Writing rate

Equation (5-6) gives the number of bimoleeular collisions per unit time and volume, but not all of these eollisions lead to reaetion, and so we write rate = eollision frequeney X fraetion of eollisions having energy equal to or greater than that required for reaetion, or... 

Suppose that the following reactions are elementary. Write rate equations for the reaction and for each of the components ... 

Using the second step which is the slow, rate-determining step, we can write rate = 2[D][B],... 

A triatomic molecule undergoes the reaction, A3 B + C, in contact with a catalytic surface. It dissociates completely on adsorption. Write rate equations for the two cases (a) Surface reaction rate controlling, adsorptive equilibrium of all participants maintained (b) Rate of desorption of substance B controlling, surface reaction equilibrium maintained. 

From other experiments involving the reaction between nitrogen tetroxide and nitrogen dioxide, chemists know that both the forward and reverse reactions involve elementary steps. Thus, you can write rate equations for the reactions. 

You can write rate equations for these reactions because they are elementary mechanisms. Guldherg and Waage, however, showed that similar results are found for any reaction, regardless of the mechanism. For any general equilibrium equation, let P, Q, R, and S represent chemical formulas and a, b, c, and d represent their respective coefficients in the chemical equation. 

We now proceed to write rate expressions for all species and solve them. Mass balances on adsorbed A and B yield... 

In chemical kinetics it is customary to write rate equations in terms of the densities or concentrations c = rij/Q. For the rate at which the reaction (1.1) occurs one takes, following Van t Hoff,... 

Taking into account these processes one may write rate equations (Daily, 1) for the individual energy levels. For a simple two-level system one has... 

After writing rate laws for the rate of fonnation of desited product, write the rate laws for each of the active inteimediates. 

To illustrate how to write rate laws for reversible reactions we will use the combination of two benzene molecules to form one molecule of hydrogen... 

When writing rate laws for these steps, we treat each step as an elementary reaction the only difference is that the species concentrations in the gas phase are replaced ly their respectiven tial pressures ... 

Treat each reaction step as an elementary reaction when writing rate laws. 

To meet the third criterion (that the mechanism conforms to the overall rate law), we first write rate laws for the elementary steps ... 

Write rate laws for both directions of the fast step and for the slow step. 

If transfer from the gas phase to the precursor state is non-activated the energy diagram in Fig. 2 is applicable. Writing rate coefficients k as the product I exp (— E/RT) and noting from Fig. 2 that... 

In writing rate equations only for it is tacitly assumed that translational relaxation is instantaneous on the time scale of all the other rate processes. Hence, a well-defined temperature, T, characterizes the translational degrees of freedom of the lasing molecules and all degrees of freedom of the nonlasing species. This heat bath temperature appears as a parameter in the collisional rate constants. It also enters the gain coefficients via the linewidth and in the case of rotational equilibrium mainly via the population inversion. Thus (1) and (2) should be supplemented by a rate equation for T. Additional kinetic equations describe the time dependence of the nonlasing species concentrations. 

In writing rate equations for reactions of the type A + B + M AB + M, for example, reaction 5.26. one must decide whether to express the rate of the reaction as A [A][B][M] or it[A][B]. This is simply an issue of notation, since the value of the rate constant k will depend on the concentration of the third body M through its appropriate formula, as given in Appendix B. We will often choose not to explicitly indicate (M) in the rate equation for such three-body reactions, keeping in mind that the value of the rate constant will depend on [M] through its appropriate formula. 

The eount rate of the event recording principle depends on the memory read and write rates. The peak count rate is limited by the write rate, the average count rate limited by the rate the FIFO can be read at the output. Currently, the count rates for deviees based on event recording techniques are substantially lower than for the multisealers employing direct accumulation techniques. 

In a gas phase chemical reaction, the pressure (or partial pressure) of a chemical species is directly related to its concentration. In just the same way we could write rate equations for solution phase reactions involving a constant multiplied by the concentrations of species, we can write rate equations for gas phase reactions that involve a constant multiplied by the partial pressures of species in the gas phase. So just like in a solution phase reaction, increasing the pressure of a reactant in the gas phase will increase the rate at which products are formed. 

---