Time, as a factor

The properties of a system at equilibrium do not change with time, and time therefore is not a thermodynamic variable. An unconstrained system not in its equilibrium state spontaneously changes with time, so experimental and theoretical studies of these changes involve time as a variable. The presence of time as a factor in chemical kinetics adds both interest and difficulty to this branch of chemistry. 

However, process chemistry has several features that distinguish it from other DOE applications. As noted, time is always a critical factor. Time can also be a response, as in time to reaction completion, but its primary role is as a factor with carefully chosen levels. Generally, time is considered a nested factor, the levels selected depend on the level of other factors in the experimental run. Reactions proceed at very different rates depending on the levels of the other factors, especially temperature, thus the time points providing the most information will differ from experiment to experiment. One can think of time as a factor that is subsampled from within the other factor combinations in the design. In fact, the design is usually built in a sequential fashion. First, the nontime factors (whole plot factors) are combined into a design, then the levels of time are determined separately for each experimental run (whole plot combination). In order to facilitate comparisons, one may choose to select some time points that are common across the experiments, but the key criteria is to choose time points that build toward quality estimates of the main responses—the reaction rates. 

If the linear factor as + b occurs n times as a factor in the denominator, there corresponds to this factor a sum of n partial fractions ... 

Erfolgsfaktor Durchlaufzeiten (Throughput times as a factor to success) Verlag TUV Rheinland, 1989 ISBN 3-88585-699-9... 

Any improvement in resolution obtained by increasing ki generally comes at the expense of a longer analysis time. This is also indicated in Figure 12.11, which shows the relative change in retention time as a function of the new capacity factor. Note that a minimum in the retention time curve occurs when b is equal to 2, and that retention time increases in either direction. Increasing b from 2 to 10, for example, approximately doubles solute B s retention time. 

In experimental work, some accidental exposures, or in the administration of medicine, the dose may be a certain quantity of the chemical administered at one time, such as in a pill, an injection, or an accidentally swallowed poison. In industry, time is a factor in most exposures, and the dose is the result of both the concentration of the toxic agent and the duration of the exposure. 

The smallest size difference that can be resolved is related to the pore volume, the solute shape, and the efficiency of the column (see Fig. 2.6). However, this is at very low loadings. At higher loadings the sample volume will contribute to zone broadening and may, in some cases, be the dominating factor for resolution. Thus, for fractionation, an optimum exists with respect to column efficiency (represented by the flow rate as operational parameter) and sample volume for processing a particular volume of feed per unit time. As a rule of thumb this optimum can be found at a relative sample volume of 2-5% of the column volume (Hagel et al., 1989). 

OS 81] [R 7] [P 61] An increase in residence time by a factor of about 3 was accomplished by changing the flow rate from 3.0 to 0.9-1.1 pi min [19[. By far the main reaction product detected was methane otherwise only traces of methanol were present. Instead, at the shorter residence hme a mixtrue containing 68% ethene, 16% ethane and 15% methane was obtained [19,138[. Hence the presence of methane demonstrates that complete cracking occurred as a consecutive reaction to dehydration. 

Dermal Absorption. To determine the toxicity of parathion following dermal application, the method of Draize, Woodard, and Calvery (3) was followed. Variables considered in the design of these experiments were concentration as a factor of area, solvent, exposure time, and number of exposures. In some cases the wettable powder was applied in the dry form, while in other cases sufficient water was added to produce a viscid paste. All doses in the table are presented as milligrams per kilogram of parathion, regardless of the concentration or solvent. 

T]he Origin of Species proposed a radically new idea, conceiving of time not as a power but as a factor whose effect could be perceived directly in distinct but complementary forms fossils, embryos, and rudimentary organs. The fossil was petrified time the embryo, operative time the rudimentary organ, retarded time. Together these bits of evidence constituted the archives of biological history —... 

The Monod equation differs from the Michaelis-Menten equation in that it includes as a factor biomass concentration [X], which can change with time. A microbe as it catalyzes a redox reaction harvests some of the energy liberated, which it uses to grow and reproduce, increasing [X], At the same time, some microbes in the population decay or are lost to predation. The time rate of change in biomass... 

Retention distance (or time) is normally used to aid the identification of a component of a mixture, provided that a known sample of the component has been subjected to separation under identical conditions. Because of the variations that can occur in the retention time due to technical factors, e.g. fluctuations in flow rate, condition of the column, the relative retention or selectivity factor (a) is sometimes used. This expresses the test retention time as a ratio of the retention time of another component or reference compound when both are injected as a mixture ... 

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