Activity and the Standard State

The numerical value of kt in (2-3) depends on how activity is defined and on the units in which concentration is expressed (molarity, mole fraction, partial pressure). Measurement of the absolute activity, or chemical potential, of an Individual ion is one of the classical unsolved problems. Since we cannot measure absolute ion activity, we are then necessarily interested in the next best—comparative changes in activities with changing conditions. To obtain comparative values numerically, we measure activity with respect to an arbitrarily chosen standard state under a given set of conditions of temperature and pressure, where the substance is assigned unit activity. The value of ki in (2-3) thus depends on the arbitrary standard state chosen accordingly, the value of the equilibrium constant also depends on the choice of standard states. 

FIGURE 2-1 Variation of a property (schematic) as a function of mole fraction, to illustrate henryan (A) and raoultian (S) reference behavior. 

For solutions the standard state usually is defined differently for solvents and for solutes. For solvents the standard state is the pure solvent, whose activity is given by 

FIGURE 2-2 Relation between concentration and a physical property of a solution. Upper lines, the value extrapolated from the lowest concentrations. Left, an expansion of the initial part of the curve, to make clear the asymptotic behavior. (This example involves the lowering of the freezing point of magnesium sulfate solutions as a function of molality.) 

Activity is given in the same units as concentration—molarity, mole fraction, and so forth. In (2-9) the concentration C usually is expressed either in moles per liter of solution (molarity M) or in moles per kilogram of solvent (molality m). In dilute aqueous solutions the molarity and molality are nearly equal in nonaqueous solutions molarity is usually larger than molality, since the density of the solvent is usually less than unity. Analytical chemists ordinarily find it more convenient to express concentration in molarity, even though it varies slightly with temperature. The analytical concentration is represented by the symbol C, to indicate the moles of solute added per liter of solution. Analytical concentration should be distinguished from the equilibrium concentration, which is indicated by enclosure in square brackets. 

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