Thermodynamics calculating entropy change

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. 

The third law of thermodynamics states that the entropy of any pure substance in equilibrium approaches zero at the absolute zero of temperature. Consequently, the entropy of every pure substance has a fixed value at each temperature and pressure, which can be calculated by starting with the low-temperature values and adding the results of all phase transitions that occur at intervening temperatures. This leads to tabulations of standard molar entropy S° at 298.15 K and 1 atm pressure, which can be used to calculate entropy changes for chemical reactions in which the reactants and products are in these standard states. 

In these researches, a mainly purpose is to acquire EPHs of cell or half-cell reactions. The EPH could be considered as a basic issue of TEC. Before the identification of this problem there had been two puzzled questions, one is that the heat effects for a reversible reaction, Q can be calculated by the formula Q = TAS where AS is the entropy change of this reaction and T temperature in Kelvin. However, this formula that is valid for most reactions is not viable at least for a reversible single electrode reaction in aqueous solution. For a reversible single electrode reaction, the experimental value of the heat effect is not in agreement with that calculated on the current thermodynamic databank of ions, that is, with which, the product of the calculated entropy change and the temperature of the electrode reaction always differs from the experimental measurements [2]. For example, for the electrode reaction at the standard state ... 

The third law of thermodynamics asserts that if the entropies of all samples of pure perfect crystalline elements are taken as zero, the entropies of all samples of pure perfect crystalline compounds can also consistently be taken as zero. Entropies relative to the entropy at zero temperature are called absolute entropies. The values of these absolute entropies can be used to calculate entropy changes of chemical reactions. 

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 ... 

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. 

To calculate the entropy of a substance, we use Boltzmann s formula, but the calculations are sometimes very difficult and require a lot of manipulation of Eq. 6. To measure the entropy of a substance, we use the thermodynamic definition, Eq. 1, in combination with the third law of thermodynamics. Because the third law tells us that S(0) = 0 and Eq. 2 can be used to calculate the change in entropy as a substance is heated to the temperature of interest, we can write... 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

C14-0087. Calculate the standard entropy change at 298 K of each of the following reactions, which are important in the chemistry of coal. Assume that coal has the same thermodynamic properties as graphite. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

For several reversible reactions, the thermodynamic parameters for reaction in the quasi-free state are given in Table 10.6 using Eq. (10.16) and the reaction scheme (I). Experimental data for AX°(X = G, H, or S) are taken from Holroyd et al., (1975, 1979) and Holroyd (1977), while Table 10.5A provides data on AX r°, except for TMS (vide supra). The chief uncertainty in these calculations is the experimental determination of V0. It is remarkable that all thermodynamic parameters of reaction in the quasi-free state are negative in the same way as for the overall reaction. In particular, the entropy change is relatively large and probably for the same reason as for the overall reaction (Holroyd, 1977). 

To calculate the entropy changes, it is necessary to consider a series of reversible steps leading from liquid water at —10°C to sohd ice at —10°C. One such series might be (1) Heat supercooled water at —10°C very slowly (reversibly) to 0°C, (2) convert the water at 0°C very slowly (reversibly) to ice at 0°C, and (3) cool the ice very slowly (reversibly) from 0°C to —10°C. As each of these steps is reversible, the entropy changes can be calculated by the methods discussed previously. As S is a thermodynamic property, the sum of these entropy changes is equal to AS for the process indicated by Equation (6.97). The necessary calculations are summarized in Table 6.2, in which T2 represents 0°C and Ti represents 10°C. 

Now that we have considered the calculation of entropy from thermal data, we can obtain values of the change in the Gibbs function for chemical reactions from thermal data alone as well as from equilibrium data. From this function, we can calculate equilibrium constants, as in Equations (10.22) and (10.90.). We shall also consider the results of statistical thermodynamic calculations, although the theory is beyond the scope of this work. We restrict our discussion to the Gibbs function since most chemical reactions are carried out at constant temperature and pressure. 

This equilibrium open-circuit potential for a H2/air fuel cell is calculated from thermodynamic data of reaction enthalpy and entropy changes. 

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. 

While the first law allows us to calculate the energy change associated with a given process, it says nothing about whether or not the process itself will take place spontaneously. This is the province of the second law of thermodynamics and leads to the introduction of another state function, entropy, S. The entropy change in a system which moves from state 1 to state 2 is defined by... 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

So far, we have been able to calculate only changes in the entropy of a substance. Can we determine the absolute value of the entropy of a substance We have seen that it is not possible to determine absolute values of the enthalpy. However, entropy is a measure of disorder, and it is possible to imagine a perfectly orderly state of matter with no disorder at all, corresponding to zero entropy an absolute zero of entropy. This idea is summarized by the third law of thermodynamics ... 

The entropy of a solution is increased by the mixing of solvents, and it is decreased by interactions among the solvent molecules or interactions of solutes with the solvent. The mixing of two miscible liquids is a thermodynamically favorable process because it increases the number of positions available to the molecules. The entropy change on going from the unmixed liquids to the mixed state can be calculated from the expression... 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

As entropy is a state function, we are free to choose a path from the initial and final states. The path along which a process takes place reversibly would be most convenient for thermodynamic calculations, because the heat absorbed or released can be directly related to the entropy change ... 

By calculating the enthalpy of the reaction and assuming no significant entropy change, the AH (based on heats of formation and heats of fusion) of Equation 3 is approximately +5.2 kcal/mole and of Equation 4 is approximately +10.5 kcal/mole. While both reactions are not favored thermodynamically, at high temperatures (i.e., 375°C), these reactions will establish an equilibrium where significant amounts of KOH and/or K+ and OH" may exist. 

In order to usefully apply the second law, it will be necessary to be able to calculate both AS, the entropy change in the system of interest, and A,S sur, the entropy change of the surroundings. (Thermodynamic functions without the subscript sur can be assumed to refer to the system.) The mathematical form of our second law then becomes... 

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