First order process

An experlnnent to determine the effect of a pH jump on the absorption of carboxymethylated horse heart cytochrome c 

Prepare a stronger buffer at the desired pH value, e.g. 0.1 m sodium phosphate pH 7. 

Fill one drive syringe with the protein solution and fill the other drive syringe with the strong buffer solution. 

Set the wavelength to give the maximum absorbance difference for the pH-dependent change, determined separately as described above. 

Discharge several shots to flush out old reagents/buffer and then record and average the data horn several reactions. 

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Multichannel time-resolved spectral data are best analysed in a global fashion using nonlinear least squares algoritlims, e.g., a simplex search, to fit multiple first order processes to all wavelengtli data simultaneously. The goal in tliis case is to find tire time-dependent spectral contributions of all reactant, intennediate and final product species present. In matrix fonn tliis is A(X, t) = BC, where A is tire data matrix, rows indexed by wavelengtli and columns by time, B contains spectra as columns and C contains time-dependent concentrations of all species arranged in rows. 

As with any first-order process, equation 13.24 can be expressed in an integrated form. 

If state n in Figure 2.2(a) is populated in excess of its Boltzmann population by absorption, the species M in this state will decay to the lower state until the Boltzmann population is regained. The decay is a first-order process, so that... 

Water-soluble peroxide salts, such as ammonium or sodium persulfate, are the usual initiators. The initiating species is the sulfate radical anion generated from either the thermal or redox cleavage of the persulfate anion. The thermal dissociation of the persulfate anion, which is a first-order process at constant temperature (106), can be greatly accelerated by the addition of certain reducing agents or small amounts of polyvalent metal salts, or both (87). By using redox initiator systems, rapid polymerizations are possible at much lower temperatures (25—60°C) than are practical with a thermally initiated system (75—90°C). 

Waste Destruction by Combustion Reaction. At the simplest level, waste destmction can be thought of as a first-order process involving the thermally excited mpture of a chemical bond. The time to achieve a given extent of reaction, T, can be found from... 

In the case of the bridged complexes, the process involves changing from a bidentate to a monodentate configuration. For these systems the mode of transformation is variable. In close-packed crystals the rearrangement is a first-order process, ie, it occurs discontinuously at a fixed pressure. For slightly less close-packed crystals the transformation occurs over some range of pressure, eg, 2—3 GPa (20—30 kbar). In the language of physics the process... 

When reactions other than first-order processes are included in the kinetic scheme, reactant concentrations may appear in the denominator of the rate equation. Scheme XIX is an example. 

Not surprisingly, we find that the relaxation is a first-order process with rate constant A , + A i. It is conventional in relaxation kinetics to speak of the relaxation time T, which is the time required for the concentration to decay to Me its initial value. In Chapter 2 we found that the lifetime defined in this way is the reciprocal of a first-order rate constant. In the present instance, therefore,... 

Enigmas abound in the world of enzyme catalysis. One of these surrounds the discussion of how the rate enhancement by an enzyme can be best expressed. Notice that the nncatalyzed conversion of a substrate S to a product P is usually a simple first-order process, described by a first-order rate constant... 

As pointed out in Chapter 11, radioactive decay is a first-order process. This means that the following equations, discussed on pages 294-295, apply ... 

Melting of ECC involving transition into the isotropic melt was shown by Flory to be a first-order process. It can be seen in Fig. 18 b that there occurs a transition from a complete order to a fully random chain arrangement in the isotropic melt (Fig. 16, point 4). 

The finite transit time (xr) in the high strain-rate region has important consequences on the scission yield curve. Since bond scission is a first-order process (Eq. 96), the degradation yield in a single pass experiment is given approximately by ... 

Malonic acid decomposed in a KBr matrix at 413—440 K to acetic acid and C02 by a first-order process with E = 96 kJ mole-1. 

The related chromium compound [1140], trans-[Cr(pn)2Br2]Br H20, undergoes rapid dehydration at 395 419 K by a first-order process for which E = 96 kJ mole-1 and this is accompanied by some 10% isomerization to the cis compound. At higher temperatures, 433-473 K, the residual anhydrous trans compound isomerizes in the solid state this is also a first-order process and E = 180 kJ mole-1. 

Early kinetic work127 showed that the formation of both ortho and para products was a first-order process and that the rates of reaction were insensitive to added acid or base and to change of solvent. The activation parameters were of the same order of magnitude for both reactions and the suggestion was made that both had a similar rate-determining step. Schmid et a/.128 showed that the formation of a dienone intermediate in the para rearrangement was also reversible since the radioactivity from allyl 2,6-dimethyl-4-allyl-y-14C phenyl ether LXXXVII became uniformly distributed in the y carbon atoms of the O- and C-allyl groups... 

Tarbell and Petropoulos159 measured the rate of formation of phenol from benzyl phenyl ether catalysed by aluminium bromide and found it to be a first-order process. Moreover, the rate coefficient was the same as that for the formation of phenol from ortho benzyl phenol. Since the ratio of products (phenol ortho benzyl phenol) was unaffected by a large change in the temperature it was argued... 

