Units and Rate Constants

If we were to calculate the value of units of the rate constant in the previous example, we could do so with relative ease. Beginning with the equation and rearranging it to solve for k, we obtain the expression  

Substituting units into this expression, we find  

For each rate law, determine a) the order of each reactant, b) the overall order of the reaction, and c) the units of the rate constant, k. Assume that all reaction rates have been expressed in M s .  

---

Express the units for rate constants when the concentrations are in moles per liter and time is in seconds for (-a) zero-order reactions (b) first-order reactions (c) second-order reactions. 

Fig. 12.2. FRET calculator. (A) Table of input parameters arbitrary concentration and time units. The rate constants selected for singlet decay (kdd = kd, excluding FRET see Eq. (12.1)) and for FRET (kt = kt) are the same, corresponding to a FRET efficiency E = 0.5. The acceptor has been assigned quite different parameters, except for triplet decay (kT — ki). The data are plotted for the indicated time scales (10, 150). (B) specification of desired output signals (see Fig. 12.1 b) xl, sg = excited donor ground state...

The units of rate constant for a first order reaction from equation (1.21) is measured as (time)-1 and can be represented as sec-1, min-1 or hour-1. 

Here we see that in concentration units the rate constants are not independent of temperature. Evaluating the activation energy from Eq. 75, and replacing numbers gives... 

T o grasp the chemical condition of water in the pressure vessel, direct measurement is practically impossible because of high pressure, high temperature, and intense radiation. In order to predict the concentrations of water decomposition products, a computer simulation should be applied. This idea was found in 1960s [1-3]. To perform the simulation, both a set of G-values for water decomposition products and a set of reactions for transient species are necessary. For these two decades, much effort has been made in Sweden, Denmark, United Kingdom, Canada, and Japan to evaluate the G-values and rate constants of the reactions at elevated temperatures up to 300 °C, and now there are practically enough accumulated data. There are several reviews of water radiolysis at elevated temperatures [4-7] and examples of practical application of the radiolysis in reactors [8,9]. 

The composition of copolymer and distribution of units in copolymer molecule can be predicted as follows. Let us designate two types of comonomer molecules as A and B and the respective radicals as A and b1 The symbols with an asterisk deal with the process proceeding on the template. In addition, let us assume that we can neglect the penultimate effect. In this case, the process of propagation is expressed by the following set of reactions and respective rates and rate constants ... 

From this equation, it is evident that an increase of 1 pH unit will cause the rate of reaction to be increased 100 times. The rate of oxygenation of manganese(II) has been shown (46) to be pH dependent, the rate likewise increasing by a factor of 100 for each increase of 1 pH unit. The rate constant for the latter reaction is such that at the concentrations of manganese (II) and oxygen normally found in natural waters and in the pH range of 7-8, the reaction is quite slow. It is possible that the oxida-... 

Finally, the development of pulse radiolysis enabled a direct observation of e aq, and a direct distinction between e aq and H could easily be made. Matheson (37) (with spectroscopic data obtained by Keene) suggested that e ag has optical absorption in the visible. Hart and Boag (26) used spectrographic plates and studied this absorption. The effect of solutes, which were known as electron scavengers led to the conclusion that the absorption was due to e aq. It was confirmed later, that the absorption belonged to unit negatively charged species by means of a salt effect (20), as well as by conductivity measurements (49). Many more papers on the absorption spectrum and rate constants of the hydrated electron have since appeared (16). 

Units for rate constants apparently not given by Quayle and Royals (2fi) but assumed to be... 

The pH-rate profiles obtained by Capon and Wu consist of a pH-independent region at higher pH, becoming proportional to [H+] at lower pH. For example, in series 27 (Ar = Ph, L = H) the break occurs between pH 7 and 6, while for the tertiary analogue (Ar = Ph, L = CH3) the change occurs ca 2 pH units slower. No downward curvature or plateau at still lower pH is readily observable in Capon and Wu s Figure (not a log-log plot). However, they do report that at lower pH values there are downward deviations, that is, the experimental rate constants are smaller than expected for a first-order dependence on [H+]. Nevertheless, at sufficiently high pH the results are correlated by equation 32, and rate constants based on adherence to this equation are listed in Table 10. 

A scientific theory, like a mathematical system, never yields more than is built into it in the way of assumptions or postulates. The phenomenological approach presented in the preceding chapters could no more than characterize the kinetic behavior of systems in terms of the macroscopic variables used to describe them. We have obtained from this approach the kinetic quantities and rate constants or, in terms of the Arrhenius formulation, the frequency factors and the energies of activation. These quantities constitute our phenomenological category of kinetic language. If we are to relate them to the molecular properties of the reacting species, we must construct a new theory and a new nomenclature which starts with the molecule as the unit under consideration. 

Indices frequently occur in chemistry in expressions for equihbrium and rate constants that involve concentrations. TTie concentration of a species is normally shown in square brackets, such as [HCl], and is expressed in units of mol dm. ... 

Fig. lOL Calculated HE plots during linear potential sweep for mono-layer adsorption, as a function of sweep rate, for = 160 iClcm. The range of sweep rates and rate constants have been chosen so as to show both the reversible and the linear Tafel regions. The Y - axis is given in units of pseudocapacitance, = i/v. Reprinted with permission from Srinivasan and Gileadi, Electrochim. Acta, 11, 321, 1966). Copyright 1966, Pergamon Press. 

Determining Reaction Orders and Units for Rate Constants... 

The reactant CsHg A) is the limiting one and even in gas phase there is no volume variation, sa=0 A + BR + S). Based on the unit of rate constant, we have a... 

---