Standard molar entropy of formation

Besides equilibriumconstants, additional thermodynamic data were included, if available, although little emphasis was put on their completeness. The data for primary master species comprise the standard molar thermodynamic properties of formation from the elements (AfG standard molar Gibbs energy of formation AfH°m standard molar enthalpy of formation ApSm- standard molar entropy of formation), the standard molar entropy (5m), the standard molar isobaric heat capacity (Cp.m), the coefficients Afa, Afb, and Afc for the temperature-dependent molar isobaric heat capacity equation... 

By a similar procedure, evaluate the standard molar entropy, the standard molar entropy of formation, and the standard molar Gibbs energy of formation of crystalline silver chloride at 298.15 K. You need the following standard molar entropies evaluated from spectroscopic and calorimetric data ... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

We have now answered the fundamental question posed at the beginning of this chapter What determines the value of the equilibrium constant—that is, what properties of nature determine the direction and extent of a particular chemical reaction The answer is that the value of the equilibrium constant is determined by the standard free-energy change, A G°, for the reaction, which depends, in turn, on the standard heats of formation and the standard molar entropies of the reactants and products. 

These are the properties of the monatomic gas at a pressure of 1 bar. It should be pointed out that this standard molar Gibbs energy is not the AfG° of thermodynamic tables because there the convention in thermodynamics is that the standard formation properties of elements in their reference states are set equal to zero at each temperature. However, the standard molar entropies of monatomic gases without electronic excitation calculated using equation 2.8-11 are given in thermodynamic tables. 

R. A. Alberty, Standard molar entropies, standard entropies of formation, and standard transformed entropies of formation in the thermodynamics of enzyme-catalyzed reactions, J. Chem. Thermodyn., in press. 

These standard transformed entropies of formation determine the contributions these reactants make to the apparent equilibrium constant for an enzyme-catalyzed reaction, but the more fundamental property, the standard molar entropies of species, are discussed in Chapter 15. 

As mentioned in Sections 1.1 and 2.9, the third law of thermodynamics makes it possible to obtain the standard Gibbs energy of formation of species in aqueous solution from measurements of the heat capacity of the crystalline reactant down to about 10 K, its solubility in water and heat of solution, the heat of combustion, and the enthalpy of solution. According to the third law, the standard molar entropy of a pure crystalline substance at zero Kelvin is equal to zero. Therefore, the standard molar entropy of the crystalline substance at temperature T is given by... 

The standard molar entropy of acetic acid at 298.15 K can be calculated using the program calcentropy298. To calculate S ° for the acetate ion in dilute aqueous solution at 298.15 K and zero ionic strength, the formation reaction is balanced by adding H (aq) on the right side. 

In this case the hydrogen ion is added to the left side to balance the formation reaction. For more complicated organic weak acids it is useful to remember that the atomic composition to be used in calcentropy298 for each species is that shown for the uncharged form in the Merck Index (9). The standard molar entropies of species in kJ K" mol are calculated using theAf5 ° in Table 15.1. 

The factors of 2 multiply 5° for NO2 and O2 because 2 mol of each appears in the chemical equation. Note that standard molar entropies, unlike standard molar enthalpies of formation AH°, are not zero for elements at 25°C. The negative A5° results because this is the entropy change of the system only. The surroundings must undergo a positive entropy change in such a way that A5jot — 0-... 

EFI/PRO] Efimov, M. E., Prokopenko, L V., Tsirelnikov, V. L, Troyanov, S. L, Medvedev, V. A., Berezovskii, G. A., Paukov, L E., Thermodynamic properties of zirconium chlorides. I. The standard molar enthalpy of formation, the low-temperature heat capacity, the standard molar entropy, and the standard molar Gibbs energy of formation of zirconium trichloride, J. Chem. Thermodyn., 19, (1987), 353-358. Cited on pages 163, 164, 333,335,338. 

Unlike enthalpies of formation, standard molar entropies of elements at the reference temperature of 298 K are not zero. 

