Point-time yields

Tops0e et determined active sites on iron catalysts for ammonia synthesis by nitrogen titration and point-time yields of ammonia (the ammonia molecules produced per second per active site in reactor) at 15% of conversion of equilibrium value at atmospheric pressure and 673 K and stoichiometric mixture. The difference between the values predicted by the models and obtained by experiments was less than three folds. 

The kinetic determination of any concentration as a function of time yields k, as in Eqs. (3-61) and (3-63). This is true no matter whether one follows [A] or [P],. The latter point, although correct, can sometimes seem illogical. Suppose one measures the buildup of P2 (say), by monitoring an infrared peak, an ultraviolet band, or an NMR signal. Assume that neither A nor any product other than P2 contributes to the signal. Surely then, will it not be k2 that is obtained from the kinetic analysis The answer is no. Consider the result from Eq. (3-63), which gives the concentration of the one product in terms of its absorbance (per unit optical path) and molar absorptivity (62) ... 

However, these investigations also point out that we need a proper definition of space-time yields for micro reactors. This refers to defining what essentially the reaction volume of a micro reactor is. Here, different definitions lead to varying values of the respective space-time yields. Following another definition of this parameter for ethylene oxide formation, a value of only 0.13 t h m is obtained -still within the industrial window [159, 162, 163]. 

The 1 1 inclusion complexes 68 composed of 2a and nitrones 67 were prepared by keeping a solution of 2a and an equimolar amount of 67 in benzene-hexane (1 1) at room temperature for 12 h 40). Melting points of the complexes 68 are shown in Table 8. Irradiation of 68 in the solid state gave optically active oxaziridines 69. Irradiation time, yields and optical purity of the products are summarized in Table 8 40). Enantioselectivity in the formation of 67d, 67f, and 67g is high, but that of 69b, 69 c, and 69 e is low. This suggests a distinct influence coming from the substituents. 

The yield of a product is a measure of the reaction extent at some point (time or position) in terms of a specified product and reactant. The most direct way of calculating the yield of a product in a complex system from experimental data is by means of a stoichiometric model in canonical form, with the product as a noncomponent. This is because that product appears only once in the set of equations, as illustrated for each of CO, CO and HCHO in Example 5-1. 

The distillate from the steam distillation is twice shaken with not too much ether, and the ethereal extract, if necessary after concentration, is transferred to a wide-mouthed bottle, into which technical sodium bisulphite solution is poured in small portions with stirring (a glass rod is used) so that the aldehyde addition compound formed sets to a thick paste. The bottle is then stoppered and vigorously shaken the stopper is removed from time to time until all the benzaldehyde has entered into combination. (Odour ) The paste is now filtered with suction, and the solid on the funnel, after washing with ether, is at once decomposed by mixing it with an excess of sodium carbonate solution the liberated aldehyde is removed without delay by steam distillation. The distillate is extracted with ether, the extract is dried over a little calcium chloride, the ether is removed by distillation, and the benzaldehyde which remains is likewise distilled. Boiling point 179°. Yield 35-40 g. (70 per cent of the theoretical). 

Hydrolysis of the Nitrile.—The nitrile, mixed in a porcelain basin with four times its volume of concentrated hydrochloric acid, is heated on the water bath until an abundant separation of crystals begins to take place on the surface of the liquid. The reaction mixture is then allowed to stand over night in a cool place, and the crystals which have been deposited, after being rubbed with a little water, are separated at the filter pump and washed with water (not too much). A further quantity of the acid is obtained from the filtrate by extraction with ether. The crude mandelic acid is pressed on a porous plate, dried, and purified by crystallisation from benzene. Melting point 118°. Yield about 10-15 g. 

Steinhaus and colleagues (66) have described another version of a stroboscopic instrument that is useful for routine lifetime measurements. They point out that switching a photomultiplier tube on and off by removal and reapplication of the high voltage may at times yield troublesome transient problems. 

