Yield curves

In order to draw the property-yield curves for gasolines , it suffices to choose the initial point, which coilild be or 20°C, the end point being variable and situated between the end point of the heaviest gasoline cut which can be produced (200-220°C) and about 350°C. 

Unlike the property-yield curves, calculations are not necessary for determining the properties of a cut. 

For any one ion type (e.g., Cs ), measurement of its abundance in a sample requires the sample to be evaporated over a period of time. The total yield of ions is obtained by integrating the area under the ion-yield curve (Figure 7.8c). 

Wold proposed Eq. (6-18), finding that it yielded curve fits as good as Eq. (6-16), with D = 0. 

The finite transit time (xr) in the high strain-rate region has important consequences on the scission yield curve. Since bond scission is a first-order process (Eq. 96), the degradation yield in a single pass experiment is given approximately by ... 

Fig. 45. Radial strain rate distribution function and its influence on the degradation yield O (r0 orifice radius, r axial distance from the orifice center) C(r2/r0) variation of the strain rate as a function of (r/r0)2 obtained from the reciprocal of the degradation yield curve of a monodisperse polymer fraction (see Fig. 46) C(r/r0) radial distribution of the strain rate in the plane of the orifice, calculated from the function C(r2/rg)...

The function C(r/r0) can be determined experimentally from the degradation yield curve of a truly monodisperse sample since the function C(r2/ro) is simply... 

Figure 8. Yield Curves for Salt-To-Pu Ratio vs Concentration of MgC12 for Extraction of Americium From NaCi-CaCl2-MgCl2 Salt Using 2-Stage Counter-Current Extraction...

Pressure = 0.3 mm Hg nickel cathode. The yield curve for NO2+ ions, not shown here, corresponds closely to that of NO+ ion % yield refers to % total ions observed... 

Time dependence of the reaction products can be seen more clearly in the time-yield curves of oligomerization in methylene chloride at —40° (Fig. 4). The yield of mixture of the cyclic tetramer and hexamer (mostly the latter), passed through a maximum value of about 40% and then decreased to nearly zero after 48 hours. On the other hand, the yield of the cyclic dimer increased rather sigmoidly with reaction time. 

Fig. 4. Time-yield curves of the oligomerization of 6,8-dh>xabicyclo[3.2.1 Joctan-7-one. Monomer, 4 g CH2Cl2 4 ml BF3Et20, l mol% to monomer temp., -40 °C , cyclic dimer o, cyclic tetramer plus cyclic hexamer45)...

Figure 2.9. The confidence interval for an individual result CI( 3 ) and that of the regression line s CLj A are compared (schematic, left). The information can be combined as per Eq. (2.25), which yields curves B (and S, not shown). In the right panel curves A and B are depicted relative to the linear regression line. If e > 0 or d > 0, the probability of the point belonging to the population of the calibration measurements is smaller than alpha cf. Section 1.5.5. The distance e is the difference between a measurement y (error bars indicate 95% CL) and the appropriate tolerance limit B this is easy to calculate because the error is calculated using the calibration data set. The distance d is used for the same purpose, but the calculation is more difficult because both a CL(regression line) A and an estimate for the CL( y) have to be provided.

In fact, this has already been illustrated in Fig. 3.73 for the differential electrolytic potentiometric titration of Ce(IV) with Fe(II), both being reversible systems. This technique can be usefully applied, for instance, to the aforementioned KF titration of water and its reverse titration (cf., Verhoef and co-workers preference for bipotentiometric detection) in these instances the potentiometric dead-stop end-point titration and the reversed potentiometric dead-stop end-point titration, respectively, yield curves as depicted in Fig. 3.83. 

The shape of the instantaneous yield curve determines the optimum reactor configuration and flow pattern for a particular reaction network. For cases where the instantaneous yield increases continuously with increasing reactant concentration, the optimum reactor configuration from a product selectivity viewpoint is a... 

For n-decane isomerization, when a good balance between the metal phase and the acidic phase of the catalysts is reached, the isomerization and cracking yield curves of the catalysts are a unique function of the conversion, meaning that these yields do not depends on the porosity nor the acidity of large pore materials. Formation of the most bulky isomers, such as 4-propylheptane and 3-ethyl-3-methylheptane was favored in mesoporous solids (figure 1). Criteria based on the formation of these particular isomers are linked with mesoporosity and could be useful to discriminate between zeolites catalysts with and without mesopores. 

One important assumption to keep in mind in the calculations outlined earlier is that the interest rate (discount rate) has been assumed to be constant over time even though it is not in practice. Examine Figure B.7, which shows how the interest rate for U.S. Treasury securities has changed over time for various durations of investment ranging from 3 months to 30 years (called the yield curve). 

In a preliminary screening, the alkylation of 2-methylnaphthalene was studied using a variety of acid zeolites with different pore widths. In principal agreement with the earlier work of Fraenkel et al. [22-25] it was found that the best selectivities for the slim alkylation products, i. e., 2,3-, 2,6- and 2,7-dimethylnaphthalene, are obtained on HZSM-5 and HZSM-11. On these catalysts it was observed that the alkylation is always accompanied by the undesired isomerization into 1-methylnaphthalene. Moreover, a peculiar deactivation behavior was encountered With time on stream, the yield of 1-methylnaphthalene always dropped while the yield of alkylation products remained practically constant or even slightly increased. An example for the conversion and yield curves is given in Fig. 4. The distribution of the dimethylnaphthalene isomers is shown for the same experiment in Fig. 5. Bearing in mind that in equilibrium one would expect roughly 12 mole-% of each of the slim isomers, the... 

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