Properties of very dilute solutions

In nature, the concentration of some substances may be very low. Their chemical properties at these very low concentration ranges can be different from the usual properties seen in macroscopic concentrations. Thus, it is difficult to perform thermodynamic calculations in very diluted solutions, and the results are often only approximate. When confronted with such problems, experiments must be performed in order to describe the exact nature of such systems. 

The phenomenon of very diluted solutions is well known in radiochemistry. Carrier-free radioactive isotopes could be mentioned as an example. The term denotes a radioisotope of an element in pure form, that is, essentially undiluted, with a stable isotope. The chemical concentration of these radioisotopes is usually very low. For example, 1 kBq radioactivity (applied typically in a tracer experiment) is equivalent to cca. 2 10 12 mol in the case of 137Cs or 90Sr isotopes. In the case of such low concentrations, no chemical system can be considered homogeneous because all surfaces, the wall of the laboratory vessels, or any contaminants in the solution (such as air bubbles, small particles, great molecules, etc.) can initiate interfacial processes and the subsequent formation of heterogeneous phases (adsorption, colloid formation, precipitation, etc.). This is the result of the simple fact that the number of molecules on the surfaces is more than, or at least similar to, the number of particles in the solution. Even in a solution containing 

The following two examples show the effect of very low concentration on complex-formation (Haissinsky 1966). In the first example, a mixture of three substances, A, B, and C, is present. A reacts with either B or C as follows  

When B and C are present in similar concentration, the formation of X is strongly preferred because of the rate constants kx/k2, and the reaction in Equation 1.53 is shifted to the right. When, however, B is present in a very low concentration (e.g., 10-12 mol/dm3), and the concentration of C is fairly high (e.g., 1 mol/dm3), the formation of Y takes place. Under these conditions, XM, if any, will dissociate. 

The second case is an example of the formation of different chemical species at very low concentration ranges. Let us see the complex formation of a cation in the presence of an excess of anions. The increase of the ratio of anion cation will obviously increase the stability of the formed complex. In the range of macroscopic concentration, if the concentration of anion and cation are similar, no complex formation can be detected. For example, in the case of lead and chloride ions, a slightly soluble compound, PbCl2, is formed. However, when the concentration of lead ions is extremely low, using, for example, the carrier-free Pb-212 isotope, and chloride anions are present in macroscopic concentration, negatively charged [PbClJ(n 2) are formed. 

---

Limiting Viscosity Number (Intrinsic Viscosity) and Related Properties of Very Dilute Solutions... 

The most important application of low concentration behavior of solutes is for solid solutes, especially electrolytes. Electrolyte solutions are examined in detail in chapter 3. Some general thermodynamic methods for describing the properties of very dilute solutions are considered in the following section. 

We shall discuss the hydrodynamic properties of very dilute solutions first, where the motions of different chains can be studied independently. The essential microscopic quantity is the monomer friction C, describing the motion of a single monomer in the solvent. The monomer friction coefficient obviously depends critically on the solvent viscosity rfo. If the monomers can be assimilated to spheres with a hydrodynamic radius a, C is given by Stokes law (C = 6nrjQa). The problem is to relate the microscopic parameter to more macroscopic quantities, such as a chain mobility or diffusion constant. 

---