Excess functions heat, volume

Gibbs energies, enthalpies, entropies, heat capacities, and volumes, as well as intensive properties, such as permitlivities or viscosities. The excess functions of extensive properties over those for ideal mixtures of the components, symbolized by y (or the respective increments for intensive quantities, symbolized by AT), are usually defined in terms of the mole fraction composition with respect to the pure components ... 

The excess functions we shall consider in this book are mainly the exce free energy, the excess enthalpy, the excess entropy and the excess volume. The excess free energy (1.7.1) is deduced from the determination of the activity coefficients (generally from vapour pressure measurements). The excess enthalpy is the heat of mixing at constant pressure per mole of solution it may be deduced either from direct measurements or from the temperature variation of the activity coefficients (cf. 1.6.6). The excess entropy is defined by (cf. 1.4.10)... 

Other interesting excess functions axe the excess specific heat (1.4.6) and the change of the excess volume with pressure. 

One sees at once that the contributions of the dipolar interactions to the excess functions in such systems are always positive. This can be explained qualitatively by considering that, in the process of mixing, the stem becomes less ordered as compared to the pure polar constituent. There is therefore an increase in entropy. Also the mixing process destroys at least partially the dipolar interactions. Therefore the heat of mixing as well as the excess volume are positive. As shown by the positive value of gf in (14.4,3), the enthalpy increase gives the dominant contribution to the excess free energy. 

We may compare (17.6.2) with the corresponding expression (10.7.4) for monomer mixtures. Apart from the combinatorial entropy and factors qjqA and CA/iA, these formulae are exactly the same, when the mole fractions xa and xb are replaced by Xa and Xb- We must also notice that in our present model the configurational specific heat at constant volume cvA vanishes as a consequence of our assumption that the cell partition functions do not depend on the temperature. Therefore the detailed discussion of the effect of intermolecular forces on excess functions presented in Ch. IX-XI, applies also to polymer mixtures. For example p will again give rise to positive deviations from ideality, positive excess entropy and heat absorption. We shall not go into more detail. 

Acid anhydrides have been employed with, and without the use of a base catalyst. For example, acetates, propionates, butyrates, and their mixed esters, DS of 1 to ca. 3, have been obtained by reaction of activated cellulose with the corresponding anhydride, or two anhydrides, starting with the one with the smaller volume. In all cases, the distribution of both ester groups was almost statistic. Activation has been carried out by partial solvent distillation, and later by heat activation, under reduced pressure, of the native cellulose (bagasse, sisal), or the mercerized one (cotton linters). No catalyst has been employed the anhydride/AGU ratio was stoichiometric for microcrystalhne cellulose. Alternatively, 50% excess of anhydride (relative to targeted DS) has been employed for fibrous celluloses. In all cases, polymer degradation was minimum, and functionalization occurs preferentially at Ce ( C NMR spectroscopic analysis [52,56,57]). 

The view that the clay surface perturbs water molecules at distances well in excess of 10 A has been largely based on measurements of thermodynamic properties of the adsorbed water as a function of the water content of the clay-water mixture. There is an extensive literature on this subject which has been summarized by Low (6.). The properties examined are, among others, the apparent specific heat capacity, the partial specific volume, and the apparent specific expansibility (6.). These measurements were made on samples prepared by mixing predetermined amounts of water and smectite to achieve the desired number of adsorbed water layers. The number of water layers adsorbed on the clay is derived from the amount of water added to the clay and the surface area of the clay. 

Urea, as a cosolvent, is at the other extreme. All the concentration dependences of the binary and ternary systems are quite regular. The excess volume (Figure 6) is positive, which is rarely observed for nonelectrolytes in water. With the exception of the heat capacities of Bu4NBr, all the parameters Beu are positive for volumes and heat capacities, and the sign of the transfer functions is always opposite what we would expect for the structural hydration contribution to V° and Cp°. 

Ambient ozone has not been clearly linked to excess mortality, possibly because it is difficult to separate ambient ozone statistically from other possible causative factors. Ambient ozone is strongly correlated with temperature (see Section 9.11.4), so that excess deaths associated with ozone are hard to separate from deaths associated with heat. However, ambient levels of ozone have been linked to impairment of respiratory functions both in laboratory studies and in studies of individuals under ambient conditions. A 10-20% reduction in forced expiratory volume (FEV) was found to result from exposure to ozone... 

If the expression for the translational partition function is inserted into equation (16.8), it is readily found, since tt, m, fc, h and V are all constant, that the translational contribution Et to the energy, in excess of the zero-point value, is equal to %RT per mole, which is precisely the classical value. The corresponding molar heat capacity at constant volume is thus f P. As stated earlier, therefore, translational energy may be treated as essentially classical in behavior, since the quantum theory leads to the s ame results as does the classical treatment. Nevertheless, the partition function derived above [[equation (16.16) [] is of the greatest importance in connection with other thermodynamic properties, as w ill be seen in Chapter IX. 

Also plotted in Fig. 1.2 is the experimental heat capacity of the liquid (at omi-stant pressure) In simple cases, such as polyethylene, the heat capacity of the liquid state could be understood by introducing a heat capacity contribution for the excess volume (hole theory) and by assuming that the torsional skeletal vibration can be treated as a hindered rotator A more general treatment makes use of a separation of the partition function into the vibrational part (approximated for heat capacity by the spectrum of the solid), a conformational part (approximated by the usual conformational statistics) and an external or configurational part. 

Generally, therefore, these additional functions are connected with the departures from additivity shown by the volume F, the heat capacity and the chemical constant i and the enthalpy H on dilution of the solution. They find their tangible expression in volume contractions, heat effects and anomalous behavior of specific heats. Physically they should be attributed to an excess or deficiency in attraction between the molecules of solvent and solute over the cohesion of identical molecules. Hildebrand has termed solutions in which additional entropy terms such as 2, 3 and 4 are missing, regular solutions (see p. 222). In them the excess and deficiency attractions may be related quantitatively to the heat of dilution, since in the insertion of molecules of one component between those of the other, a heat effect other than zero results because the energy necessary for the separation of identical molecules differs from that obtained in bringing together dissimilar particles. 

Because Gibbs energy as a function of T and P is a fundamental equation ( 4.12.1), excess Gibbs energies can be used to calculate not only activity coefficients but all other deviations from ideal behavior, such as osmotic coefficients, excess enthalpies, excess heat capacities, excess volumes, and so on ( 10.4), so it is potentially quite informative. Also, properties calculated from in this way will be entirely self-consistent, which might not be the case if each property was determined separately. 

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