Equihbrium calculations

A simple equihbrium calculation reveals that, at 25°C and atmospheric pressure, fluorine is less than 1% dissociated, whereas at 325°C an estimated 4.6% dissociation of molecular fluorine is calculated. Obviously, less than 1% of the coUisions occurring at RT would result in reaction if step la were the only important initiation step. At 325°C the fluorine atom initiation step should become more important. From the viewpoint of energy control, as shown in Table 1, it would be advantageous to have step lb predominate over step 2a and promote attack by molecular rather than atomic fluorine. Ambient or lower temperatures keep the atomic fluorine concentration low. 

The equiHbrium approach should not be used for species that are highly sensitive to variations in residence time, oxidant concentration, or temperature, or for species which clearly do not reach equiHbrium. There are at least three classes of compounds that cannot be estimated weU by assuming equiHbrium CO, products of incomplete combustion (PlCs), and NO. Under most incineration conditions, chemical equiHbrium results in virtually no CO or PlCs, as required by regulations. Thus success depends on achieving a nearly complete approach to equiHbrium. Calculations depend on detailed knowledge of the reaction network, its kinetics, the mixing patterns, and the temperature, oxidant, and velocity profiles. 

Based on Hquid—Hquid equiHbrium principles, a general model of octanol—water partitioning is possible if accurate activity coefficients can be determined. First, phase equiHbrium relationships based on activity coefficients permit Hquid—Hquid equiHbrium calculations for the biaary octanol—water system. Because the two components are almost immiscible ia each other, two phases form an octanol-rich phase containing dissolved water, and a water-rich phase containing dissolved octanol. 

We present results for two standard tin oxide precursors, DMTC and MBTC, as well as for tin tetrachloride. The latter compoimd is included in the analysis to provide perspective on the thermal stabihty of the inorganic system relative to the organometalhc ones. All chemical equihbrium calculations were performed with the EQUIL-code from the CHEMKIN-suite [ 100], using the thermochemical data discussed in the previous sections. The temperature range selected was 298-1023 K, the concentration of tin precursor was kept at 2 mol %, while the concentrations of oxygen and water were held at 20 mol % and 5 mol %, respectively. The total pressure was 1 atm. These conditions are similar to those used in commercial tin oxide CVD processes. Note that in the following discussion of reaction mechanisms, all heats of reaction (AHg) are given at 298 K. 

The equihbrium calculations for DMTC decomposition in N2 (Fig. 16) are consistent with previously reported experimental investigations, which show that DMTC decomposes above 670 K into SnCl2 and Ci, and C2 hydrocarbons [102]. The only discrepancy is the predicted formation of CeHe, which has not been foimd during experiments. This is not surprising, since the... 

Crude oil and its derived products are mixtures of many types of compounds. Although the exact composition of a product is desired to make equihbrium calculations, this information generally is unavailable because product quality is based on engineering specifications like octane number and not on a specific composition. Furthermore, many compounds of interest are... 

We wiU encounter equihbrium calculations of solution and gaseous species in Chapter 21, Electrochemistry. ... 

As is explained in more detail on page 9, hydrogen ions do not have an independent existence in water, so what we write as [H" "] is really a more complicated species. Furthermore, if the total concentration of ions of all kinds in the solution exceeds about 0.001 M, a significant fraction of them will be associated into neutral pairs such as H C1 , for example, and thus reducing the concentration of free ions to smaller value which we will call the effective concentration. It is the effective concentration of H" " that determines the degree of acidic character of a solution, and this is what methods for determining the pH actually measure. For this reason pH is now defined in terms of the effective H concentration. You need not be concerned with the details of this at the moment, but it is something you should know about later on in coimection with acid-base equihbrium calculations. 

Teh, Y.S. and Rangaiah, G.P. (2003) Tabu Search for global optimization of continuous functions with application to phase equihbrium calculations. Computers Chemical Engineering, , 1665-1679. 

Carravetta V, dementi E (1984) Water-water interaction potential An approximation of electron correlation contribution by a functional of the SCF density matrix. J Chem Phys 81 2646-2651 Chen B, Xing J, Siepman JI (2000) Development of polarizable water force fields for phase equihbrium calculations. JPhys ChemB, 104 2391-2400... 

