Half time

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Eigen M 1954 Methods for investigation of ionio reaotions in aqueous solutions with half-times as short as 10 sec Discuss. Faraday Soc. 17 194-205... 

Argon is two and one half times as soluble in water as nitrogen, having about the same solubility as oxygen. Argon is colorless and odorless, both as a gas and liquid. Argon is considered to be a very inert gas and is not known to form true chemical compounds, as do krypton, xenon, and radon. 

Calculating the extra integrals takes time. MNDO, AMI, and PM3 calculations typically take about one and one-half times as long as INDO orMINDO/3 calculations. 

Scale-up and performance of a 1.47-m Scheibel column have been reported (98,154,155), as have detailed description and design criteria for the Scheibel column (156) and scale-up procedures (157). The same stage efficiency can be maintained on scale-up, and total throughput can be increased by three and one-half times at the expense of higher HETS. As of this writing, Scheibel columns up to 2.75 m in diameter are in service. 

Transformations in the Solid State. From a practical standpoint, the most important soHd-state transformation of PB involves the irreversible conversion of its metastable form II developed during melt crystallization into the stable form I. This transformation is affected by the polymer molecular weight and tacticity as well as by temperature, pressure, mechanical stress, and the presence of impurities and additives (38,39). At room temperature, half-times of the transformation range between 4 and 45 h with an average half-time of 22—25 h (39). The process can be significantly accelerated by annealing articles made of PB at temperatures below 90°C, by ultrasonic or y-ray irradiation, and by utilizing various additives. Conversion of... 

The disaccharide stmcture of (12) (trade name SPLENDA) is emphasized by the manufacturer as responsible for a taste quaUty and time—intensity profile closer to that of sucrose than any other high potency sweetener. The sweetness potency at the 10% sucrose solution sweetness equivalence is between 450 and 500X, or about two and one-half times that of aspartame. When compared to a 2% sugar solution, the potency of sucralose can be as high as 750X. A moderate degree of synergy between sucralose and other nonnutritive (91) or nutritive (92) sweeteners has been reported. 

The largest single market is the United States at approximately 40,000 t. Europe as a whole is approximately two and a half times greater than the United States mainly because of the extensive use of chlorinated paraffins as secondary plasticizers in plasticized PVC, which is virtually absent in the United States. 

Molecular modifications of the morphine skeleton have produced numerous derivatives with antitussive properties, some of which have become commercially significant. Ethyknorphine [76-58-4] (29), a simple homologue of codeine, is prepared by ethylating morphine. It is pharmacologically similar to codeine but is seldom used clinically. Pholcodine [509-67-1] (30), the morpholinoethyl derivative of morphine, is used as an antitussive in a number of European countries. It is about one and a half times as potent as codeine, has Htde or no analgesic activity, and produces minimal physical dependence. The compound is prepared by the amino alkylation of morphine (48). 

FIG. 7-1 Constants of the power law and Arrhenius equations hy linearization (a) integrated equation, (h) integrated fimt order, (c) differential equation, (d) half-time method, (e) Arrhenius equation, (f) variahle aotivation energy, and (g) ehange of meohanism with temperature (T in K),... 

From Half-Times The time by which one-half of the reactant has been converted is called the half-time. From Eq. (7-24),... 

Now equation (22.4) as suggested hy BS 7430 will apply, which is based on our di.scussions in Section 21.3.1, where the ground system is normally predetermined for three times the rated eurrent of the eireuit for an FIRC fuse-protected system or one and a half times for an over current release-protected system ... 

The turbine undergoes three basic tests, these are hydrostatic, mechanical, and performance. Hydrostatic tests are to be conducted on pressure-containing parts with water at least one-and-a-half times the maximum operating pressure. The mechanical run tests are to be conducted for at least a period of four hours at maximum continuous speed. This test is usually done at no-load conditions. It checks out the bearing performance and vibration levels as well as overall mechanical operability. It is suggested that the user have a representative at this test to tape record as much of the data as possible. The data are helpful in further evaluation of the unit or can be used as base-line data. Performance tests should be conducted at maximum power with normal fuel composition. The tests should be conducted in accordance with ASME PTC-22, which is described in more detail in Chapter 20. 

