. When two ions collide, how does this sphere influence the parameters that go into the calculation of the activity coefficient ... 

The Debye-Htickel model considered the solvent to be a structureless medium whose only property is to reduce the interactions between ions in a vacuum by a factor given by the macroscopic relative permittivity, e. No cognisance was taken of the possibility of ion-solvent interactions, and the size of the ion was assumed to be that of the bare ion. Gurney in the 1930s introduced the concept of the co-sphere and this has proved to be a useful concept in the theory of electrolyte solutions. Many recent theories of conductance are based on the Gurney co-sphere concept (see Section 12.17). 

This is where the Gurney co-sphere concept makes its first appearance in the theory. An extra term is added to the potential energy, and this discusses what happens between r = a and an upper limit. This upper limit is r,- + rj + d, where d is twice the thickness of a co-sphere, taken by some workers to be equal to the diameter of a molecule of solvent, here H20(l), and r, and / are the crystallographic radii of the ions. 

This modification is applicable to distances between r = r, + rj and r = r, -I- rj + d and the upper limit corresponds to when the Gurney co-spheres cease to overlap (see Figure 10.15). Any value of r between the lower limit r, + rj and the upper limit n + rj + d corresponds to overlap of the co-spheres. Overlap of the co-spheres contributes a constant term, no matter how extensive the overlap is. 

The Gurney co-sphere defines a region around the ion which has solvent molecules whose structure has been modified by the field of the ion (see Section 10.16). Outside this region, the solvent has its macroscopic bulk structure. The diameter of the Gumey cosphere takes a value, R. The distance between the centre of ions with such co-spheres where the co-spheres just touch is also R (see Figure 12.4). This assumes that the ions are spherical, and the situation could well prove to be different if the ions are non-spherical. In addition, ion association was taken to be an integral part of the model and theory rather than an added-on factor used to explain deviations from a conductance equation based on the concept of complete dissociation. All ion association takes place within the Gurney CO-sphere. 

Fuoss now allowed two types of ion pair to occur within the Gurney co-spheres of the central ion and an ion of opposite sign, i.e. within the distance, R/2 from the centre of the ion. The new description now involves ... 

Developments from the Gurney concept of the co-sphere a new model... 

Gurney introduced the idea of a co-sphere around each ion, which can loosely be identified with a region of hydration. Outside each co-sphere the water is treated as unmodified bulk water with aU the properties of pure water. However, within the co-sphere the water is no longer treated as unmodified bulk water. Allowance is also made for the possibility that the individual co-spheres of ions could overlap with water being squeezed out (see Figures 10.14(a) and 10.14(b)). 

Figure 10.15 A Gurney diagram showing co-spheres just touching.

This involves a modified core term where the hard core or hard sphere repulsion is replaced by a non-hard sphere short range repulsion which is proportional to This replaces the Debye-Hiickel core term. The Gurney term remains proportional to the volume of overlap of the co-spheres. 

I- (the Gurney term which is proportional to the volume of overlap of the co-spheres ... 

Figure 12,4 A Gurney Lype diagram showing Lwo ions with co-spheres just touching. R is the distance between the centres of the ions and is the Gurney diameter.

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