Activity, definition molal

For such solutions, the definition of activity is completed by the requirement that the activity approach the molality ratio in the limit of infinite dilution. That is. 

If followed in experimenrtally accessible dilute solutions, Henry s law would be manifested as a horizontal asymptote in a plot such as Figure 19.3 as the square of the molality ratio goes to zero. We do not observe such an asymptote. Thus, the modified form of Henry s law is not followed over the concentration range that has been examined. However, the ratio of activity to the square of the molality ratio does extrapolate to 1, so that the data does satisfy the definition of activity [Equations (16.1) and (16.2)]. Thus, the activity clearly becomes equal to the square of the molality ratio in the limit of infinite dilution. Henry s law is a limiting law, which is valid precisely at infinite dilution, as expressed in Equation (16.19). No reliable extrapolation of the curve in Figure 19.2 exists to a hypothetical unit molality ratio standard state, but as we have a finite limiting slope at = 0, we can use... 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

Table 19.1 summarizes the empirical expression of the limiting law and the definitions of the ionic activities, molality ratios, and activity coefficients for a few substances and for the general case of any electrolyte. 

The exact definition of the equilibrium constant given by IUPAC requires it to be defined in terms of fugacity coefficients or activity coefficients, in which case it carries no units. This convention is widely used in popular physical chemistry texts, but it is also common to find the equilibrium constant specified in terms of molar concentrations, pressure or molality, in which cases the equilibrium constant will carry appropriate units. 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

When the amount of material present is measured by either concentration, c or molality (= amount of solute/mass of solvent) i the definition of activity differs slightly from the case (equation (39.4)) where a dimensionless measure (like mole fraction, x) is used. Equations for chemical potential, fi, involving mole fractions, x apply quite well when one is examining equilibria in solution. However in other cases concentration, c or molalities, m are often used. Activity will then be defined in relation to a standard concentration, c° ... 

In cases where activity is associated with concentration (equation 39.15) or molality (equation (39.17) Frame 39) measurements, the definition of the standard state is required before activity is truly defined. In the case of concentration this is usually 1 mol dnT3, or in the case of molality, 1 mol kg-1 and so accordingly the corresponding A G° values given in equation (A.2) will be defined with respect to these standard states. 

The concept of a chemical potential is germane to a discussion of water activity (aw), which is technologically defined as the ratio of the equilibrium water vapor pressure over a solution or dispersion (p0) and the water vapor pressure over pure water (jb ). Also by definition, the chemical potential of a solvent ( jl0) or a solute (p ) is the rate of change in energy of either with a change only in the molal content of that component in solution. 

From the context of the current discussion, it should be evident that the mean activity coefficient cited above is related to molarity. On the other hand, as is to be proved in Exercise 4.2.2, the definition of S remains virtually unaltered by switching from molarity to molality in aqueous solutions at ordinary conditions of temperature and pressure. Thus, the quantity specified by Eq. (4.2.3a) may be considered to represent either 7 (T,P,c) 7 (c) or 7 (T,P,m) 7 nonaqueous solvents are employed, or whenever T and P deviate greatly from standard conditions, the two preceding quantities cannot be used interchangeably Eq. (4.2.3a) specifies 7 [Pg.392]

Activities of Electrolytes.—When the solute is an electrolyte, the standard states for the ions are chosen, in the manner previously indicated, as a hypothetical ideal solution of unit activity in this solution the thermodynamic properties of the solute, e.g., the partial molal heat content, heat capacity, volume, etc., will be those of a real solution at infinite dilution, i.e., when it behaves ideally. With this definition of the standard state the activity of an ion becomes equal to its concentration at infinite dilution. 

The product 7 + 7- is experimentally measurable. The quantity (7 referred to as the mean molal activity coefficient The mean ionic molality is defined as im+mJ) and is simply m for a univalent-univalent electrolyte. Summarizing these definitions for a nonideal, univalent-univalent solution, where the solute is component 2. 

The experimental method by which S0rensen proposed to measure pH did not, however, actually provide an unequivocal value for the hydrogen ion concentration in solutions of unknown composition. Introduction of the concept of activity (a) and the activity coefficient (y, concentration scales or y, molality scale) led to a modified definition (10) for which a modified symbol pan was first suggested ... 

Both these considerations would be taken into accoimt if the activation process were assumed to occur at a constant pressure, p, such that the partial molar volume of the solvent is independent of the temperature, though this possibility does not appear to have been considered. A full discussion is beyond the scope of this chapter, but the resulting heat capacities of activation are unlikely to differ greatly from those determined at a constant pressme of, say, 1 atm. (see p. 137). Unfortunately, this approach requires the definition of rather clumsy standard states for solutes, e.g., hypothetically ideal, 1 molal, under a pressure such that a given mass of the pure solvent occupies a particular volume. 

The standard state is the hypothetical ideal solution of molality 1 molkg (or the relative activity of H 3 O+,aH3O+ = 1) at standard pressure. The standard pressure is 1 bar (earlier 1 atm = 1.01325 bar however, the shift is only 0.00026 V at the potential scale). By definition, the potential of this electrode is zero. Although the standard potential should not depend on the material of the metal, the SHE exclusively contains a platinum wire or a platinum sheet covered with platinum black (platinized platinum). Owing to the spontaneous dissociation (dissociative chemisorption) of H2 at Pt... 

In the examples that follow we shall always use the definition of activity based on unit molality as the standard state. 

To determine the standard electrode potential of an element M we set up a cell as illustrated in Fig. 7,6. The element is placed in a solution of its ions at unit activity (standard state, based on the unit-molality definition) and coupled to a standard hydrogen electrode.f The potential of element M with respect to the platinum of the hydrogen electrode is called the standard electrode potential of M. (If the element M is positive with respect to the hydrogen electrode then the standard electrode potential of M is positive and vice versa.) If the metal in the cell is zinc we find... 

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