The standard molar entropy of hydration of an ion, Ahydr5° , should contain contributions from the formation of the ionic hydration shell and also from the limitation of the ionic rotation of a multiatomic ion in the solution compared with the gas. Hence, such contributions should be deducted, according to Krestov (1962, 1962a), from Ahydr5° in order to obtain the water structural effects of the ion beyond the hydration shell, Astmc (AS ii in the notation of Krestov) ... 

Because entropy is a state function and because the third law allows us to obtain a value for the standard molar entropy of any substance, we can derive a useful equation for the entropy change in a reaction. Figure 10.5 shows how the entropy change in a reaction may be determined by a method that is reminiscent of the way we used heats of formation and Hess s law in Chapter 9. 

Any time we are asked to calculate the standard entropy change for a reaction, our first thought should be to look up values for standard molar entropy and use them in Equation 10.3. The two main things we need to be careful about are (1) to watch the state of the substances (in this case all are gases) and (2) to make sure we don t forget to include the stoichiometric coefficients in our calculations. Unlike heats of formation, the standard molar entropy of an element in its standard state is not zero, so we need to be sure to include everything appearing in the equation. 

Recall that the standard molar enthalpies of formation needed in Eq. 11.8.23 can be evaluated by calorimetric methods (Sec. 11.3.2). The absolute molar entropy values S° come from heat capacity data or statistical mechanical theory by methods discussed in Sec. 6.2. Thus, it is entirely feasible to use nothing but calorimetry to evaluate an equilibrium constant, a goal sought by thermod5mamicists during the first half of the 20th century. ... 

Use the following experimental information to evaluate the standard molar enthalpy of formation and the standard molar entropy of the aqueous chloride ion at 298.15 K, based on the... 

Apart from standard molar enthalpies of formation Af T (r) of substances B (see Section 8), most commonly given at T = 298.15 K and at r -> 0, and standard molar entropies iS (3T) (see Section 9) and standard molar heat capacities C, b(T), each most commonly given at T = 298.15 K, other quantities found in thermodynamic tables include values of the increments in the standard molar enthalpies, especially... 

Structural Entropy A molar structural entropy of ions in solution, A 5, is obtained from the standard molar entropy of solvation of the ion, when certain irrelevant quantities are subtracted from the latter. These include the compression entropy (change of available volume) on transfer from the gas to the solution and contributions from the formation of the ionic solvation shell and possible limitation of the ionic rotation of a polyatomic ion in the solution compared with the gas. The terms kosmottopes for water structure-making ions and chaotropes for water structure-breaking ions were introduced by Collins [48] (Section 5.1) according to whether A S < or respectively. This view sfressed the competition... 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

But how do we find the standard entropies of the reactants and products Recall from Chapter 6 that we defined standard molar enthalpies of formation (A/7 ) to use in calculating A. We now need to define standard molar entropies (S ) to use in calculating A. ... 

The heats of formation, the standard molar entropies at 298 K, are given below. 

Calculate the standard Gibbs free energy of formation of HI(g) at 25°C from its standard molar entropy and standard enthalpy of formation. 

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

Entropy changes are important in every process, but chemists are particularly interested in the effects of entropy on chemical reactions. If a reaction occurs under standard conditions, its entropy change can be calculated from absolute entropies using the same reasoning used to calculate reaction enthalpies from standard enthalpies of formation. The products of the reaction have molar entropies, and so do the reactants. The total entropy of the products is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients in the balanced chemical equation. The total entropy of the reactants is a similar sum for the reactants. Equation... 

Self-Test 7.17A Calculate the standard free energy of formation of NH3(g) at 25°C from the enthalpy of formation and the molar entropies of the species involved in its formation. 

Write a chemical equation for the formation reaction and then calculate the standard free energy of formation of each of the following compounds from the enthalpies of formation and the standard molar entropies, using AGr° = AH° — TAS° (a) NH3(g) ... 

---