Equilibrium plotting

Figure 5-18. Rate-equilibrium plot for the isomerization of substituted 5-aminotriazoles at 423 K. ...

Note that yo = xp on the diagonal of the equilibrium plot, and 7i and xj are points of intersection with the equilibrium curve. For an abnormal equilibrium curve (as compared to regular or normal shape) see Figure 8-34. 

For practical design, select L/V = (1.5) (0.525) = 0.7875. Select L/V internal reflux lines and add to the equilibrium plot, similar to that shown for a normal curve of Figure 8-35, but unlike the abnormal ethanol curve shown. 

Fig. 16 A rate-equilibrium plot of log k for the solvolyses of benzhydryl chlorides in 85% aqueous acetone (Fox and Kohnstam, 1964 Fujio et al., unpublished) against pikR- for benzhydrols (Mindl and Vecera, 1971, 1972 Mindl, 1972).

Where W is the equilibrium adsorption capacity. Wo is the total volume of the micropores aecessible to the given adsorbate, k is a characteristic constant related to the pore structure of the adsorbent, P is an affinity coefficient, Csai is the saturation concentration in the gas phase of liquid adsorbate at the adsorption temperature T, and C is the eoncentration of adsorbate vapor in equilibrium. Plotting ln(W) versus [RTln(Csai/C)] the parameters K/p and Wo in the DR equation were determined by the slope and the intercept of the linear lines respeetively. The obtained results and correlation coefficients are eompiled in Table 2. This Table shows the DR equation parameters and the... 

Figure 3-36. Comparison of data obtained by labeling the mRNA described in Figure 3-34 by pulse and equilibrium techniques. Subsequent to the time indicated by an arrow, the equilibrium plot is linear.

Perform the material balance and plot the operating line on the equilibrium plot. 

With a binary equilibrium plot, Fig. 7, the distribution of extract and raffinate following one stage of contact is readily determined. Representing a mass balance of the solute transferred ... 

FIGURE 3.17 Distribution of two products at equilibrium plotted as a function of the difference in free energy (AG°) at 25°C between them. 

FIGURE 13.1-1 Equilibrium plot for univalent-univalent exchange. 

Here the relationship berwnea y and xA bcconias greatly dependent on the value of C, the solution-phase concentration. A typical equilibrium plot is shown in Fig. 13.1 <2 and it is obvious that the preference for... 

FIGURE 13.1-2 Equilibrium plot for divalent-univaiem exchange... 

Sulfating equilibrium plots are presented in Figure 10 for copper, lead, and nickel. The huge values of the equilibrium constants indicate that base metal sulfates form readily as long as any oxygen is present. There is little evidence that sulfates of noble metals are stable. 

Vapor pressures at 25°C are Pf = 2.452 psia (16.9 kPa) and P = 1.886 psia (13.0 kPa). Activity coefficients can be computed from the van Laar equation in Table 5.3. The resulting equilibrium plot is shown in Fig. 5.9, where it is observed that over much of the liquid-phase region three values of y] exist. This indicates phase instability. Experimentally, single liquid phases can exist only for cyclohexane-rich mixtures of X) = 0.8248 to 1.0 and for methanol-rich mixtures of X) =0.0 to 0.1291. Because a coexisting vapor phase exhibits only a single composition, two coexisting liquid phases prevail at opposite ends of the dashed line in Fig. 5.9. The liquid phases represent solubility limits of methanol in cyclohexane and cyclohexane in methanol. 

Methods for the determination of solubility have been thoroughly reviewed [5,7,8], especially with respect to the characterization of pharmaceutical solids [9], Solubility is normally highly dependent on temperature, so the temperature must be recorded for each solubility measurement in addition to the precise nature of the solvent and the solid phase at equilibrium. Plots of solubility against temperature are commonly used for characterizing pharmaceutical solids and have been extensively discussed [5,10], Frequently (especially over a relatively narrow temperature range), a linear relationship can be given either by a van t Hoff plot ... 

Different types of cation exchange behaviour observed in zeolites. Isotherms represent equilibrium plots of the fractional concentration of extra-framework cations in the zeolite compared with the fractional concentration of cations in the solution in contact with the zeolite (see text for discussion). In case (a) cation M is taken in preference over a competing cation type for the entire relative concentration range, whereas the preference is inverted in case (c). The situation where there is no preference is represented by (b). Type (d) isotherms occur when only a certain fraction of the cations may be exchanged (experimentally, kinetic barriers may also result in this behaviour). Finally, isotherms of type (e) indicate that the selectivity changes as the relative concentration of the cations in solution changes. 

The dependence of rate upon concentration means that reaction rates are time dependent, because the reactant s concentration changes as a function of time. The rate decreases as the concentration of reactant(s) decreases. Commonly, the rate of a reaction is at its highest at inception (those reactions without an induction period) and slows down to zero at the end of reaction or when the system has reached equilibrium. Plotting the concentration of product as a function of time gives plots similar to those shown in Figure 7.4. 

Fig. 39. Force for equilibrium plotted against the absolute temperature for fibrous natural rubber. Tm is the melting point at zero force (0th and Flory, 1958).

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