Decay rate law

Deactivation by sintering m in some cases be a function of the mainstream gas concentration. Although other forms of the sintering decay rate law exist, one of the most commonly used decay laws is second-order with respect to the present activity ... 

The activity, as before, is a function of the time the catalyst has been in contact with the reacting gas stream. The decay rate law is... 

If we ROW differentiate Equation (10-122) and combine it with the decay rate law, we obtain... 

The catalytic deactivation is independent of gas-phase concentration and follows a first-order decay rate law, with a decay constant of 0.72 reciprocal minutes. The feedstream is diluted with nitrogen so that as a first approximation, volume changes can be neglected with reaction. The reactor contains 22 kg of catalyst that moves through the reactor at a rate of lOkg/min. The gas oil is fed at a rate of 30mol/min at a concentration of 0.075 mol/dm, Determine the conversion that can be achieved in this reactor. 

Consequently, both fcg and kj can be found from a plot of [Ca/(Cao C )] versus t, as shown in Figure 10-32. We can continue assuming decay orders in this manner until the decay rate law is found. 

The general idea of the three previous cases (i.e., Figures 10-31 through 10-33)is to arrange the data in such a fashion as to arrive at functional groupings of measured variables that will be linear with time. The particular functional groups will vary with (1) type of reactor used to collect the data, (2) reaction order of the main reaction, and (3) the decay reaction order. For the three main types of reactors, three main reaction rate laws, and three decay rates, 27 different types of plots could result. We leave derivation of the equation for each of these plots to the reader and point out that only one additional step is needed in our solution algorithm. That step is the decay rate law ... 

The conditions chosen make the reaction appear to be first-order overall, although the reaction is really not first-order overall, unlessjy and happen to be 2ero. If a simple exponential is actually observed over a reasonable extent (at least 90—95%) of decay the assumptions are considered vaUdated and is obtained with good precision. The pseudo-first-order rate constant is related to the k in the originally postulated rate law by... 

Ohmic charge decay processes obey a first order rate law from which the charge Q remaining at any time t can be expressed in terms of the initial charge Qq and relaxation time constant r. Using Eqs. (2-3.4) through (2-3.5) the time constant r can alternatively be expressed as... 

The luminescence of an excited state generally decays spontaneously along one or more separate pathways light emission (fluorescence or phosphorescence) and non-radiative decay. The collective rate constant is designated k° (lifetime r°). The excited state may also react with another entity in the solution. Such a species is called a quencher, Q. Each quencher has a characteristic bimolecular rate constant kq. The scheme and rate law are... 

As in a unimolecular chemical reaction, the rate law for nuclear decay is first order. That is, the relation between the rate of decay and the number N of radioactive nuclei present is given by the law of radioactive decay ... 

In this context, k is called the decay constant. The law tells us that the activity of a radioactive sample is proportional to the number of atoms in the sample. As we saw in Section 13.4, a first-order rate law implies an exponential decay. It follows that the number N of nuclei remaining after a time t is given by... 

A radioactive isotope X with a half-life of 27.4 d decays into another radioactive isotope Y with a half-life of 18.7 d, which decays into the stable isotope Z. Set up and solve the rate laws for the amounts of the three nuclides as a function of time, and plot your results as a graph. 

A sample of any unstable nuclide undergoes nuclear decay continuously as its individual nuclei undergo reaction. All nuclear decays obey the first-order rate law Rate = C. This rate law can be treated mathematically to give Equation, which relates concentration, c, to time, t, for a first-order process (Cq is the concentration present at... 

As an example of the use oftbe expooneiniaL d logarithmic functions in physical chtStustiy, CQij er a finst-oider chemical reaction, such as a radioactive decay. It follows the rate law... 

Figure 6 shows the measured dynamic structure factors for different momentum transfers. The solid lines display a fit with the dynamic structure factor of the Rouse model, where the time regime of the fit was restricted to the initial part. At short times the data are well represented by the solid lines, while at longer times deviations towards slower relaxations are obvious. As it will be pointed out later, this retardation results from the presence of entanglement constraints. Here, we focus on the initial decay of S(Q,t). The quality of the Rouse description of the initial decay is demonstrated in Fig. 7 where the Q-dependence of the characteristic decay rate R is displayed in a double logarithmic plot. The solid line displays the R Q4 law as given by Eq. (29). 

A radioactive substance is one in which the atomic nuclei are unstable and spontaneously decay to form other elements. Because the nuclei decay, the amount of the radioactive material decreases with time. Such decreases follow the straightforward kinetic rate laws we discussed above. 

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