The only kinetic data reported are in a Ph.D. thesis (41). Integral order kinetics were usually not obtained for the reaction of a number of ketones with piperidine and a number of secondary amines with cyclohexanone. A few of the combinations studied (cyclopentanone plus piperidine, pyrrolidine, and 4-methylpiperidine, and N-methylpiperazine plus cyclohexanone) gave reactions which were close to first-order in each reactant. Relative rates were based on the time at which a 50% yield of water was evolved. For the cyclohexanone-piperidine system the half-time (txn) for the 3 1 ratio was 124 min and for the 1 3 ratio 121 min. It appears that an... 

Proteins that can flip phospholipids from one side of a bilayer to the other have also been identified in several tissues (Figure 9.11). Called flippases, these proteins reduce the half-time for phospholipid movement across a membrane from 10 days or more to a few minutes or less. Some of these systems may operate passively, with no required input of energy, but passive transport alone cannot establish or maintain asymmetric transverse lipid distributions. However, rapid phospholipid movement from one monolayer to the other occurs in an ATP-dependent manner in erythrocytes. Energy-dependent lipid flippase activity may be responsible for the creation and maintenance of transverse lipid asymmetries. 

FIGURE 14.4 Plot of the course of a first-order reaction. The half-time, <1/9, is the time for one-half of the starting amonnt of A to disappear. 

Hydroxy-8-azapurine was shown by rapid-reaction techniques (see Section II, E) to be anhydrous in the anion and hydrated in the neutral species. The hydration reaction has a half-time of about 0.5 second, which is too rapid for exact measurements with existing apparatus. The cation of 2-amino-8-azapurine was shown to have an anomalous value and ultraviolet spectrum, although its 6-methyl derivative is quite normal. Hydration in this case proved to be too fast to register in the rapid-reaction apparatus. 

Zweibadverfahren, n. two-bath process, zwel-baslsch, a. dibasic, -deutig, a. ambiguous, equivocal, -einhalbfach, a. two-and-a-half-fold. -einhalbmal, adv. two and a half times. 

Fig. 9-6. Steady state internal concentration profiles in the TMB approach and SMB cases at half-time between switchings for the more retained component.

A 26,000 gallon outdoor vertical storage tank contains benzene. The tank is not insulated, but has a dike around it tvith a volume equal to one-and-a-half times the volume of the tank. Size 15 diameter X 20. Tank does not have weak roof. Temp. = 60°F, pressure = 14.7 psia. 

The test pressure shall be twice the working pressure up to 5,000 psi (inch). For working pressures above 5,000 psi, the test pressure shall be one and one-half times the working pressure. 

Propane cracking is similar to ethane except for the furnace temperature, which is relatively lower (longer chain hydrocarbons crack easier). However, more by-products are formed than with ethane, and the separation section is more complex. Propane gives lower ethylene yield, higher propylene and butadiene yields, and significantly more aromatic pyrolysis gasoline. Residual gas (mainly H2 and methane) is about two and half times that produced when ethane is used. Increasing the severity... 

This is the one major property where there is an important difference between LPG vapor and natural gas. Natural gas is lighter than air propane and butane vapors are, respectively, one and half times and twice as heavy as air. This is important in two areas. First, when converting equipment mnning on natural gas to mn on propane or butane the amount of gas which issues from a fixed orifice at a fixed pressure is inversely proportional to the square... 

Drug elimination may not be first order at high doses due to saturation of the capacity of the elimination processes. When this occurs, a reduction in the slope of the elimination curve is observed since elimination is governed by the relationship Vmax/(Km- -[conc]), where Vmax is the maximal rate of elimination, Km is the concentration at which the process runs at half maximal speed, and [cone] is the concentration of the drug. However, once the concentration falls below saturating levels first-order kinetics prevail. Once the saturating levels of drugs fall to ones eliminated via first-order kinetics, the half time can be measured from the linear portion of the In pt versus time relationship. Most elimination processes can be estimated by a one compartment model. This compartment can... 

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