Thermodynamics first principle

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

In many cases one can apply the first principles of thermodynamics and chemical kinetics to natural systems only with caution. The reason... 

Later we shall see how fundamental quantities such as /i can be estimated from first principles (via a basic knowledge of the molecule such as its molecular weight, rotational constants etc.) and how the equilibrium constant is derived by requiring the chemical potentials of the interacting species to add up to zero as in Eq. (20). The above equations relate kinetics to thermodynamics and enable one to predict the rate constant for a reaction in the forward direction if the rate constant for the reverse reaction as well as thermodynamic data is known. 

Stampfl C, KreuzerHJ, Payne SH, PfniirH, Scheffler M. 1999. First-principles theory of surface thermodynamics and kinetics. Phys Rev Lett 83 2993. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

Wang JH and Liu M. Surface regeneration of sulfur-poisoned Ni surfaces under SOFC operation conditions predicted by first-principles based thermodynamic calculations. 

First law of thermodynamics, 24 645-648 First limiting amino acid, 2 601 First-order irreversible chemical kinetics, 25 286-287, 292-293 First-principle approach, in particle size measurement, 13 153 First sale doctrine, 7 793 Fischer, Emil, 16 768 Fischer carbene reaction, 24 35-36 Fischer esterification, 10 499 Fischer formula, 4 697 Fischer-Indole synthesis, 9 288 Fischer lock and key hypothesis, 24 38 Fischer-Tropsch (FT) synthesis, 6 791, 827 12 431... 

Theoretical calculations [43] based on first principles molecular dynamics discussed in Sect. 3.2.6 have suggested that Mg Al LDHs are most stable for n = 3 (i.e. x = 0.25) and indeed many minerals, including hydrotalcite itself, have this stoichiometry [4]. It has been reported that the synthesis of LDHs (with benzoate or terephthalate anions in the interlayers) from solutions containing Mg/Al = 2, leads to LDHs having the same composition when the synthesis is carried out at moderate temperatures but LDHs with Mg/Al = 3 (plus AlOOH) when the reaction is carried out under hydrothermal conditions [44]. It was proposed that the latter ratio represents the thermodynamically most favorable product. A similar observation has been reported [45] for solutions with Ni VPe = 2, where hydrothermal preparation led to segregation of an LDH with Ni VPe = 3 and Ni Fe 204. An attempt to synthesize a Co sAl LDH resulted in partial oxidation of the Co and formation of a Co o.yCo o.s LDH with complete migration of Al " from the layers to generate interlayer aluminum oxy-species [46]. 

Y. Nakamori, K. Miwa, A. Ninomiya, H. Li, N. Ohba, S.-l. Towata, A. Ziittel, S.-l. Orimo, Correlation between thermodynamical stabilities of metal borohydrides and cation electronegatives First principles calculations and experiments , Phys. Rev. B 74 (2006) 45126. 

K. Miwa, N. Ohba, S. Towata, Y. Nakamori, A. Ztittel, S. Orimo, First-principles study on thermodynamical stability of metal borohydrides Aluminum borohydride A1(BH )2 , J. Alloys Compd. 446-447 (2007) 310-314. 

This is the fun (and frustration) of chemical reaction engineering. While thermodynamics, mass and heat transfer, and separations can be said to be finished subjects for many engineering apphcations, we have to reexamine every new reaction system from first principles. You can find data and construct process flowsheets for separation units using sophisticated computer programs such as ASPEN, but for the chemical reactors in a process these programs are not much help unless you give the program the kinetics or assume equihhrium yields. 

Given that quantum chemistry calculations directly provide electronic energies, which formally correspond to zero temperature and pressure, ways for connecting to finite, realistic temperature and pressure are needed. One method is first-principles thermodynamics (FPT), the basic concept of which is that the thermodynamically prevailing state of a surface is the one that minimizes the surface free energy, y, subject to external conditions such as temperature and the chemical potentials of the various components of the system ... 

For CFD modeling a detailed chemical mechanism for the relevant gas phase and surface reaction steps is necessary. Due to the difficulty involved in determining kinetic and thermodynamic parameters for the elementary steps, these are often based on empiricism and even guessing. Here, theoretical first-principles methods can be very helpful. 

Further improvement of the centroid method came with the introduction of centroid dynamics.Here the fundamental idea is to construct a centroid Hamiltonian in the full phase space of the system and the bath. The Boltzman factor is then the one obtained from this centroid Hamiltonian while seal time dynamics is obtained by running classical trajectories. This method has been applied to realistic systems " and recently derived from first principles.244 The main advantage of the centroid methodology is that thermodynamic quantum effects can be computed numerically exactly as it is not too difficult to converge numerically the computation of the centroid potential. 

The most common applications of DSC are to the melting process which, in principle, contains information on both the quality (temperature) and the quantity (peak area) of crystallinity in a polymer [3]. The property changes at Tm are often far more dramatic than those at Tg, particularly if the polymer is highly crystalline. These changes are characteristic of a thermodynamic first-order transition and include a heat of fusion and discontinuous changes in heat capacity, volume or density, refractive index, birefringence, and transparency [3,8], All of these may be used to determine Tm [8],... 

Dr. Berkowitz I must question the validity of Dr. Teichmiiller s rather definite conclusions about the relative roles of time, temperature, and pressure in the coalification process. From an examination of Ruhr coals, Dr. Teich-miiller said that only temperature plays a significant role. I suggest that conclusions drawn from data for coals in other areas (e.g., Alberta and Pennsylvania) would lead to the conclusion that pressure rather than temperature was the determining variable therefore, I doubt whether Dr. Teichmiiller s quite unqualified statements could have general validity. Indeed, from first principles one would deduce a rather complex and variable situation. Thermodynamically, one could perhaps rule out time as an important parameter since, unless one accepted the concept of a "tunnelling factor, time alone will not... 

First-principle calculations of the thermodynamic properties are more or less hopeless enterprise. One of the most famous phenomenological approaches was suggested by van der Waals [6, 8, 9]. Using the dimensionless pressure it = p/pc, the density v = n/nc and the temperature r = T/Tc, the equation of state for the ideal gas reads it = 8zzr/(3 -u) — 3zA Its r.h.s. as a function of the parameter v has no singularities near u = 1 v = it = t = is the critical point) and could be expanded into a series in the small parameter 77 = [n — nc)/nc with temperature-dependent coefficients. Solving this... 

In the realni of classical thermodynamics, equations of state arc assumed given. They can be derived from first principles only by the methods of statistical mechanics and quantum mechanics These rely on the adoption of suitable molecular models for substances, and so far no universal, generally applicable model has heen discovered even for narrow classes of subslunces such as gases. 

Type I. Figure 1 illustrates reversible refrigeration machines of Type I. This machine receives an amount of heat q reversibly at temperature Tc and discharges it reversibly at a higher temperature, Ta. By the first principle of thermodynamics the necessary energy input, w, must also be discharged reversibly at Ta. The coefficient of performance of this machine is the same as that of a Carnot refrigeration machine. Thus we have... 

---