Mean molal definition

To achieve a uniform definition of y + for all electrolytes, it is convenient to define a mean molality m+ (for BaCl2, for example) as... 

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... 

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. 

In this equation, the following definition of the chemical potential of ion i in the hypothetical state of the pure ions dissolved in pure water to give an ideal solution at unit mean molality, under the standard state pressure has been used ... 

From this expression comes the definition of the mean activity coefficient. Y+. in terms of the ionic activity coefficients Yc and Ya The mean activity coefficient is the property which is determined or calculated from experimental measurements. A similar expression results for the mean molality m, which is not generally used in reporting experimental measurements ... 

Recalling the definitions of the mean activity coefficient and mean molality from Chapter II ... 

The partial molal free energy of a spray of finely dispersed droplets is not so simply related to escaping tendency as it is in systems usually treated by thermodynamic methods. Even the definition of the partial molal free energy is not entirely devoid of difficulty. To discuss equilibrium we wish to think of the transfer of a small amount of adsorbent from each droplet in the spray to another phase— e.g., the gas phase (16). If a little material leaves each droplet, there must be a concomitant decrease in surface area, A, and an increase in specific area, quantity related to escaping tendency of material is not the derivative of free energy with respect to n, the number of moles in the spray at either constant area or constant specific area. The condition is that the number of droplets, v, be constant. (This means that area divided by mass to the 2/3 power is nearly invariant.)... 

In the definition mB denotes the molality of solute B, and mA denotes the mass of solvent A thus the same symbol m is used with two different meanings. This confusion of notation may be avoided by using the symbol b for molality. 

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]

This table gives mean activity coefficients at 25°C for molalities ences, and data over a wider concentration range, in the range 0.1 to 1.0. See the following table for definitions, refer-... 

In the current discussion, the mean activity coefficient is related to molarity. On the other hand, the definition of ionic strength involves molality as the basic concentration variable. However, as is to be proved in Exercise 4.2.3, for aqueous solutions at ordinary temperatures and pressures the definition of 5, remains virtually unaltered by switching from molarity to molality. Thus, the quantity... 

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