Scale mole fraction

On the mole fraction scale in kilocalories per mole. Reference solvent is methanol... 

All free energies are in kilocalories per mole on the mole fraction scale, relative to DMF. See Table 8-5 for rate data. 

Equilibrium constant on the molar concentration scale Michaelis constant Ionization constant of water Equilibrium constant on the mole fraction scale General rate constant Boltzmann s constant Rate constant of step i... 

The deviation of a solvent from the limiting-law behavior of Raoult s law is described conveniently by a function called the activity coefficient, which is defined (on a mole fraction scale) as... 

The deviation of a solute from the limiting behavior of Hemy s law, on the mole fraction scale, is also described conveniently by the activity coefficient, which in this... 

Solute in Solution. When the mole fraction scale is used, it is convenient to choose a standard state such that the activity would approach the mole fraction in... 

This figure evidently is a typographical error. The correct figure is near 145.2. It also is hkely (D. H. Volman, private correspondence) that the International Critical Tables did not interpret correctly the mole fraction scale used by the original investigator [8]. 

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) ... 

If Z9b(ai) can be equated with P calculated from the entries in Table 2.5, then Z9b(a2) in any other solvent Ab can be estimated from Eq. (2.62). Equation (2.62) is actually a combination of four expressions of the form of Eq. (2.8) (see section 2.2.2), two for water and solvent Ai and two for water and solvent A2, presuming them to be immiscible pairs of liquids. It employs concentrations on the mole fraction scale, and assumes that the systems behave as regular solutions (which they hardly do). This eliminates the use of the solubility parameter 8 of water, which is a troublesome quantity (see Table 2.1). Solvent Ai need not, of course, be 1-octanol for Eq. (2.62) to be employed, and it suggests the general trends encountered if different solvents are used in solvent extraction. 

Adopting the mole fraction scale and introducing standard chemical potentials and activity coefficients as follows... 

This expression can be formally identified with the chemical potential MiIS of the central ion in the ideal solution, where c is the ionic concentration on the mole fraction scale ... 

In this section, we shall adopt the mole-fraction scale (7.80a), so that... 

It should be noted that k and K must be based on the same concentration scale. If we select the mole-fraction scale, x, we obtain ... 

The vapor curve KLMNP gives the composition of the vapor as a function of the temperature T, and the liquid curve KKMSP gives the composition of die liquid as a function of die temperature. These two curves have a common point M. The state represented by M is that in which the two states, vapor and liquid, have the same composition xaB on die mole fraction scale. Because of die special properties associated with systems in this state, the Point M is called an azeotropic point and the system is said to form an azeotrope. In an azeotropic system, one phase may be transformed to the other at constant temperature, pressure and composition without affecting the equilibrium state. This property justifies the name azeotropy, which means a system diat boils unchanged. 

This is a special form applicable to an electrolyte such as sodium chloride. j is the mean ionic activity coefficient on the mole-fraction scale which is equal to y at this dilution. The activity of water is linear with m in this region and hence accurate values are obtained merely by interpolation (9). For 50% recovery from a feed of 5000 p.p.m., the following values were calculated ... 

FREE ENERGIES OF TRANSFER, ON THE MOLE FRACTION SCALE, FROM METHANOL TO OTHER SOLVENTS OF TETRAALKYLTINS, IODINE, AND THE TETR A A LK Y LTIN/lODI NE... 

The difficulty in dealing with solvent influences on reaction rates is that the free energy of activation, AG, depends not only on the free energy of the transition state but also on the free energy of the initial state. It is therefore of considerable interest to dissect solvent influences on AG into initial-state and transition-state contributions. As far as electrophilic substitution at saturated carbon is concerned, the only cases for which such a dissection has been carried out are (a) for the substitution of tetraalkyltins by mercuric chloride in the methanol-water solvent system (see page 79), and (b) for the iododemetallation of tetraalkylleads in a number of solvents (see p. 173). Data on the latter reaction (6) are more useful from the point of view of the correlation of transition-state effects with solvent properties, and in Table 13 are listed values of AG (Tr), the free energy of transfer (on the mole fraction scale) of the tetraalkyllead/iodine transition states from methanol to other solvents. 

Besides using the mole fraction scale for concentration, solubility in water can also be expressed in molar concentrations usir%, which can be approximated as the producfeDSnd the molarity... 

The mole fraction scale is useful when one is concerned with physical properties of solutions (Chapter 14), which are expressed most clearly in terms of relative numbers of solvent and solute molecules. Sometimes, the physical properties are affected by the number of particles in solution. Then, the molality of ions becomes important, not just that of the molecules—NaCl (Na+ and Cl- in solution) and Na2SC>4 (2Na+ and SO - in solution) affect some physical measurements differently. 

Benzene and toluene form an ideal solution, which follows Raoult s law, and has the activity coefficient on the mole fraction scale equal to 1 at all concentrations. If we described this solution by a molality-based Henry s law, would the activity coefficient be equal to 1 at all concentrations. If not, why ... 

See, for example, Chap. 9 in K. Denbigh, The Principles of Chemical Equilibrium, Cambridge University Press, Cambridge, 1981. ThelUPAC recommendation for the symbol to represent rational activity coefficients is yx, which is not used in this book in order to make the distinction between solid solutions and aqueous solutions more evident. In strict chemical thermodynamics, however, all activity coefficients are based on the mole fraction scale, with the definition for aqueous species (Eq. 1.12) actually being a variant that reflects better the ionic nature of electrolyte solutions and the dominant contribution of liquid water to these mixtures. (See, for example, Chap. 2 inR. A. RobinsonandR. H. Stokes,Electrolyte Solutions, Butterworths, London, 1970.)... 

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