Molality, definition

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... 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

To determine the number of moles of solute from the definition of molality, m = (moles solute)/(kg solvent), first find the mass of solvent using its density ... 

The IUPAC definition of pH39 is based upon a 0.05M solution of potassium hydrogenphthalate as the reference value pH standard (RVS). In addition, six further primary standard solutions are also defined which between them cover a range of pH values lying between 3.5 and 10.3 at room temperature, and these are further supplemented by a number of operational standard solutions which extend the pH range covered to 1.5-12.6 at room temperature. The composition of the RVS solution, of three of the primary standard solutions and of two of the operational standard solutions is detailed below, and their pH values at various temperatures are given in Table 15.4. It should be noted that the concentrations are expressed on a molal basis, i.e. moles of solute per kilogram of solution. 

Like mole fraction but unlike molarity, the molality is independent of temperature. The units of molality are moles of solute per kilogram of solvent (mol-kg 1) these units are often denoted m (for example, a 1 m NiS04(aq) solution) and read molal. Note the emphasis on solvent in the definition. To prepare a l m NiS04(aq) solution, we dissolve 1 mol NiS04 in 1 kg of water (Fig. 8.26). 

Now the origin of the scale must be defined, i.e. a pH value must be selected for a standard (as close as possible to the value expected on the basis of definition 1.4.46). A solution of potassium hydrogen phthalate with a molality of 0.05 mol kg-1 has been selected as the reference value pH standard (RVS). 

The molality of the solution, based on the definition of molality, would be ... 

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... 

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

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 behavior of a few typical electrolytes is illustrated in Figure 19.13. By definition, 7+ is one at zero molality for all electrolytes. Furthermore, in every case, 7+ decreases rapidly with increasing molality at low values of m2. However, the steepness of this initial drop varies with the valence type of the electrolyte. For a given valence type, 7 + is substantially independent of the chemical nature of the constituent ions, as long as m2 is below about 0.01. At higher concentrations, curves for 7 + begin to separate widely and to exhibit marked specific ion effects. 

Like the difference in their names, the practical difference between molarity and molality is subtle. Take a close look at their definitions, expressed next to one another in the following equations ... 

From the standpoint of the operational definition of the standard state for the above free energy changes, we must remember that, while mole fractions are strongly recommended composition measures (61 Mil), in practice, both molalities, m, and concentrations, c, are widely used. For dilute aqueous solutions at moderate temperatures the numerical values of m and c are only slightly different. This no longer holds for other solvents. 

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. 

NiS04(aq) solution) and read molal. Note the emphasis on solvent in the definition. Therefore, to prepare aim NiS04(aq) solution, we dissolve 1 mol NiS04 in 1 kg of water (Fig. G.13). 

The main feature that distinguishes molality from molarity is its definition in terms of the mass of solvent used to make up the solution the molarity is expressed in terms of the volume of the resulting solution (not the volume of solvent used to make the solution). As a result, the molality is useful when we want to emphasize the relative numbers of molecules of the components of a mixture. That will be required only rarely in this text, so molality will appear much less frequently than molarity (it is used only in Chapter 8). If a concentration given as a molarity needs to be converted into molality, the mass of solvent in the solution must be known. To calculate this mass, the density of the solution is needed. 

If equilibrium has not been reached between a mixture of components, the condition is referred to as partial saturation. At partial saturation the gas mixture obeys real gas laws. There are several ways to express the concentration of a vapor in a mixture of gases. Most often, weight or mole fraction is used. Other definitions are relative saturation (relative humidity), molal saturation (molal humidity) and absolute saturation (absolute humidity). 

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