Concentration changes with time

Thus, it can be said that in practically all activities there are risks to health related to the presence of chemical agents. To evaluate their severity we should consider whether the exposure occurs continuously or at irregular intervals, the possible entry routes to the body, the concentration changes with time and place, as well as the aggregation state of the contaminant in liquid, dust, mist, fume, or vapor form. 

Equation is one of the few rate statements that follow from knowledge of the reaction stoichiometry. Almost all other rate information must be determined by carrying out experiments on how concentrations change with time. Example illustrates the application of Equation. ... 

Equations and describe how concentration changes with time when only a single reactant is involved. However, most reactions involve concentration changes for more than one species. Although it is possible to develop equations relating concentration and time for such reactions, such equations are more complicated and more difficult to interpret than the equations that involve just one reactant. Fortunately, it is often possible to simplify the experimental behavior of a reaction. We describe two experimental methods that accomplish this, the isolation method and the method of initial rates. 

The time savings and improved spatial resolution of MRI measurements over traditional measurements are profound advantages of MRI. MRI can provide similar information in less than 1 h when literally it would otherwise require days. This would be of particular interest in diffusion type experiments where spatial concentration changes with time are measured. In addition, the same sample can be... 

In contrast, unsteady mass transport means that there exists a concentration change with time, depicted mathematically by... 

Kinetic schemes involving sequential and coupled reactions, where the reactions are either first-order or pseudo-first order, lead to expressions for concentration changes with time that can be modeled as a sum of exponential functions where each of the exponential functions has a specific relaxation time. More complex equations have to be derived for bimolecular reactions where the concentrations of reactants are similar.19,20 However, the rate law is always related to the association and dissociation processes, and these processes cannot be uncoupled when measuring a relaxation process. 

In a batch vessel, the reactants are loaded at once, then the concentration changes with time, but at any one time it is uniform throughout. The horizontal portion of Fig 4.1(b) corresponds to a period before reaction starts, before injection of catalyst, say, or before the temperature has been adjusted properly. 

Equation (5.1) is extremely useful to evaluate the flux whenever the concentration gradient can be considered constant with time (i.e., when we can assume a steady state). When a steady state cannot be assumed, the concentration change with time must also be considered. The non-steady-state diffusion is expressed by Pick s second law of diffusion ... 

The temperature and composition of the contents of an ideal batch reactor are uniform at any instant, but the concentration changes with time. Since the composition is uniform, the mass balance may be performed over the whole reactor. 

In cases where an acceptable kinetic mechanism can be established, it may be possible to obtain expressions, such as those in Sect. 2, which predict concentration changes with time when the values for the rate coefficients are known. However, the use of these expressions to evaluate rate coefficients from experimental data is not always straightforward, particularly with coupled reaction systems where a key reactant participants in a reversible step. Initial rate measurements are often of insufficient accuracy and, with very complex sj stems, it becomes necessary to obtain a great deal of data from experiments in which initial concentrations can be varied. 

The number of mobile phase components whose concentrations change with time ... 

If the growth rate is controlled by both interface reaction and diffusion (Figure 1-1 Id), then (i) the concentration profile is not flat, (ii) the interface concentration changes with time toward the saturation concentration, (iii) the diffusion profile propagates into the melt, and (iv) the growth rate is not constant, nor does it obey the parabolic growth law. 

Figure 5-25 (a) Diffusion profile across a diffusion couple for a given cooling history. This profile is an error function even if temperature is variable as long as D is not composition dependent, (b) Diffusion profile across a miscibility gap for a given cooling history. Because the interface concentration changes with time, each half of the profile is not necessarily an error function. 

If the liquid phase is reacting and batch, the system becomes dynamic as the liquid phase concentrations change with time. To simplify the reactor model, we consider the common case of constant gas-phase concentration. Furthermore, the liquid phase is considered to be under complete mixing condition. 

This law states that the local concentration change with time due to a diffusive transport process is proportional to the second spatial derivative of the concentration. 

Now the probability of reactants 1 and 2 simultaneously being at rj and r2 is n(r1,r2). The two-body density or concentration changes with time due to a net flux into the small volume drtdr2, that is the law of conservation of matter or the equation of continuity of mass... 

Chemical kinetics (concentrations changing with time). 

It can be readily discerned that the reactor equation for the batch reactor (5.12) and the plug-flow reactor (5.13) are identical. In the former, the concentration changes with time, in the latter, with location. In contrast to the situation in the other two ideal reactors, the residence time T in a CSTR is only an average, as every volume element has a different residence time throughout the reactor. 

Figure 8.7 Plasma concentration changes with time in intravenous infusion...

Flow-through microcells which are used for preconcentration of substances (stripping techniques) or to get a fast response if the concentration changes with time. In applications with large current densities the electrolyte flow guarantees the supply of educt or the removal of products. 

The first law of Pick tells one how the concentration gradient is related to the flux under steady-state conditions it says nothing about how the system goes from nonequilibrium to steady state when a diffusion source or sink is set up inside or at the boundary of the system. Thus, it says nothing about how the concentration changes with time at different distances from the source or sink. In other words. Pick s first law is inapplicable to nonsteady-state diffusion. For this, one has to go to Pick s second law... 

The Teclanche cell has the disadvantage that its concentrations change with time, and thus the voltage of the battery falls as it is used. In an alkaline dry cell, the ammonium chloride is replaced by potassium hydroxide, and the half-cell reactions become... 

The set of differential equations in Equation 1 relates properties of target and mAb, and its solution will result in concentration changes with time. Figure 18.1 explores the effects of mAb affinity, mAb dose, target synthesis/clearance rate, and target concentration on dosing interval. As expected, mAb with higher dose... 

The diffusion across this thin film is considered to be a steady-state problem. There are no concentration changes with time, as indicated in Fig 5.13. 

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