Antoine equation: 11, Table

From the Antoine equation (Table B.4). the vapor pressure of carbon tetrachloride at 34" C is... 

Assume that the vapor pressures of benzene and toluene are given by the Antoine equation. Table 6.1-1 that Raoult s law—Equation 6.4-1—applies and that the enthalpies of benzene and toluene liquid and vapor are linear functions of temperature. Specific enthalpies at two temperatures are given here for each substance in each phase. 

You have been assigned to simulate a flash evaporator that separates a liquid feed stream containing benzene and toluene at temperature Tf ( C) into liquid and vapor product streams m equilibrium at temperature T( C) and pressure P mm Hg). The compositions of the product streams are related by Raoulfs law (Equation 6.4-1), and the component vapor pressures are expressed by the Antoine equation (Table B.4). 

Vapor pressure The pressure at which pure liquid A can coexist with its vapor at a given temperature. In this text, vapor pressures can be determined from tabulated data (e.g,. Tables B.3 and B.5-B.7 for water), the Antoine equation (Table B.4), or the Cox chart (Figure 6.1-4). 

The jacket steam pressure, Pj, is itself a function of the jacket steam temperature, Tj, as listed in steam tables or as correlated by the Antoine equation for vapour pressure, where... 

Example 4.3 A mixture of ethane, propane, n-butane, n -pentane and n-hexane is given in the Table 4.3. For this calculation, it can be assumed that the K-values are ideal. For the mixture in Table 4.3, an equation of state method might have been a more appropriate choice. Flowever, this makes the calculation of the K-values much more complex. The ideal K-values for the mixture can be expressed in terms of the Antoine Equation as ... 

Vapor pressure in bar can be predicted for temperature in Kelvin from the Antoine equation using coefficients in Table 4.73. Data... 

Example 4.5 2-Propanol (isopropanol) and water form an azeotropic mixture at a particular liquid composition that results in the vapor and liquid compositions being equal. Vapor-liquid equilibrium for 2-propanol-water mixtures can be predicted by the Wilson equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.113. Data for the Wilson equation are given in Table 4.126. Assume the gas constant R = 8.3145 kJ-kmol 1-K 1. Determine the azeotropic composition at 1 atm. 

Table 4.11 Antoine equation coefficients for 2-propanol and water6.

The system methanol-cyclohexane can be modeled using the NRTL equation. Vapor pressure coefficients for the Antoine equation for pressure in bar and temperature in Kelvin are given in Table 4.176. Data for the NRTL equation at 1 atm are given in Table 4.186. Assume the gas constant R = 8.3145 kIkmol 1-K 1. Set up a spreadsheet to calculate the bubble point of liquid mixtures and plot the x-y diagram. 

In the book, Vapor-Liquid Equilibrium Data Collection, Gmehling and colleagues (1981), nonlinear regression has been applied to develop several different vapor-liquid equilibria relations suitable for correlating numerous data systems. As an example, p versus xx data for the system water (1) and 1,4 dioxane (2) at 20.00°C are listed in Table El2.3. The Antoine equation coefficients for each component are also shown in Table E12.3. A12 and A21 were calculated by Gmehling and colleaques using the Nelder-Mead simplex method (see Section 6.1.4) to be 2.0656 and 1.6993, respectively. The vapor phase mole fractions, total pressure, and the deviation between predicted and experimental values of the total p... 

Vapor pressure data are important in the identification, separation, and general manipulation of known compounds on the vacuum line and for the characterization of new compounds. This appendix was prepared with these applications in mind. It is introduced with a discussion of the use and limitations of several analytical expressions for the representation of vapor pressure data. A description of a least-squares treatment of vapor pressure data for fitting to the Antoine equation is then presented. Finally, a table of vapor pressures at convenient slush bath temperatures is presented for 479 compounds. 

B. Example Calculation The Antoine Equation for Water. Table V. l lisls the vapor pressure dalu for water from 20 to 80°C. Values of au, ba, and c0 are calculated from the data at 20, 50, and 80°C by solving the following three simultaneous equations ... 