A clean first-order process may erroneously appear to be a biphasic one, and vice versa. If the distortion to the property-time curve is not so evident as in the example, there might be a smooth rise or fall from reactant to product. The linearity of the plot of In (Y, - Kcc) versus time depends on the end point reading Yr.. One must be cautious, however, in ascribing a mildly curved plot of In Y, - W) versus time to a biphasic pattern. Were the observed value of Yx off by a small amount, a simple adjustment could give a straight-line plot indicative of first-order kinetics. Of course, if Tec is adjusted to force linearity, one must surely ask whether the revised value of Yx represents a reasonable extrapolation of the data, lest the proper but more complex reaction pattern be concealed. 

In a consecutive step, a first-order process, the hydroxycyclohexadienyl radicals decompose to give the sulfinic acids as is given in reaction 30. The rate constants /c, and k2 are also given in Table 1. In this case kt was calculated from the build-up of the hydroxycyclohexadienyl radicals. 

Self-Test 13.7B Cyclopropane isomerizes to propene in a first-order process. How long does it take for the concentration of cyclopropane to decrease from 1.0 mol-L 1 to 0.0050 mol-L 1 at 500.°C Use the data in Table 13.1. 

The half-life, f1/2, of a substance is the time needed for its concentration to fall to one-half its initial value. Knowing the half-lives of pollutants such as chlorofluoro-carbons allows us to assess their environmental impact. If their half-lives are short, they may not survive long enough to reach the stratosphere, where they can destroy ozone. Half-lives are also important in planning storage systems for radioactive materials, because the decay of radioactive nuclei is a first-order process. 

In 1989 a teenager in Ohio was poisoned by breathing vapors from spilled mercury. The mercury level in his urine, which is proportional to its concentration in his body, was found to be 1.54 mg-L. Mercury(ll) is eliminated from the body by a first-order process that has a half-life of 6 days (6 d). What would be the concentration of mer-cury(II) in the patient s urine in milligrams per liter after 30 d if therapeutic measures were not taken ... 

For a first-order process, calculate the rate constant, elapsed time, and amount remaining from the half-life (Example 13.6 and Self-Test 13.9). 

Such important materials as organic peroxides, azo compounds, as well as many other types of materials, are described by the first-order process and as such follow the general development given in this work. The efficiency will be assumed constant and the same for all initiators with 0.5. 

Sink. A flux (S) of material out of a reservoir -very often this flux is assumed to be proportional to the content of the reservoir (S = kM). In such cases the sink flux is referred to as a first-order process. If the sink flux is constant, independent on the reservoir content, the process is of zero order. Higher-order fluxes, i.e. S = kM with a > 1, also occur. 

Cell Death. Spontaneous death or sporulation of cells is commonly modeled as a first-order process. Equation (12.8) (or 12.12)) is modified to include a disappearance term ... 

The traditional arrangement of simple spherical glassware and Isomantles with full-power on-off controllers monitored by mercury thermometers, would still be widely recognised. So too would be the plug-shot piston pumps set up and monitored by use of measuring cylinders. Although tried and tested this hardware system requires constant attention by a skilled lab. technician to achieve control and reproducibility of even the first-order process parameters manual data collection is hardly feasible at better than 10-15 minute intervals. 

Cheletropic elimination of the in situ generated phosphinidene complex 8 from the 7-phosphanorbornadiene precursor is believed to be the rate-determining step before 1,2-cycloaddition occurs to the unsaturated hydrocarbon. Without catalysts these are first-order processes that depend only on the concentration of the precursor and not on that of any substrate [47]. The configu-... 

Thus if one starts with one pure isomer of a substance, this isomer can undergo first-order transitions to other forms, and in turn these other forms can undergo transitions among themselves, and eventually an equilibrium mixture of different isomers will be generated. The transitions between atomic and molecular excited states and their ground states are also mostly first-order processes. This holds both for radiative decays, such as fluorescence and phosphorescence, and for nonradiative processes, such as internal conversions and intersystem crossings. We shall look at an example of this later in Chapter 9. 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

Equation does not contain the concentration of A, so the half-life of a first-order reaction is a constant that is independent of how much A is present. The decomposition reactions of radioactive isotopes provide excellent examples of first-order processes, as Example illustrates. We describe the use of radioactive isotopes and their half-lives to determine the age of an object in more detail in Chapter 22. 

C15-0124. Phosphorus-32 is a radioactive isotope that decomposes in a unimolecular first-order process. The... 

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... 

The rapid first-order exchange rate ° for Ni(CO)4 is to be contrasted with the much slower rates for the carbonylate anions Co(CO)4 and Fe(CO)4 , and this is quite in accordance with a higher M-C bond order in these two latter compounds, provided that the primary reaction step is a dissociative one. The group VI hexacarbonyls exchange CO several orders of magnitude more slowly than Ni(C0)4 by a first-order process in the gas phase There is very good... 

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