Entropy of Reactions

Both for reaction in and IV the order with respect to catalyst is 0.5. The activation enthalpies are 96.6 3.4 and 97.6 3.4 kJ mol-1 respectively when Ti(OBu)4 is used as the catalyst. This is not too far from the activation enthalpies200 for the Sn(II)-cata-lyzed esterification of B with isophthalic acid (85.1 4.9) and with 2-hydroxyethyl hydrogen isophthalate (85.8 4.2). It is also close to the Ti(OBu)4-catalyzed esterification of benzoic acid with B (85.8 2.5)49. This is probably due to the formation of analogous intermediate complexes and similar catalytic mechanisms. On the other hand, the activation entropies of reactions III and IV are less negative than those of the reaction of benzoic or isophthalic acid with B. This probably corresponds to a stronger desolvation when the intermediary complex is formed and could be due to the presence of the sodium sulfonate group. 

Fortunately, there is evidence of a quite different kind available which at least provides a strong indication as to which mechanism is the more probable. In Table 2 are summarised the entropies of reaction (AS°ss) and activation (AS+) for the polymerisations of DXL, DXP, and THF. Four features are immediately evident (1) The AS1 is about the same for DXL and DXP initiated by perchloric acid (2) the AS+ for DXL is about the same for initiation by perchloric acid and by (VII) (3) the AS+ for DXL and DXP are much more negative than for THF and (4) for DXL and DXP the AS1 are considerably more negative than the corresponding AS°ss. 

Table 2 Entropies of reaction (AS°ss) and activation (AS ) for polymerisation of DXL, DXP, and THF in cal deg1 mol1 (rounded to nearest...

We may also calculate AG° for a reaction by using the standard enthalpy and standard entropy of reaction ... 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

It is difficult to discuss the accuracy of the thermochemical results reported by Oldani and Bor, because they rely on some estimated data of unknown reliability. Based on a simple model that is used to predict reaction entropy changes, we anticipate that the entropy of reaction 14.21 would be considerably larger than 300 J K-1 mol-1, possibly even higher than 400 J K-1 mol-1 [226]. 

Conventional absorptiometric and fluorimetric pH indicators show a shift of band positions in absorption and emission spectra between the protonated and deprotonated forms. This feature allows the spectroscopic measurement of the acid dissociation constant in the ground state, Ka, and also the evaluation of the dissociation constant in the excited state, Ka (Eq. (5.5)), from the Forster cycle under the assumption of equivalent entropies of reaction in the two states.<109 112)... 

Examples 31-33 are for the steam dealkylation of toluene. The reaction is complicated, and there are several possibilities for a rate-determining step. For Example 31 Kochloefl 103) found that water adsorbs better than toluene, suggesting the possibility of Step 11 for H2O, for which log L= 14. Grenoble 104) reported several transition-metal catalyzed dealkylations of toluene one of his systems is described in Example 32. The orders in the various reactions reported vary in several the order in toluene is negative. But log L = 8 for Step 11 for toluene in Example 32 is rather low. It is just possible that in Examples 31-33 that a modification of Step 5 should be considered. The modification would take into account the fact that HjO and toluene compete for sites and the entropy of reaction is not zero, contrary to the usual entropy assumption made for Step 5. 

The entropy of reaction is the difference in the entropy of the products and reactants ... 

This negative entropy of reaction would tend to inhibit this reaction from proceeding. 

The entropy of reaction by itself, however, is not sufficient to predict the direction of a reaction. At 25° C, you know that H2O (1) is the stable phase, not H20(g). Moreover, the second reaction... 

Given a listing of free energies of formation, the free energy change of a chemical reaction may he calculated in the same manner as you evaluated enthalpies of reaction and entropies of reaction. For the reaction that was discussed earlier,... 

Data for secondary master species and product species include the stoichiometry and logI0 K° of the formation reactions, the standard Gibbs energy of reaction (ArGm), the standard enthalpy of reaction (Athe standard entropy of reaction (Ar5m), the standard isobaric heat capacity... 

At any given temperature T, the thermodynamic equilibrium constant K° for a given reaction is related to the standard enthalpy of reaction AH and the entropy of reaction AS , by... 

Typical pressure-composition isotherms for the LaNi5-H2 system are shown in Figure 2 (14). From plots of In Pplateau vs- 1 / T, several workers determined the experimental heats and entropies of Reaction 1. The enthalpies are the heats of formation for the /J-phase hydride from the a-phase hydrogen-saturated alloy (see Table I). 

It is for this reason (that AG = 0) that we were able to calculate standard entropies of transition by simply dividing the enthalpies of transition by the Kelvin temperature of transition as we did on p 214. Entropies of reaction cannot be calculated this way the more general expression must be used. 

AGrxn has two components, the enthalpy of reaction, AHrxn, and the entropy of reaction, ASrxn. These are defined by the following formulas ... 

Standard Molar Entropies and Standard Entropies of Reaction... 

Once we have values for standard molar entropies, it s easy to calculate the entropy change for a chemical reaction. The standard entropy of reaction, AS°, can be obtained simply by subtracting the standard molar entropies of all the reactants from the standard molar entropies of all the products ... 

Calculate the standard entropy of reaction at 25°C for the synthesis of ammonia ... 

To determine the sign of AStotai = ASsys + ASsurr/ we need to calculate the values of ASsys and ASsurr. The entropy change in the system equals the standard entropy of reaction and can be calculated using the standard molar entropies in Table 17.1. To obtain ASsurr = —AH°/T, first calculate AH° for the reaction from standard enthalpies of formation (Section 8.10). 

The standard molar entropy, S°, of a substance is the absolute entropy of 1 mol of the pure substance at 1 atm pressure and a specified temperature, usually 25°C. The standard entropy of reaction, AS0, can be calculated from the relation AS° = S°(products) — S°( reactants). 

What is meant by the standard molar entropy of a substance How are standard molar entropies used to calculate standard entropies of reaction ... 

What are the units of (a)standard molar entropies and (b) standard entropies of reaction Why are standard molar entropies sometimes called absolute entropies ... 

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