Entropy, translational

Vibrational frequencies Rotational enthalpy and entropy Vibrational enthalpy and entropy Translational enthalpy and entropy... 

Solubility of polymers, that is, ability to dissolve spontaneously in low-molecular-weight solvent and to form thermodynamically stable molecular solutions, is determined by a delicate interplay between the gain in conformational entropy, translational and orientational entropy of solvating molecules of low-molecular-weight solvent, and enthalpy change upon polymer dissolution. Therefore, solubility of polymer in a particular solvent strongly depends on temperature. Usually, polymers with nonpolar monomer groups are more soluble in nonpolar solvents, whereas polymers whose... 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

Fig. 3-11 shows that, foi watei, entropy and heat capacity ai e summations in which two terms dominate, the translational energy of motion of molecules treated as ideal gas paiticles. and rotational, energy of spin about axes having nonzero rnorncuts of inertia terms (see Prublerris). 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

Values extracted and in some cases rounded off from those cited in Rabinovich (ed.), Theimophysical Fropeities of Neon, Ai gon, Kiypton and Xenon, Standards Press, Moscow, 1976. This source contains an exhaustive tabulation of values, v = specific volume, mVkg h = specific enthalpy, kj/kg s = specific entropy, kJ/(kg-K). The notation 3.49.—4 signifies 3.49 X 10 . This book was published in English translation by Hemisphere, New York, 1988 (604 pp.). 

The standard entropies of monatomic gases are largely determined by the translational partition function, and since dris involves the logarithm of the molecular weight of the gas, it is not surprising that the entropy, which is related to tire translational partition function by the Sackur-Tetrode equation,... 

FIGURE 16.4 Formation of the ES complex results in a loss of entropy. Prior to binding, E and S are free to undergo translational and rotational motion. By comparison, the ES complex is a more highly ordered, low-entropy complex. 

Translational Contribution to Entropy We start with equation (10.82)... 

Solution Ar is a monatomic gas with Zm.eica = 1. The translational contribution is the only one we need to consider. For Ar, M = 0.039948 kg-mol-1. We want the standard state entropy when p = 1.000 x 105 Pa. Substituting into the equation in Table 10.4 gives... 

In crystals for which n0 is large, such as iodine, the lowest symmetric and the lowest antisymmetric state have practically the same energy and properties, and each corresponds to one eigenfunction only. As a result a mixture of symmetric and antisymmetric molecules at low temperatures will behave as a perfect solid solution, each molecule having just its spin quantum weight, and the entropy of the solid will be the translational entropy plus the same entropy of mixing and spin entropy as that of the gas. This has been verified for I2 by Giauque.17 Only at extremely low temperatures will these entropy quantities be lost. 

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