Chemical equilibrium condensed phases

The understanding of isotope effects on chemical equilibria, condensed phase equilibria, isotope separation, rates of reaction, and geochemical and meteorological phenomena, share a common foundation, which is the statistical thermodynamic treatment of isotopic differences on the properties of equilibrating species. For that reason the theory of isotope effects on equilibrium constants will be explored in considerable detail in this chapter. The results will carry over to later chapters which treat kinetic isotope effects, condensed phase phenomena, isotope separation, geochemical and biological fractionation, etc. 

At equilibrium condensed phase, the rotation of motor has equal probabilities of forward and backward motions based on the principle of detailed balance. Therefore, unidirectional motion results only when the motor is at nonequilibrium state because of some chemical or electrochemical force hence the motion of motor is a dissipative process taking place at nanoscale and affected by thermal flucmations. The cycle of the motor corresponds to the full revolution (360°) with 5 = 6 substeps and to the hydrolysis of three ATP molecule ... 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

Chemical equilibrium methods provide useful predictions of the EOS of detonation processes and the product molecules formed, but no details of the atomistic mechanisms in the detonation are revealed. We now discuss condensed-phase detonation simulations using atomistic modeling techniques to evaluate reaction mechanisms on the microscopic level. 

Notice most often that studies on chemical equilibrium in the gas phase are carried out at constant T and V, while those involving only condensed phases will usually be studied at constant T and P. Condition 4.35 applies to either situation. 

STANJAN The Element Potential Method for Chemical Equilibrium Analysis Implementation in the Interactive Program STANJAN, W.C. Reynolds, Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, 1986. A computer program for IBM PC and compatibles for making chemical equilibrium calculations in an interactive environment. The equilibrium calculations use a version of the method of element potentials in which exact equations for the gas-phase mole fractions are derived in terms of Lagrange multipliers associated with the atomic constraints. The Lagrange multipliers (the element potentials ) and the total number of moles are adjusted to meet the constraints and to render the sum of mole fractions unity. If condensed phases are present, their populations also are adjusted to achieve phase equilibrium. However, the condensed-phase species need not be present in the gas-phase, and this enables the method to deal with problems in which the gas-phase mole fraction of a condensed-phase species is extremely low, as with the formation of carbon particulates. 

The quasi-equilibrium theory (QET) of mass spectra is a theoretical approach to describe the unimolecular decompositions of ions and hence their mass spectra. [12-14,14] QET has been developed as an adaptation of Rice-Ramsperger-Marcus-Kassel (RRKM) theory to fit the conditions of mass spectrometry and it represents a landmark in the theory of mass spectra. [11] In the mass spectrometer almost all processes occur under high vacuum conditions, i.e., in the highly diluted gas phase, and one has to become aware of the differences to chemical reactions in the condensed phase as they are usually carried out in the laboratory. [15,16] Consequently, bimolecular reactions are rare and the chemistry in a mass spectrometer is rather the chemistry of isolated ions in the gas phase. Isolated ions are not in thermal equilibrium with their surroundings as assumed by RRKM theory. Instead, to be isolated in the gas phase means for an ion that it may only internally redistribute energy and that it may only undergo unimolecular reactions such as isomerization or dissociation. This is why the theory of unimolecular reactions plays an important role in mass spectrometry. 

If we equate the chemical potential of the solute in the condensed phase with the chemical potential of the solute in the gas phase at equilibrium, we obtain... 

Although these chemical effects are important in deciphering the genesis of ore minerals, it must be emphasized that the differences in the 8 8 values among coexisting condensed phases (hence the fractionation factor) at equilibrium are constant in each case because they depend only on T. 

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