Entropy change, from

Doubling the number of molecules increases the number of microstates from W to W2, and so the entropy changes from k In W to k In W2, or 2k In W. Therefore, the statistical entropy, like the thermodynamic entropy, is an extensive property. 

This equation shows how to calculate the total entropy change from information about the system alone. The limitation is that the equation is valid only at constant temperature and pressure. 

Deducing the electronic entropy change from the specific heat, it appears that about one-third is due to the electrons. The rest must be the result of soft phonon modes. 

Typically the experiment with a transactinoid element lasts days or even weeks, and results in a single experimental value of the adsorption constant. The only possibility to obtain an estimate of the adsorption enthalpy based on such a result is to calculate the entropy change from the first principles [4] and substitute it into Eq. 5.7. The values of Aa( sS are calculated from the formulae of statistical mechanics for the particular model of the adsorbed state. The evaluation starts with the partition function of single molecule qm and with the molar partition function Z to calculate the absolute molar entropy from the general equation ... 

AS° = iiS°(products) — HjS°(reactants) -AH,y, surr Y [19.8] [19.9] Calculating the standard entropy change from standard molar entropies The entropy change of the surroundings for a process at constant temperature and pressure... 

B. The final state (O in this case is a vapor-liquid mixture that contains a vapor fraction Xv = 0.47 and a liquid fraction Xl = 0.53. The entropy change from the initial state up to saturated vapor is the same as before. When the... 

The entropy change caused by mixing polymer and swelling agent. The entropy change from this source is positive and favors swelling. 

AS° = 2 S°(products) — mS°(reactants) [19.8] Calculating the standard entropy change from standard molar entropies... 

Estimating magnetic entropy change from magnetization measurements... 

The two effects are independent. The entropy change from dehydration, and from other changes involving the solvent, is included in the observed association constant and binding free energy. The important loss of translational and rotational entropy refers to the loss of the quantities needed to reach the transition state. The observed entropy of activation includes both of these contributions, which are not easily distinguishable. The contribution of translational and rotational entropy is estimated by comparison of the rate constants for bimolecular and intramolecular reactions. 

To proceed further with the analysis it is necessary to isolate the contribution of the conformational entropy change from the total entropy of fusion. A simplifying assumption that can be made is that A5 is the sum of two parts the entropy change due to the latent volume change in melting, A5y, and entropy change that takes place at constant volume (A5 ) .(225,226) Thus, in this approximation... 

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