Equilibrium curve calculation

This chapter treats after-H2S04-making SO2 oxidation as a completely new problem. This is necessary because selective SO3 removal from gas during H2S04(f) making invalidates Appendix B s before-H2S04-making equations. 

The after intermediate H2SO4 making equilibrium curve equation is  

1) is similar to before-H2S04-making equilibrium Eqn. (10.13), Section 15.1. It is derived the same way. 

2 After-H2SO4-making % SO2 oxidized defined After-intermediate-H2S04-making % SO2 oxidized is defined as  

When equilibrium is attained in an after-H2S04-making catalyst bed, 0 becomes  

O = equilibrium percentage of after-H2SO4-making input SO2 that is oxidized in 

After-intermediate-H2S04-making % SO2 oxidized is defined as  

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Ternary equilibrium curves calculated by Scott,who developed the theory given here, are shown in Fig. 124 for x = 1000 and several values of X23. Tie lines are parallel to the 2,3-axis. The solute in each phase consists of a preponderance of one polymer component and a small proportion of the other. Critical points, which are easily derived from the analogy to a binary system, occur at... 

The Eqn. (10.2) definition is used in all our 1st catalyst bed equilibrium curve calculations. 

Free Energy Equations for Equilibrium Curve Calculations... 

In general, the equilibrium curves calculated from the two curves do not match exactly, and each is used for its respective portion of the column. Plates are stepped off between the operating lines and equilibrium curves in the usual manner. 

Appendix C Free energy equations for equilibrium curve calculations... 

When the equilibrium curve is not straight, there is no strictly logical basis for the use of an overall transfer coefficient, since the value of m will be a function of position in the apparatus, as can be seen from Fig. 5-27. In such cases the rate of transfer must be calculated by solving for the interfacial compositions as described above. 

The end points of the operating line on an XY plot (Fig. 15-13) are X., Y, andXy, Y., and the number of theoretical stages can be stepped off graphically. The equilibrium curve is taken from the Hand type of correlation shown earlier (Fig. 15-9). When the equilibrium line is straight, its intercept is zero, and the operating line is straight, the number of theoretical stages can be calculated with one of the Kremser equations [Eqs. (l5-14) and (15-15)]. When the intercept of the eqnihbrinm line is not zero, the value of YJK, should be used... 

The local equilibrium curve is in approximate agreement with the numerically calculated profiles except at very low concentrations when the isotherm becomes linear and near the peak apex. This occurs because band-spreading, in this case, is dominated by adsorption equilibrium, even if the number of transfer units is not very high. A similar treatment based on local eqnihbrinm for a two-component mixture is given by Golshau-Shirazi and Gniochou [J. Phys. Chem., 93, 4143(1989)]. 

The procedure to calculate the points for an equilibrium curve is to start with x = 0, and calculate the value of y for a given value of a. A second point is calculated by incrementing the value of x and repeating the calculation for y. This calculation is repeated until the value of x = 1. 

Now substitute this value x = 0.88 into the equation and calculate the vapor coming up from the first plate below the top (t - 1). Thus, if x = top plate, yn + i = vapor from plate below top. Now, read equilibrium curve aty(j i) and get X(n +1) or Xt 1 which is liquid on plate below top. Then using Xf 1, calculate yt- 2 (second plate below top, etc.). Then, read equilibrium curve to get corresponding liquid X( 2- Continue until feed plate composition is reached, then switch to equation of stripping section and continue as before until desired bottoms composition is reached. Operating line of stripping section ... 

For the condition of straight operating and equilibrium curves, the number of plates can be calculated including the reference plate (number seven in this case) [59]. 

To calculate the equilibrium curve at 90°F (constant temperature) for the system aqua ammonia-ammonia-inert vapors follow the steps listed ... 

To calculate the equilibrium curve taking the heat of solution into accoimt, i.e., operate adiabatically with liquid temperature variable, follow the steps ... 

We will compare the change in the free energy per macromolecule in the formation of folded-chain (curve 1) and fibrillar (curve 2) crystals as a function of /J. Figure 8 b shows these curves calculated for the corresponding equilibrium values [a]. The increase... 

As an alternative to drawing the equilibrium curve for the system, point values may be calculated from ... 

Using equation 11.15, a new equilibrium curve may be calculated as follows ... 

With the two equations (i) and (ii) and the equilibrium curve, the composition on the various plates may be calculated by working either from the still up to the condenser, or in the reverse direction. Since all the vapour from the column is condensed, the composition of the vapour y, from the top plate must equal that of the product xj, and that of the liquid returned as reflux xr. The composition x, of the liquid on the top plate is found from the equilibrium curve and, since it is in equilibrium with vapour of composition, y, = 0.90, x, = 0.79. 

At atmospheric pressure (101.325 kPa), a quartz is in equilibrium with (3 quartz at 847 + 1.5K [8]. The enthalpy change of the transition from a quartz to (3 quartz is 728 + 167 J mol Berger et al. [9] measured the volume change by an X-ray diffraction method, and they reported a value of 0.154 + 0.015 cm mol Use these values to calculate the slope at atmospheric pressure of the equilibrium curve between a quartz and 3 quartz in Figure 13.1. Compare your results with the value of the pressure derivative of the equilibrium temperature dT/dP, which is equal to 0.21 K (Mpa) [10]. 

The results of one such set of calculations are shown in Fig. 8.2. The more extractable species A competes strongly for the ligand, so that the equilibrium curve of A in the presence of B is depressed only slightly below that for the extraction of A on its own. In contrast, the equilibrium curve for the extraction of B in the presence of A is depressed markedly relative to the extraction of free B. The effect of this is to improve the product purity significantly over what would have been possible at low concentrations of the extracted species in the extract. Thus, at high concentrations, saturation effects can improve product purity to a far greater extent than the equilibrium isotherms of the individual species would indicate superficially. 

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