Entropy change calculations

Thermodynamic methods, which have been those most widely used in the past, utilize isotherms and heats of adsorption as their foundations. Entropy changes calculated from such data are not easy to transform unambiguously into specific descriptions of the adsorbed phase. 

Figure 17.3c compares if , G and TS with the entropy change calculated from... 

This section outlines procedures for calculating entropy changes that occur in the system and in the surroundings during several types of processes. The final subsections show how entropy changes calculated for the thermodynamic universe (system plus surroundings) predict whether a particular contemplated process can occur spontaneously when attempted in the laboratory or in a chemical plant. 

It is this concept of reversibility which must be applied when entropy changes are calculated. There is, however, no reason why the actual process should occur reversibly, because entropy is a function of state, and AS is the same, whatever the route. It is frequently necessary to devise, on paper, a reversible route merely to perform the entropy-change calculation. Let us apply these ideas to specific examples. 

Due to the negative entropy change calculated above, we expect that AG° will become positive at some temperature higher than 300°C. We need to find the temperature at which AG° becomes zero. This is the temperature at which reactants and products are equally favored (Kp = 1). 

Die above calculated results utilize the 5 MHz mechanical resonance. They further demonstrate how readily calculations based on the dynamic structure given in Rgure 3 calculate experimental dielectric relaxation data with inherent relevance to entropic elastic force. The values for entropy change calculated... 

Association constants were determined spectrophotometrically in chloroform at 20 by utilising the different spectra of the two stereochemical forms. Enthalpies of association were determined calorimetrically. where possible, and the corresponding entropy changes calculated. The results refer, for the most part, to complexes of Co(lI) though thermodynamic data are also available for a few Ni(ll) systems. 

Clausius s analysis showed that, although is not a state function and is path dependent, the entropy changes calculated using Equation 8.7 are independent of the path taken, so entropy is a state function. 

Table 19.2 shows the parameters of the conversion including enthalpy and entropy changes calculated from the temperature dependence of the equilibrium constants (relative spectral area were considered proportional to chemical concentrations). 

We are not ready yet to carry out calculations involving power plants. We will do it after we discuss entropy change calculations. 

We are ready now to carry out entropy change calculations and use them in applications of the second law, such as the establishment of the feasibility of processes and the efficient utilization of energy in them. 

A moment s reflection will convince us that these probabilities can be used as thermodynamic probabilities in Eq. (3.21) to calculate the entropy change on stretching ... 

The small value of the entropy change reflects the fact that only liquids are involved in tlris reaction. The heat balance in canying out tlris reaction may be calculted, according to Hess s law, by calculating tire heat change at room temperarnre, and subtracting tire heat required to raise the products to the hnal teirrperamre. The data for tlris reaction are as follows ... 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

Table 17.1 can be used to calculate the standard entropy change, AS°, for reactions, using the relation... 

AS° for this system at 25°C and 1 atm can be calculated from a table of standard entropies it is found to be —358.4 J/K. The negative sign of AS° is entirely consistent with the second law. All the law requires is that the entropy change of the surroundings be greater than 358.4 J/K, so that ASunIverse > 0. 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

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