Partition coefficients for systems with polymers

For dilute concentrations of a in a liquid the molar concentration in terms of the weight fraction is  

In some cases it is more convenient to define a molal activity coefficient for the solute in the polymer phase and a molar activity coefficient for the liquid phase. Combining Eq. (4-33) and (4-43) one gets  

Sometimes volume fractions, a, are used which can be defined  

Using the above expressions for partition coefficients defined on the basis of weight fraction and volume fraction activity coefficients one avoids the difficulty of trying to define what exactly the molar volume of a polymer is. 

In general the corresponding molar volume for nonpolymeric liquids can be obtained without difficulty, because the densities are available from tables or can easily be determined experimentally. 

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