Vigreux column. When no more methanol distills over (ca. 24 h), the dark brown reaction mixture is reduced in volume by the distillation of 100 mL of toluene. While the flask is still hot, 300 mL of cyclohexane are added with vigorous stirring and a yellow, crystalline solid comes out of solution. At this point, the copious amount of solid makes stirring difficult. The mixture is allowed to stand overnight and the yellow solid is collected by suction filtration. The solid is washed with 2 1 cyclohexane/toluene (ca. 300 mL) and, then cyclohexane and is allowed to air dry. The solid is then dried in a vacuum dessicator (25°C, 24 h) to remove the last traces of N,N-dimethylformamide dimethylacetal (a small amount of sublimation of the product will occur). Failure to completely remove the last traces of N,JV-dimethylformamide dimethylacetal results in the gradual darkening of the product over several months time. Yield 190.3 g (86% based on 2-acetylpyridine), mp 127-128°C. 

TABLE I. Reaction Times, Yields, and Melting-Point Determinations for [Re(CO)4LI] [L = P(OMe)j, PMe2Ph, PPh3]... 

Approx 50 ferrites are available with Curie points in a practical temp range. The 50 ferrites, used in combinations of 5 at a time, yield a... 

Every (bio)catalyst can be characterized by the three basic dimensions of merit -activity, selectivity and stability - as characterized by turnover frequency (tof) (= l/kcat), enantiomeric ratio (E value) or purity (e.e.), and melting point (Tm) or deactivation rate constant (kd). The dimensions of merit important for determining, evaluating, or optimizing a process are (i) product yield, (ii) (bio)catalyst productivity, (iii) (bio)catalyst stability, and (iv) reactor productivity. The pertinent quantities are turnover number (TON) (= [S]/[E]) for (ii), total turnover number (TTN) (= mole product/mole catalyst) for (iii) and space-time yield [kg (L d) 11 for iv). Threshold values for good biocatalyst performance are kcat > 1 s 1, E > 100 or e.e. > 99%, TTN > 104-105, and s.t.y. > 0.1 kg (L d). ... 

Inspection of Table 18.3 reveals that in principle any reaction catalyzed by orga-nometallic catalysts is amenable to running in a CMR. Further, enanhoselechvities seem to be just as high in the non-heterogenized case. The space-time yields achieved, often in excess of 1 kg (L d) 1, point to the potentially very favorable volumetric productivities of a CMR configuration. 

An enzyme membrane reactor allows continuous transketolase-catalyzed production of L-erythrulose from hydroxypyruvate and glycolaldehyde with high conversion, stable operational points, and good productivity (space-time yield) of 45 g (L d) 1, thus best overcoming transketolase deactivation by substrates (Bongs, 1997). 

A catalytic process is commercially viable if the catalyst transformation is achieved within definite, practical limits of space and time. To quantify this aspect, one can determine the so-called space-time yield. This measure of activity is simply the amount of product obtained per unit time and per unit reaction space (where reaction space is usually the reactor volume). Weisz (79) pointed out that in industry the useful space-time yield is rarely less than 10"6 g/mol of reactant per cubic centimeter of volume of reactor space per second. This has been called the Weisz window on reality. Figure 9 (79) shows the Weisz window and other windows of chemical activity that apply to biochemistry and petroleum geochemistry (79). 

From the engineering point of view, mass transport is usually the main factor determining the space-time yield of an electrochemical reactor, that is, the amount of product that can be generated in a given... 

The macroscopic stress cr is this force times the number of interparticle bonds that cross a unit area of the sample this latter factor should scale as 0 /a (Russel et al. 1989). As long as the local applied force increases with increased strain, cr increases with increasing strain, and the gel maintains its mechanical stability. But once the strain reaches the point -that the slope W of the potential is a maximum (see Fig. 7-23), any further strain produces a decreasing force, and the interparticle structure breaks apart. This corresponds to the point of yield. Thus, the yield strain yy is given by the condition that the second derivative W of W D) is zero that is, W" Dy) = 0, where Dy = lyyU + (yy + 1)Dq is the value of D for which W" = 0. Very roughly, we might expect that W is a maximum (W — 0) when separation D = Dy % on the order of twice Dq, the value of D at static equilibrium. This would imply that the yield strain yy is roughly hence, for particles 100 nm in... 

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