Activities and Standard States

The term activity is used in the description of the departure of the behaviour of a solution from ideality. In any real solution, interactions occur between the components which reduce the effective concentration of the solution. The activity is a way of describing this effective concentration. In an ideal solution or in a real solution at infinite dilution, there are no interactions between components and the activity equals the concentration. Nonideality in real solutions at higher concentrations causes a divergence between the values of 

Depending on the units used to express concentration we can have either a molal activity coefficient, a molar activity coefficient, /(., or, if mole fractions are used, a rational activity coefficient, y.  

In order to be able to express the activity of a particular component numerically, it is necessary to define a reference state in which the activity is arbitrarily unity. The activity of a particular component is then the ratio of its value in a given solution to that in the reference state. For the solvent, the reference state is invariably taken to be the pure liquid and, if this is at a pressure of 1 atmosphere and at a definite temperature, it is also the standard state. Since the mole fraction as well as the activity is unity y =l. 

Several choices are available in defining the standard state of the solute. If the solute is a liquid which is miscible with the solvent (as, for example, in a benzene-toluene mixture), then the standard state is again the pure liquid. Several different standard states have been used for solutions of solutes of limited solubility. In developing a relationship between drug activity and thermodynamic activity, the pure substance has been used as the standard state. The activity of the dmg in solution was then taken to be the ratio of its concentration to its saturation solubility. The use of a pure substance as the standard state is of course of limited value since a different state is used for each compound. A more feasible approach is to use the infinitely dilute solution of the compound as the reference state. Since the activity equals the concentration in such solutions, however, it is not equal to unity as it should be for a standard state. This difficulty is overcome by defining the standard state as a hypothetical solution of unit concentration possessing, at the same time, the properties of an infinitely dilute solution. Some workers have chosen to 

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Chapter 6 - Fugacity, Activity, and Standard States, Pages 247-323... 

We have now said everything necessary about activities and standard states, but the overall effect for the newcomer is often one of confusion at this stage. To try to draw the various threads together we consider in Figure 12.5a a hypothetical three-phase equilibrium at temperature T and pressure P. A solid crystalline solution of B in A is in contact with an aqueous solution of A(aq) and B(a<7), which is in turn in contact with a vapor phase containing A(v) and B(v) in addition to water vapor. We can suppose the dissolution of (A,B)(5) to be stoichiometric so that the ratio of A to B is the same in all three phases, but this is irrelevant to our development as we consider only component A. Let s say that for a solid solution composition of A"a = 0.5, Vr = 0.5, the concentration of A aq) at equilibrium rri/ ) is 10 molal, and the fugacity of A in the vapor (/a) is 10 bars. Assuming activity coefficients in the solid and liquid... 

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