Vapor Estimation

A volatile compound of chlorine has been analyzed to contain 61.23% of oxygen (Op and 38.77% of chlorine (Cl ) by weight. At 1 atm and 27°C, 1000 cm of its vapor weighs 7.44 g. Assuming ideal gas behavior for the vapor, estimate its molecular weight and deduce its molecular formula. 

Example 25.2 An airstream contains acetone vapor. Estimate the following. 

One mortality study of a cohort of workers with at least 6 months exposure to hydroquinone at exposure concentrations of 0.1-6.0mg/m for the dust and from less than 0.1 to 0.3 for the vapor (estimated 8-hour time-weighted averages) found statistically signifi-... 

A related study of 3,6-diphenyl-l,2,4,5-tetroxane resulted in enthalpies of formation of the sohd and gaseous species of 134.0 1.3 and 99.7 1.3 kJmor. Again, while computational theory and experiment are in good agreement, the sublimation enthalpy of 34.3 kJmoU seems too low. We would have suggested a lower bound of ca 71 kJmoU based on our enthalpy of vaporization estimation approach given above. 

The compilations of CRC (1-2), Daubed and Danner (3), TRC (11-12), and Yaws (15-33) were used extensively for enthalpy of vaporization. Estimates for enthalpy of vaporization at the boiling point were primarily based on the Kistiakowsky rule (9) and Riedel method (9). The Joback method (9) was used for estimating critical temperature. 

Gedzelman and Arnold (1994) built on this isotopic approach, but with a more realistic two-dimensional, non-steady-state, cloud model. The model was mn for several idealized, classical stratiform and convective storm situations and the resulting isotope ratios of precipitation and water vapor estimated and compared to observations. The model reproduces many of the salient features of isotope meteorology when applied to snowstorms, stratiform rain, and convective precipitation. Also noticeable is the fact that isotope ratios are particularly low when the rain derives from a recirculation process in which air previously charged by vapor from falling rain subsequently rises. This provides a reasonable explanation for extraordinary low isotope ratios observed in some hurricanes and organized thunderstorms. 

Walton M (1960) Molecular diffusion rates in supercritical water vapor estimated from viscosity data. Am JSci 258 385-401... 

Hydrogen sulfide can react with M0O2 to produce molybdenum disulfide and water. The stabilities of the dioxide and disulfide depend upon the relative partial pressures of hydrogen sulfide and water vapor. Estimates of the effect of temperature upon the equilibrium are summarized in Fig. 7. 

A fresh feed stream consisting of ethylene gas (63 mol %) and pure O2 gas (37 mol %) at 20 °C and 303 kPa enters an oxidation reactor system with a molar flowrate of 120 kmol/hr plus recycled gasses/vapors (estimated by HYSYS). The reaction is promoted by a solid catalyst and occurs isothermally at 230 °C. The feed stream must therefore be pre-heated to 230 °C before it is fed into the oxidation reactor. 

For liquid carbon tetrachloride in contact with its vapor, estimate the surface energy per unit area, using the enthalpy change of vaporization to estimate the net attractive energy of the molecules. 

The enthalpy of vaporization, estimated according to Zaitsau et al. [175] as shown above yielded the ce = Ay// - RT and the ced, which were then used for other purposes by Singh and Kumar [185]. This approach was also used by Xu et al. [202] to obtain the Ay// and values of four imidazolium carboxylate RTlLs... 

Example 5.7 Estimation of Diffusivity of Hydrogen and Oxygen in Water Vapor Estimate the diffusivity of hydrogen in water vapor and oxygen in water vapor at 1 atm and 307 K and compare with experimental data in Table 5.4. 

Detailed and extensive information on the UNIFAC method for estimating activity coefficients with application to vapor-liquid equilibria at moderate pressures. 

This chapter presents a general method for estimating nonidealities in a vapor mixture containing any number of components this method is based on the virial equation of state for ordinary substances and on the chemical theory for strongly associating species such as carboxylic acids. The method is limited to moderate pressures, as commonly encountered in typical chemical engineering equipment, and should only be used for conditions remote from the critical of the mixture. 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

Both vapor-liquid flash calculations are implemented by the FORTRAN IV subroutine FLASH, which is described and listed in Appendix F. This subroutine can accept vapor and liquid feed streams simultaneously. It provides for input of estimates of vaporization, vapor and liquid compositions, and, for the adiabatic calculation, temperature, but makes its own initial estimates as specified above in the absence (0 values) of the external estimates. No cases have been encountered in which convergence is not achieved from internal initial estimates. 

Subroutine VLDTA2. VLDTA2 loads the binary vapor-liquid equilibrium data to be correlated. If the data are in units other than those used internally, the correct conversions are made here. This subroutine also reads the estimated standard deviations for the measured variables and the initial parameter estimates. All input data are printed for verification. 

ZT,ZJ Temporary true vapor composition estimates. k6 True vapor composition estimate flag (0 = a priori ... 

FOR NO PREVIOUS PHI VALUES AVAILABLE (KO = 0) MAKE FIRST ESTIMATES OF ACTUAL VAPOR COMPOSITION... 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

A estimate of vapor to feed mole ratio, if known ... 

Y(I) vector of estimated equilibrium the vapor composition (mole fraction) if known (I = 1, N) otherwise can be any vector not summing to 1. 

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