Of course, the vapour pressure is very temperature dependent, and reaches P° = 101.325 kPa at the normal boiling point, Tb. The isochoric thermal pressure coefficient, dp/dT)v = otp/KT, can be obtained from the two quantities on the right hand side listed in Table 3.1. Except at T it does not equal the coefficient along the saturation line, (dp/dT)a, which is the normal vapour pressure curve. The latter temperature dependence is often described by means of the Antoine equation ... 

Estimate the saturation temperature at P = 5 bar using the Antoine Equation and values from Table B.2... 

Fitting the vapor pressure data to the Antoine equation allows A, B, and C to be determined. If the density of the liquid is available, the molar volume, V, is easily obtained. Then the solubility parameter can be calculated using Eq. (3.19). Table 3.11 shows solubility parameters for a variety of liquids. 

By changing the temperature between 7 fat and TP1, we estimate the saturation pressures Pfl and Pfl from the Antoine equation at each temperature. From Eq. (2.215), we estimate the equilibrium compositions at each temperature and prepare Table 1.9. Figure 1.9 displays the Tyx diagram with the saturated liquid and saturated vapor lines plotted from Table 1.9. 

Component vapor pressures Pr in psia (Table 11.3 > are calculated by using the Antoine equation, with the Antoine coefficients based on the... 

Finally, we must select appropriate methods of estimating thermodynamic properties. lime (op. cit.) used the SRK equation of state to model this column, whereas Klemola and lime (op. cit.) had earlier used the UNIFAC model for liquid-phase activity coefficients, the Antoine equation for vapor pressures, and the SRK equation for vapor-phase fugacities only. For this exercise we used the Peng-Robinson equation of state. Computed product compositions and flow rates are shown in the table below. 

The bubble-point temperature may be calculated by trial and error as the value of Tbp that satisfies this equation all that is needed is a set of relationships for p T), such as the Antoine equation or vapor-pressure charts or tables. Once Tbp is known, the composition of the vapor phase can easily be determined by evaluating the partial pressures of each component from Equation 6.4-3 and determining each vapor-phase mole fraction as y, = pj P. 

The solution procedure is to choose a temperature, evaluate p and pj for that temperature from the Antoine equation using constants from Table B.4, evaluate /(Tbp) from the above equation, and repeat the calculations until a temperature is found for which /(Tpp) is sufficiently close to 0. 

Estimate the vapor pressure of acetone (mm Hg) at 50 C (a) from data in Perry s Chemical Engineers Handbook and the Clausius-Clapeyron equation, (b) from the Cox chart (Figure 6.1-4), and (c) from the Antoine equation using parameters from Table R4. 

In this table, A, B, and C are Antoine equation constants, al, av, and bv are the coefficients of the given heat capacity formulas Tbp(°C) and DHv(kJ/mol) (A v) are the normal boiling point and heat of vaporization, xF(mol pentane/mol) is the mole fraction of pentane in the feed. TfCC) is the feed temperature, P(mm Hg) is the system pressure. HAF (Haf) and HBF (Hbf) are the specific enthalpies of pentane and hexane in the feed stream, pA is the vapor pressure of n-pentane (to be determined using the Antoine equation), x and nL x and l) are the mole fraction of pentane in the liquid product stream and the molar flow rate of that stream, respectively, y and nV are the corresponding properties of the vapor product stream. HAL is the specific enthalpy of pentane in the liquid product stream, and DH (A//) is the expression given in Equation 5 for the change in total enthalpy from inlet to outlet. 

Solutions to some of the problems of tliis chapter require vapor pressures as a function of temperature for species which constitute systems in VLE. Table 10.2 lists paranietervalues for tlie Antoine equation. 

Use method (iv) to find p and Y. Make an initial estimate of say, using a psychrometric chart. Calculate Yas from Eq. (12-6). Find p from Table 12-1 and from Antoine equation (12-5). Repeat until iteration converges (e.g., using spreadsheet). 

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