Steady-state expressions

In the preceding subsection we described the preequilibrium assumption. Let us now see how that assumption is related to the steady-state approximation. Scheme XIV will serve for the discussion. The equilibrium and steady-state expressions for the intermediate concentration are... 

What makes this more difficult is the occurrence of paths for the loss of A that are second-order and first-order with respect to [A], The steady-state expression for [A] gives... 

Before we discuss the merits of kss versus kpe, we shall consider one other approximate solution. Some authors refer to it as the improved steady-state solution. 2 We shall present two derivations. In the first, the approximation for d[ ]/dt is refined by differentiating the steady-state expression for [I]ss, which gives... 

Since reactions E/Ei and E2/E jointly govern the kinetics of the primary catalytic loop, [E, ] and [EiQ] are negligible. The forms remaining into play are thus E, ES, E2, E2Q, and E3. The following expression of the E2 concentration follows from the steady-state expression of the concentrations of the various forms of the enzyme, taking into account that 3[Q] > 4 [S] ... 

The approach considered as a starting point is a generalized form of Eq. (3.7) of Chapter 3, but not as a steady-state expression. Thus, the overall rate of change of the concentration of chain carriers (R) is expressed by the equation... 

The steady-state expression for this same scheme (in which the forward rate constants are ki, kg, kg, kj, and... 

The steady-state expression for v for this scheme is rather complex, containing squared terms in [S] and in [A] in... 

Under initial rate conditions, where the product concentrations are effectively zero [P] 0, [Q] 0, and [R] 0), the steady-state expression for this reaction mechanism is... 

The steady-state expression for this reaction scheme, in the absence of any products and abortive complexes, is... 

Alternatively, experiments were also carried out under conditions of excess of substrate, that is, S0 C0. Under these circumstances initial velocities V0 are measured and the steady-state expression for the scheme in (25) is... 

Physically, this is essentially the same process as the adsorption/desorption in reaction 11.41 when i becomes large. Assuming that the governing equilibrium constant is thus the same as in Eq. 11.47, the steady-state expression result is... 

Insertion of the steady-state expression for the H concentration yields... 

The diffusion coefficient for a gas can be experimentally measured in an Arnold diffusion cell. The device is shown in Figure 3.6 consisting of a narrow tube partially filled with pure liquid A. The system is maintained under constant pressure and gas B flows across the open end of the tube. Component A vaporizes and diffuses into the gas phase, hence the rate of vaporization can be physically measured. Develop a general steady-state expression to describe the diffusion of one gas through a second stagnant gas. Assume that the gas has negligible solubility in liquid A and is also chemically inert in A. 

Pick out the intermediates and formulate a steady state expression, +d[intermediate]/ df 0, where possible. From these, find expressions for each steady state concentration, and then formulate the overall rate of reaction in terms of the rate of production of CH4. 

Inhibition can be reduced to virtually zero if initial rates are used. Very little product, HBr, will have built up during the period of experimental measurements and the rate of the inhibition step will be virtually zero. In the steady state expression for [H ], Equation (6.85), the term in 2 will drop out, leaving... 

The steady state expression for Br, Equation (6.86), then reduces to... 

A very important point to notice. The steady state analysis shows that not all the individual rate constants can be found from the steady state reaction. In this case the steady state expression only involves three of the rate constants lc3 does not appear. 

This is exactly the same expression as the approximate steady state expression, Equation (8.157), corresponding to the condition, k2[Y ] -C i [X ], which, in turn, corresponds to most of the R+ being removed by the back reaction, rather than by reaction with Y. ... 

CH3CHO decomposition - determination of the mechanism, 211-213 the steady state analysis, 233-238 setting up of the steady state expression for the overall activation energy in terms of the activation energies for the individual steps, 238-239 H2/Br2 reaction - a steady state analysis on the reaction with inhibition, 213-216 without inhibition 216-217 determination of the individual rate constants, 217-218 Stylised Rice-Herzfeld mechanisms, 221-224, with surface termination, 240-243 RH/Br2 reaction - a steady state analysis, 225-227... 

However, this is not the final form of the rate law for the overall reaction because it contains the concentration of an intermediate. We can remove this concentration from the rate law by solving the steady-state expression... 

Construct a steady-state expression for each intermediate I by applying the criterion... 

In support of reaction (28) was the observation that OCIO mixed with ozonized O2 produced CI2O6 (which exists as CIO3 in the vapor). This mechanism leads to the steady-state expression... 

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