Osmotic Equilibrium in Charged Systems

We have had no occasion as yet in this book to note that colloidal solutes may possess an electrical charge just like their low molecular weight counterparts. Portions of Chapter 4 and Chapters 11-13 are concerned with those properties of colloids that are direct consequences of 

At this point we shall not concern ourselves any further with the origin of the charge of a colloidal system rather, our attitude is that charge is one more characteristic that must be measured and understood in order to characterize certain systems fully. 

In physical chemistry it is convenient to express concentrations as molalities and to use molality units to express the activity of the components. This is the convention we follow in this section. Accordingly, the standard state for a component consists of a solution in which that component has an activity of 1.0 mole (kg solvent)  

The specific situation we wish to consider is the osmotic equilibrium that develops in an apparatus that has a semipermeable membrane impermeable to the macroion only. That is, the membrane is assumed to be permeable not only to the solvent but also to both of the ions of the low molecular weight electrolyte, but not to the colloidal ion Pz+. At equilibrium the low molecular weight ions will be found on both sides of the membrane, but not in equal concentrations, because of the presence of the macroions on one side of the membrane. We have already come across an example of such a situation in the vignette at the beginning of this chapter on the role of Donnan equilibrium on the so-called resting states of nerve cells. 

For the purpose of our discussion, we designate the side of the membrane that contains the macroions as the a phase and the solution from which the macroions are withheld as the /3 phase. Equation (12) continues to describe the equilibrium condition applying it to component 3 leads to the following  

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