Li and King [32] also reported on COS formation above ZnO. Experiments were performed on a dry base at concentrations of 25 ppmv H2S, at temperatures of 150-250°C and at high space velocities of 75 000h h The sum of CO and CO2 always amounted to 21%, whereas CO was varied between 0 and 12%. Their experiments showed that CO has a negative effect on the sulfur removal capacity, which was attributed to COS formation over ZnS. COS measurements were not performed. Equihbrium calculations for a mixture of 3% CO, 13% CO2, 32% H2, and 23% steam (balanced He as inert gas) led to a concentration of 234 ppmv COS via formation from CO and 7 ppmv COS via formation from CO2. A coupling effect by the WGS reaction was neglected as ZnO does not catalyze this reaction. 

Nichita et al applied the pseudo-component method to the wax precipitation from hydrocarbon mixtures. To do so a general form of a two-parameter equation of state was used for vapour and liquid phases. The heavy components were assumed to precipitate in a single solid solution. Because lumping in pseudo-components often results in difficulties in solid-liquid equihbrium calculations the authors proposed a delumping procedure (mentioned in section 9.3.1). Lira-Galeana et al calculated wax precipitation in petroleum mixtures by assuming the wax consisted of several solid phases each described as a piue component or pseudo-component immiscible with other solid phases. 

Stapleton, M. R., and Panagiotopoulos, A. Z. 1990. J. Chem. Phys. Application of excluded volume map sampling to phase equihbrium calculations in the Gibbs ensemble. 92 1285. 

The problem is to obtain the concentradon of H30 or OH in this equilibrium mixture. To do the equilibrium calculadon, you need the starting concentrations in the solution obtained by mixing the NH3 and NH4CI solutions. For this, you calculate the moles of NH3 and moles of NILi added to the buffCT solution, then divide by the total volume of buffo. Then you are ready to do the equihbrium calculation. 

GOAL 18 Given K, for a weak acid, HA, determine the ratio between [HA] and [A ] that will produce a buffer of specified pH. GOAL 19 Given equilibrium concentrations of species in a gas-phase equihbrium, or information from which they can be found, and the equation for the equihbrium, calculate the equilibrium constant. 

Equilibrium compositions of liquid phases at equilibrium are calculated by equaling the component fugacities, similar to vapor-liquid equihbrium calculations desoibed in more detail in Chapter 2. The activity coefficients may be calculated by equations presented in Section 1.3.3, in particular the UNIQUAC and NRTL equations. The composition dependence of these equations is developed to the point where the same equation with the same constants can predict activity coefficients over wide ranges of composition, thus allowing it to predict two immiscible liquid phases at equiUbrium. 

The equilibrium constant. Kp is 158. Analysis shows that the partial pressure of O2 is 0.25 atin at equihbrium. Calculate the pressure of NO and NO2 in the mixture. 

Problem. Derive, using thermodynamic equihbrium calculations, an expression for the membrane potential AF = /(pH, pH ef) between an electrolyte with unknown pH and a reference electrolyte with known pH = pH gf based on this, give a rough outline of the principle in a setup for measuring pH using a glass electrode. 

These three concentration measures (or their English engineering unit equivalents) are widely used in process calculations in the United States. They are seldom used in equihbrium calculations and will be seldom be used in this book. 

At this point we may give a simple answer to the obvious question. What is the fugacity For a pure ideal gas the fugacity is identical to the pressure, and has the same dimensions as the pressure. Thus, we may think of it as a corrected pressure that enters many equihbrium calculation in place of the real pressure. Equations 7.8 and 7.10 show that we commonly show pure species fugacities as the dimensionless ratio off/P. The mathematics of Appendix C show why that occurs. For pure species, the plot of the fugacity most often seen is Figure 7.1, which is somewhat similar to the common compressibility factor chart (z chart). This plot is shown in Appendix A.5 along with the same information in an alternative format. In both//P and z charts, an ideal gas is represented by a horizontal line with value... 

Equilibrium separation involves the two-phase region between the two curves. Equihbrium calculations, often referred to as "flash calculations," are based upon a combination of the vapor— liquid equilibrium relationship and material balance equations. 

Thus, if Ag ean be obtained by some means as a lunction of composition, the chemical potentials can be computed using Eqs. (9.2.15) and (9.2.16). The chemical potentials are, in turn, needed for phase equihbrium calculations. 

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