Initial rates of exchange

Note that (a) the reverse steps are needed for steady-state treatment (b) the k-4 step is not shown because the initial rate of exchange is being measured and (c) only the unlabeled enzyme concentration is included in the derivation because the concentration factors of labeled enzyme forms will cancel out during the derivation. Also, each enzyme form is assigned a number for reference purposes. 

A typical curve of exchange is shown in Figure 2. Generally, P. t=g=0, so that the initial rate of exchange may be computed, in this instance, by a simple equation nV... 

Effect of metal loading (samples 1-5). In this series of catalysts was varied by two orders of magnitude our findings allowed us to determine the initial rates of exchange r over a wide range of metal areas. The results are plotted in Arrhenius coordinates in Fig.3. For this series of catalysts,... 

Fig 3 Arrhenius plot of the initial rates of exchange on Rh/A O catalyst. 

Initial Rates of Exchange over Platinum and Silver Films... 

The activation energies, Et and Ec, for exchange and deuteration, were determined in the usual manner, and the values are given in Table VI, together with the frequency factors Ab and Ac. For the purpose of comparing the relative activities of different metals for the two reactions, the temperatures Tb and Tc, at which the initial rates of exchange and deuteration were 1%/min. 10 mg., are also included in Table VI. The results obtained over palladium films were the most extensive and accurate. 

Five catalysts were prepared by addition of chlorine (0.1 and 0.5 wt.% Cl), sulfln (4.5 wt.% 3042 ) or potassium (0.2 and 1.5 wt.% K" ") on the RhA parent catalyst. OSC values and coefficient Ds of surface diffiision (deduced from the initial rates of exchange of 1 02 with the of the support) were measured on these samples. Fig. 4 gives the relative variations (JE%) in the values of OSC and of Ds of the modified catalysts compared to the parent catalyst. 

In most cases, diffusivities are deduced from the initial rates of exchange. In the very beginning of exchange, curves P x x and P xx vs. time can be assimilated to straight lines... 

The above method is practical when one has to determine the rate of exchange after a considerable approach to equilibrium. Another approach is to measure the initial rate of exchange directly by sampling the first 10% of the reaction, which is then reasonably hnear. Then, for analysis, one plots the amount of labeled product formed against time, and the slope of the line is equal to the initial velocity. 

At 910°C the experimental points deviate appreciably from the theoretical curve. This may be due to the fact that the crystallites do not approach a spherical geometry, so that the presence of sharp corners, for example, will imply a high initial rate of exchange. This is equivalent to suggesting that there may be a distribution of particle sizes rather than a unique particle size a. Substitution of a ==166 A from Fig. 5 yields the value D (910°C) = 4.2 X 10"cm sec" ... 

Calculate the initial rate of rise of temperature (K/s) of the hydrocarbon as it enters the heat exchanger. The outside film coefficient = 6.0 kW/m2 K. The inside film coefficient h is given by ... 

When a zinc strip is dipped into the solution, the initial rates of these two processes are different. The different rates of reaction lead to a charge imbalance across the metal-solution interface. If the concentration of zinc ions in solution is low enough, the initial rate of oxidation is more rapid than the initial rate of reduction. Under these conditions, excess electrons accumulate in the metal, and excess cationic charges accumulate in the solution. As excess charge builds, however, the rates of reaction change until the rate of reduction is balanced by the rate of oxidation. When this balance is reached, the system is at dynamic equilibrium. Oxidation and reduction continue, but the net rate of exchange is zero Zn (.S ) Zn (aq) + 2 e (me t a i)... 

It is theoretically possible that equilibrium between liquid and resin will be maintained at all points of contact. Liquid and solid concentrations are then related by the sorption isotherm. It is usual, however, that pellet or film diffusion will dominate or control the rate of exchange. It is also possible that control will be mixed, or will change as the ion exchange proceeds. In the latter case, the initial film-diffusion control will give way to pellet-diffusion control at a later stage. 

The initial concentration of N02(g) is zero. The initial rate of the forward reaction, Jcf, is relatively large, while the initial rate of the reverse reaction, Jq, is zero. The initial conditions correspond to the first exchange in the ExpressLab on page 325, where the reactant cylinder was full and the product cylinder was empty. As the reaction proceeds, the rate of the forward reaction decreases because the concentration of N204(g) decreases. At the same time, the rate of the reverse reaction increases because the concentration of N02(g) increases. At equilibrium, Jcf = Jq. There are no further changes in the relative amounts of N2O4 and NO2. 

One can imagine two protons, and He, being part of the same molecule and undergoing chemical exchange, at a rate knu- When is irradiated, it remembers the new condition and transfers this information to Hj as a result of the chemical exchange. The newly arrived He proton does not contribute to the normal amount of signal intensity in the final NMR spectrum. If the initial intensity of Hj is 4, and the final intensity for Hg as a result of irradiation of is If, then the rate of exchange knu is defined by Eq. (7), where Tj refers to the spin-lattice relaxation time. 

Figure 1. Initial rate of isotopic exchange of the oxygen of oxides with molecular oxygen at 370°C, Curve 1 and their relative activity in hydrogen oxidation at 340°C, Curve 2. The activity of lanthanum oxide is taken to be unity (1).

In order to gain a fuller insight into the nature of any exchange reaction, it is necessary to determine a second rate constant k, representing the initial rate of disappearance of the light hydrocarbon C H in percentage per unit time. This may be obtained by using the empirical first-order equation... 

Flanagan and Rabinovitch were able to establish another point of general interest. They deduced from the relative rates of exchange and isomerization of isotope effect in the rupture of the carbon- hydrogen bond when adsorbed ethyl radicals dissociate to form adsorbed ethylene molecules. The ratio of the rupture probabilities of C—H and C—D decreased from 15.9 at —78° to 1.4 at 429°. More evidence of this kind would obviously be valuable because it suggests that some revision may be necessary of the theory for calculating initial distributions of... 

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