Half time data

Half time relations are useful for finding specific rates from data because of the simplicity of the their formulas. To find the order, it is necessary to have half time data with several starting concentrations. 

P3.05.09. RATE EQUATION FROM HALF TIME DATA... 

Find the order and specific rate of a reaction for which these two half time data are known ... 

A sorption isotherm on excised human abdominal stratum corneum (female, age 68) is presented in Figure 9. The data were obtained on separate pieces of skin which were initially dried and then exposed to an air stream with a given RH uptake was followed until equilibrium was reached. Values of D calculated from half-time data for each humidity interval were 1.37-5.10 X 10 cm /sec. Scheuplein and Blank (16) reported a value of 5 X 10 cm /sec for human stratum corneum. The range of our values would indicate that D is concentration dependent. Full details will be reported in the future. 

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... 

Let us now assume that these matters have been attended to properly. At this stage we can but assume that the reaction orders were correctly identified and correct mathematical procedures followed. During the course of the work, the investigator should make the occasional quick calculation to show the values are roughly correct. (Does the rate constant yield the correct half-time ) Also, one should examine the experimental data fits to see that the data really do conform to the selected rate equation. Deviations signal an incorrect rate law or complications, such as secondary reactions. 

The logarithmic plot is not linear, of course, since this is not a first-order reaction. Note, however, that even In [A], is linear in time to about 50 percent reaction. One cannot use these procedures to establish the kinetic order without data taken to at least two half-times, and preferably longer. 

Second-order kinetics, (a) Derive expressions for the half-time and lifetime of A if the rate law for its disappearance is v = fc[A]2 (b) calculate t]/i and t for the data presented in Section 2.2 (c) calculate the second half-life, t /i(2), i.e., the time elapsed between 50 percent and 75 percent completion, for the same reaction (d) compare fj/2(l) and fi/>(2), and contrast this result with that from first-order kinetics. 

Under conditions where the dismutation reaction is slow the exchange between Au(III) and Au(I) has been shown to proceed at a measurable rate at 0 °C in 0.09 M HCl, an exchange half-time of about 2 min was observed. The isotopic method ( Au) and a separation method based on the precipitation of dipyridine -chloroaurate(III) was used to obtain data. An acceleration in the exchange rate was observed as the HCl concentration was increased. ... 

Figure 8.1 shows the number and proportion of professional and administrative staff responsible for registration, and the equivalent number of full-time personnel. For part-timers, if there are no data on the amount of work-time, it has been assumed that they work half-time (0.5). For Cypms and Zimbabwe, where staff perform multiple functions, the total numbers of staff have been used. 

Example. A tablet containing 100 mg of a drug was administered to a healthy volunteer and the plasma concentration (Cp) versus time data shown in Table 6 were obtained. Figure 11 shows a semi-log plot of these Cp versus time data. The half-life for elimination of the drug can be estimated from the straight line tail of the plot to be 4.7 hours. The overall elimination rate constant is then... 

The essential features of the above picture are shown schematically in Fig. 6. Hydrogen or deuterium adsorbs and desorbs rapidly on these sites (half-time less than 1 min) hence, the slower H2-D2 equilibration (half-time about 8 min) appears to be determined by the site-to-site migration required for exchange. Poisoning experiments show that water also prefers these sites in agreement with the limited IR data, Fig. 6 shows the adsorbed water yields surface hydroxyls (10). 

Radiocerium absorbed into the systemic circulation will be transported by blood proteins and be deposited predominantly in liver and bone. Deposition fractions will be about 0.45 for liver, 0.35 for bone, and 0.1 for other soft tissues with the remainder excreted in urine and feces. The retention times in liver and bone are long compared to the radioactive half-lives of the cerium isotopes. Therefore, their effective biological half-times in these organs will be approximately equal to their physical half-lives. Experimental data on internal organ distri-... 

Data on the absorption of simple salts of the lanthanide elements injected intramuscularly into rats are summarized in Figure 10.4 The dependence of the fraction remaining at the injection site on the administered mass is apparent. When the amount injected was less than 0.01 jug, about 0.5 was absorbed in the first few days another 0.4 was absorbed with a half-time of about 25 days and the remaining 0.1 left the injection site with a half-time of 100 to 200 days. As the total mass injected was increased, the fraction absorbed in the first few days declined, and the amounts associated with the lower absorption rates increased. If 100 jug or more were injected, only 0.05 to 0.1 was absorbed during the first few days, and absorption was very slow thereafter. 

Biological half times of cadmium in humans is lengthy. Based on body burden and excretion data, cadmium may remain in the human body for 13 to 47 years. Although cadmium is excreted primarily in urine and feces, it tends to increase in concentration with the age of the organism and eventually acts as a cumulative poison (Hammons et al. 1978). These phenomena have not been documented adequately in wildlife species. 

Figure 32.8 Relation between diet, metabolism, and body weight with half-time retention of longest-lived component of cesium-137. Data are shown for selected ruminant and nonruminant mammals (Richmond 1989) and ectotherms (Hinton and Scott 1990.)... 

A sample of iodine-128 was produced in a Szilard-Chalmers reaction by irradiating a sample of ethyl iodide in a neutron source. The radio-iodine was extracted with sodium thiosulfate solution and then counted in a Geiger counter at various time Intervals. Use the tabulated data of t in minutes against C counts/min to find the rate equation and the half time. 

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