Ratio of rate constants

Relative rate meaning, here, simply the ratio of nitro-alkylbenzene to nitrobenzene, multiplied by the initial ratio of alkylbenzene to benzene. This is not precisely the same as the ratio of rate constants for nitration. ... 

In the Sharpless epoxidation of divinylmethanols only one of four possible stereoisomers is selectively formed. In this special case the diastereotopic face selectivity of the Shaipless reagent may result in diastereomeric by-products rather than the enantiomeric one, e.g., for the L -(-(-)-DIPT-catalyzed epoxidation of (E)-a-(l-propenyl)cyclohexaneraethanol to [S(S)-, [R(S)-, [S(R)- and [R(R)-trans]-arate constants is 971 19 6 4 (see above S.L. Schreiber, 1987). This effect may strongly enhance the e.e. in addition to the kinetic resolution effect mentioned above, which finally reduces further the amount of the enantiomer formed. 

Ratio of rate constant k for indicated alkyl bromide to k for methyl bromide at 25 C... 

The vapor pressure ratio measures the intrinsic tendency of component 1 to enter the vapor phase relative to component 2. Likewise, ri measures the tendency of Mi to add to Mi - relative to M2 adding to Mi-. In this sense there is a certain parallel, but it is based on Mi - as a reference radical and hence appears to be less general than the vapor pressure ratio. Note, however, that ri = l/r2 means kn/ki2 = k2i/k22- In this case the ratio of rate constants for monomer 1 relative to monomer 2 is the same regardless of the reference radical examined. This shows the parallelism to be exact. 

Calculate the ratio of rate constants at 30°C and 20°C for a reaction whose activation energy is 20 kcal/mol. 

According to this important result, the ratio of product concentrations is equal to the ratio of rate constants, independently of time. Even if the reactions are too fast to follow by conventional techniques, final product analysis will give the rate constant ratio (provided no subsequent reactions introduce artifactual changes). 

The study of relative rates by the competitive method can be useful. The principle was discussed in Section 3.1 in the context of parallel reactions, for which the ratio of the product concentrations is equal to the ratio of rate constants (provided the concentrations are under kinetic control). 

Consider a bimolecular reaction between a substrate and a reagent. Upon each encounter of these two species there is a probability P that reaction will occur. If the solution contains two substrates Sj and S2, each characterized by a probability of reaction P, and P2 with the common reagent, evidently the ratio P2lP is a measure of the selectivity of this process for S2 relative to S,. If the two substrates are not markedly dissimilar, the ratio P2IP1 will be similar to the ratio of rate constants, 2/ 1- Leffler and Grunwald pp define the selectivity as... 

It is worth noting that the ratio of rate constants ki/k2 = 30.55 of the first and the second reaction, as well as the ratio kiKjL/k2Kc = 36.95, i.e. the expression by which the selectivity of catalytic reactions is usually defined, is quite high and it would correspond to the maximum relative concentration of the intermediate product around 90%, which contrasts with Fig. 7. However, it is necessary to bear in mind that the rate equations (20a) and (20b) for the first and the second reaction are of different form and that the expression (22) results for the selectivity from their ratio. 

Ratios of Rate Constants and of Adsorption Coefficients in Parallel Dehydrogenation (1) and Dehydration (2) of Isopropyl Alcohol on Some Oxide Catalysts (123)... 

Clearly, this scheme produces the various products in relative yields [Pi] [Pi] [P ], which correspond to the ratios of rate constants Jkj k2 kn. The product yields can be measured at completion or at any midway point. Products formed in such ratios are said to be kinetic products, as distinct from thermodynamic products. The latter would be present in those ratios that would prevail when equilibrium had been established among Pi, Pi, etc. 

This equation is given in a linearized form. The slopes and intercepts allow one to calculate the desired ratios of rate constants. 

These and other competition methods can provide only the ratios of rate constants, not absolute values. Provided each ratio is referred to a common standard, the set of values defines the reactivity pattern of the given species. Of course, if it becomes feasible to measure any one of the rate constants, then the entire set can be placed on an absolute scale. 

The ratio of rate constants for attack of a chlorine atom on the primary (kp) and tertiary (k,) hydrogen atoms is 1 4.2. Calculate the expected ratio of I II. 

Equation (10.12) is the simplest—and most generally useful—model that reflects heterogeneous catalysis. The active sites S are fixed in number, and the gas-phase molecules of component A compete for them. When the gas-phase concentration of component A is low, the k a term in Equation (10.12) is small, and the reaction is first order in a. When a is large, all the active sites are occupied, and the reaction rate reaches a saturation value of kjkd-The constant in the denominator, is formed from ratios of rate constants. This makes it less sensitive to temperature than k, which is a normal rate constant. 

The ratio of rate constants = kM/kD) can be obtained (13) from the concentrations of D and M measured at various degrees of reduction x according to... 

The non-linear equations 21 and equations 35-38 can be solved iteratively to give directly, the instantaneous efficiencies and the the ratios of rate constants (kx/kp), (ktc/kp2) and (ktc /kp2). The values obtained for the rate constants have been summarized in Table III and in Figures 3 and 6. The results from the calculations show a small difference (ie less than 1 ) betwen ktc and ktc. Therefore, for all practical purposes they can be considered equal... 

We will use a numerical averaging procedure to evaluate the ratio of rate constants. Thus... 

For first-order and pseudo first-order reactions of the series type several methods exist for determining ratios of rate constants. We will consider a quick estimation technique and then describe a more accurate method for handling systems whose kinetics are represented by equation 5.3.2. 

If we let and t2 represent the times corresponding to reaction progress variables and <5J, respectively, the time ratio t2/tl for fixed values of <5 and <5 will depend only on the ratio of rate constants k. One may readily prepare a table or graph of <5 versus k t for fixed k and then cross-plot or cross-tabulate the data to obtain the relation between k and ktt at a fixed value of <5. Table 5.1 is of this type. At specified values of <5 and S one may compute the difference log(fe1t)2 — log f) which is identical with log t2 — log tj. One then enters the table using experimental values of t2 and tx and reads off the value of k = k2/kv One application of this time-ratio method is given in Illustration 5.5. 

There are experimental evidences that some ortAo-substituents in 1,1-dimethylethylbenzoyl peresters strongly accelerate the decomposition of peresters. The ortAo-substituents in 1,1-dimethylethylbenzoyl peresters and values illustrating the ratio of rate constants d(o-substi-tuted)/Ad(H) at 333 K are given below [3,4] ... 

This problem was first approached in the work of Denisov [59] dealing with the autoxidation of hydrocarbon in the presence of an inhibitor, which was able to break chains in reactions with peroxyl radicals, while the radicals produced failed to contribute to chain propagation (see Chapter 5). The kinetics of inhibitor consumption and hydroperoxide accumulation were elucidated by a computer-aided numerical solution of a set of differential equations. In full agreement with the experiment, the induction period increased with the efficiency of the inhibitor characterized by the ratio of rate constants [59], An initiated inhibited reaction (vi = vi0 = const.) transforms into the autoinitiated chain reaction (vi = vio + k3[ROOH] > vi0) if the following condition is satisfied. 

---