Entropy units

Give an equation for A5 in ealories per mole per degree Kelvin. (This combination of units is called an entropy unit, eu.)... 

The mechanism of the cycloaddition of phenyl azide to norbornene has been shown to involve a concerted mechanism with a charge imbalance in the transition state (199). In a similar manner the cycloaddition of phenyl azide to enamines apparently proceeds by a concerted mechanism (194, 194a). This is shown by a rather large negative entropy of activation (—36 entropy units for l-(N-morpholino)cyclopentene in benzene solvent at 25°C), indicative of a highly ordered transition state. Varying solvents from those of small dielectric constants to those of large dielectric constants has... 

AS n values for fragmentation reactions like the one shown above are typically of the order of 40 to 60 eu (1 eu or entropy unit = 1 cal/mol-K). Use an average value for AS and your calculated AH n to estimate AG at 298 K (use equation 1). Do these new data affect any of your conclusions about which alcohols are likely to be stable and which are likely to be nonexistent ... 

Returning now to silver chloride, let us apply these ideas to its saturated aqueous solution at 25°. From the value given in Table 42, we see that in solid AgCl the entropy per ion pair is almost exactly 1 milli-electron-volt per degree, which is equivalent to 23.0 cal/deg/mole. It makes no difference whether we express the entropies per ion pair in electron-volts per degree or in the equivalent calories per degree per mole. In the electrochemical literature the calorie per degree per mole is used and is called one entropy unit. (This is abbreviated e.u.) ... 

Heats of fusion, AHfus, are generally expressed in kcal/mol or kJ/mol and entropies of fusion, ASlus in cal/mol-K (e.u. or entropy unit) or J/mol K. The fugacity ratio F, as discussed in Section 1.2.8, is used to calculate the supercooled liquid vapor pressure or solubility for correlation purposes. In the case of liquids such as benzene, it is 1.0. For solids it is a fraction representing the ratio of solid-to-liquid solubility or vapor pressure. 

When using AG° = AH°rxn - T A5°rxn, pay particular attention to your enthalpy and entropy units. Commonly, enthalpies will use kj and entropies J. 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

Barrer (3) makes similar calculations for the entropies of occlusion of substances by zeolites and reaches the conclusion that the adsorbed material is devoid of translational freedom. However, he uses a volume, area or length of unity when considering the partition function for translation of the adsorbed molecules in the cases where they are assumed to be capable of translation in three, two or one dimensions. His entropies are given for the standard state of 6 = 0.5, and the volume, area or length associated with the space available to the adsorbed molecules should be of molecular dimensions, v = 125 X 10-24 cc., a = 25 X 10-16 cm.2 and l = 5 X 10-8 cm. When these values are introduced into his calculations the entropies in column four of Table II of his paper come much closer together, as is shown in Table I. The experimental values for different substances range from zero to —7 cals./deg. mole or entropy units, and so further examination is required in each case to decide... 

It is of some interest to apply Trouton s rule (entropy of vaporization at the boiling point is a constant) to the above data. Unfortunately, boiling points are known only for nitric acid and some of the aliphatic nitrates. Their Trouton constants (AH p/Tbp) are 20.2 and ca 22.8 entropy units, respectively. Thus they straddle the normal Trouton constant of 21 eu. This observation, coupled with the observed constancy of the specific heat of vaporization, suggests that intermolecular bonding in nitrate esters may be relatively weak, or at least consistent... 

For very many liquids, the entropy of vaporization at the normal boiling point is approximately 21 cal/mole °C water is not typical. The units for changes in entropy are the same as those for molar heat capacity, and care must be used to avoid confusion. When referring to an entropy change, a cal/mole °C is often called an entropy unit, abbreviated e.u. In order to avoid later misunderstanding, note now that this method of calculating AS from A HIT is valid only under equilibrium conditions. For transitions, for example, this method can be used only at temperatures where the two phases in question can coexist in equilibrium with each other. 

Entropy is measured in units of joules per kelvin (or °C) or calories per K, the latter sometimes being abbreviated as e. u. (entropy units). Since the melting of ice at 0°C is a reversible process, the second law asserts that the entropy of the surroundings decreases by the same amount that the entropy of the water increases. The value of T AS is numerically equal to the heat of fusion, 6.008 kj mol1 in the case of water at 0°C. Thus, the entropy increase in the ice as it melts at 0°C is 6.008 x 103 J/273.16 K = 22.0 J K1. 

Stiff vibrations, as found in most covalent bonds, make very low individual contributions to the entropy. Low-frequency vibrations, where the atoms are less constrained, can contribute a few entropy units. Internal rotations have entropies in the range of 13 to 21 J/deg/mol (3 to 5 cal/deg/mol) (Table 2.4). 

The transition has also been detected in dielectric studies at frequencies from 103 to 107 cps (Mikhailov, Kabin, and Smolyanskii). The activation energy for the transition is 18 kcal per mole, and the activation entropy is 45 entropy units per mole. From the breadth of the loss peak in Fig. 8, it has been determined that more than a single relaxation time is required. 

Thus for a 3% error in k2 and kx and a 25-35° temperature interval, the statistical error in AS is + 2.6 e.u. From this analysis it is evident that only kinetic data of high precision will serve to establish entropies of activation to within one entropy unit. 

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