Molality scale

The values for unit weight of solvent (molality scale) can be obtained by multiplying the corresponding values for unit volume by the square root of the density of water at the appropriate temperature. 

This table gives values of pKw on a molal scale, where Kw is the ionic activity product constant of water. Values are from W. L. Marshall and E. U. Franck, 7. Phys. Chem. Ref. Data, 10 295 (1981). 

Ionic Equilibria.. The ion product constant of D2O (see Table 3) is an order of magnitude less than the value for H2O (24,31,32). The relationship pD = pH + 0.41 (molar scale 0.45 molal scale) for pD ia the range 2—9 as measured by a glass electrode standardized ia H2O has been established (33). For many phenomena strongly dependent on hydrogen ion activity, as is the case ia many biological contexts, the difference between pH and pD may have a large effect on the iaterpretation of experiments. 

Ideal and Nonrideal Solutions. Treatment of Solutions by Statistical Mechanics. A Solution Containing Diatomic Solute Particles. A Solution Containing Polyatomic Solute Particles. An Interstitial Solution. Review of Solutions in General. Quantities De-pendent on, and Quantities Independent of, the Composition of the Solution. Unitary Quantities and Cratic Quantities. Molality and Activities on the Molality Scale. 

Molality and Activities on the Molality Scale. In order to give a numerical value to the concentration of a solution, it is customary to... 

There are several different scales 011 which the activity of a solute may be defined.1 In thermodynamic expressions for a solute in a non-ideal solution the activity on the molality scale plays the same part that is played by the molality of a solute in an ideal solution. Since the activity is expressed in the same units as the molality, the ratio of the activity to the molality—the activity coefficient—is a pure number whose value is independent of these units it is also indopendont of the particular b.q.s. that has been adopted. Thus the numerical values of all activities and molalities would change in the same ratio, if at any time a new choice were made for the b.q.s. 

Let x and x denote the mole fractions of the two sparingly soluble solids in their respective saturated solutions let y and y denote their mole ratios, m and ml their molalities, and a and a their activities on the molality scale. If the saturated solutions are sufficiently dilute, we may, with sufficient accuracy, neglect the differences between the four ratios x/x, y/yf, m/m, and a/a. We can express the difference between the cratic terms by means of any of these quantities, thus,... 

In agreement with (98), the left-hand side is just the standard free energy of solution AF°. Here y, as defined by (106), is the usual activity coefficient on the molality scale. In particular, when the solid is in contact with its saturated solution, there is no change in the free energy when additional ions are taken into solution. In this case, if in (108) we write m, t and y,at, the values of m and y in the saturated solution, we may set AF equal to zero. This will be discussed in Sec. 100. 

This choice of a standard state seems like impossible mental gymnastics, but it allows activity to follow a molal scale, so that in dilute solutions activity and molality - despite the fact that activity is unitless - are equivalent numerically. A species molality m , the number of moles of the species per kilogram of solvent, is related to its activity by... 

The chemical potential on a molality scale of the solute that follows Henry s law is given by Equation (16.10) with 72 = 1-... 

If the vapor is ideal, Henry s law is expressed, on the molality scale, as... 

Table 4.1. Single ion activity coefficients (molal scale) for uni-univalent chlorides at 25° C derived from hydration theory [11].

The composition of a mixture need not be given in terms of the mole fractions of its components. Other scales of concentration are frequently used, in particular, when one of the components, say. A, can be designated as the solvent and the other (or others), B, (C,...) as the solute (or solutes). When the solute is an electrolyte capable of dissociation into ions (but not only for such cases), the molal scale is often employed. Here, the composition is stated in terms of the number of moles of the solute, m, per unit mass (1 kg) of the solvent. The symbol m is used to represent the molal scale (e.g., 5 m = 5 mol solute/1 kg solvent). The conversion between the molal and the rational scale (i.e., the mole fraction scale, which is related to ratios of numbers of moles [see Eq. (2.2)] proceeds according to Eqs. (2.32a) or (2.32b) (cf. Fig. 2.4) ... 

A concentration scale for solutes in aqueous solutions, equal to moles of solute/55.51 mol water. It is frequently used in studies of solvent isotope effects. As pointed out by Schowen and Schowen the choice of standard states can change the sign for the free energy of transfer of a species from one solvent to another, even from HOH and DOD. The commonly used concentration scales are molarity, mole fraction, aquamolality, and molality. Free energies tend to be nearly the same on all but the molality scale, on which they are about 63 cal mol more positive at 298 K than on the first three scales. The interested reader should consult Table I of Schowen and Schowen ... 

Here, p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

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