Units second-order rate constant

Therefore, for this type of second-order reaction, a plot of 1/ca vs. t is linear, with the slope equal to k. The usual units of a second-order rate constant are liters per mole-second (M s" ). 

We can reach two useful conclusions from the forms of these equations First, the plots of these integrated equations can be made with data on concentration ratios rather than absolute concentrations second, a first-order (or pseudo-first-order) rate constant can be evaluated without knowing any absolute concentration, whereas zero-order and second-order rate constants require for their evaluation knowledge of an absolute concentration at some point in the data treatment process. This second conclusion is obviously related to the units of the rate constants of the several orders. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

To analyze the rate constant problem we start with Eq. (5-43), k = (kT/h)K. The term (kT/h) has the unit second", so consistency is achieved if the concentration units of k and are identical. As before, we pass to pure numbers, writing (for a second-order rate constant)... 

First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu-... 

The rate is proportional to the concentrations of both A and B. Because it is proportional to the product of two concentration terms, the reaction is second-order overall, first-order with respect to A and first-order with respect to B. (Were the elementary reaction 2A P + Q, the rate law would be = A[A] second-order overall and second-order with respect to A.) Second-order rate constants have the units of (concentration) time) as in M sec. ... 

Fibrinolytics. Figure 4 Inactivation of plasmin by a2-plasmin inhibitor Effect of fibrin. The inactivation rate of free plasmin is very rapid (the second order rate constant k 430 104M-1s-1), while of fibrin bound plasmin is slow (the second order rate constant k 1 104M"1s"1). Inactivation of plasmin in the figure is shown in arbitrary units. Abbreviations plasmin (P), fibrin (F). 

The first-order rate constants have units of s 1 and the second-order rate constants have units of L mol 1 s"1. 

Second-order rate constant for the exchange of a particular solvent molecule. b In aqueous solution. c Diluent = d3-nitromethane. d Units tire dm3 mol"1 s l. 

Note that because kon is a second-order rate constant, and koff is a first-order rate constant, the units of Ka will be reciprocal molarity and the units of Kd will be molarity. 

The reaction of E with S is of a different type, called second order. Second-order reactions are usually found in reactions of the type A + B —> C. The velocity of a second-order reaction depends on how easy it is for E and S to find each other in the abyss of aqueous solution. Obviously, lower E or lower S concentration make this harder. For second-order reactions, the velocity depends on the product of both of the reacting species (v = k[S [E]). Here k must have units of reciprocal molar minutes (M-1 min-1) so that the units on the left and right sides balance. The second-order rate constant in the mechanism of Fig. 8-3 is kx. 

The specificity constant, kcJKm, is the second-order rate constant for the reaction of E and S to produce product. It has units of M Wn-1. 

What about reactions of the type A + B — C This is a second-order reaction, and the second-order rate constant has units of M min-1. The enzyme-catalyzed reaction is even more complicated than the very simple one shown earlier. We obviously want to use a second-order rate constant for the comparison, but which one There are several options, and all types of comparisons are often made (or avoided). For enzyme-catalyzed reactions with two substrates, there are two Km values, one for each substrate. That means that there are two kcJKm values, one for each substrate. The kcJKA5 in this case describes the second-order rate constant for the reaction of substrate A with whatever form of the enzyme exists at a saturating level B. Cryptic enough The form of the enzyme that is present at a saturating level of B depends on whether or not B can bind to the enzyme in the absence of A.6 If B can bind to E in the absence of A, then kcJKA will describe the second-order reaction of A with the EB complex. This would be a reasonably valid comparison to show the effect of the enzyme on the reaction. But if B can t bind to the enzyme in the absence of A, kcat/KA will describe the second-order reaction of A with the enzyme (not the EB complex). This might not be quite so good a comparison. 

Analysis of the variation of the overall rate constant of reaction with [surfactant] was discussed in Section 3 (p. 222) and the treatment allows calculation of the second-order rate constants of reaction in the micellar pseudophase. These rate constants can be compared with second-order rate constants in water provided that both constants are expressed in the same dimensions and typically the units are M-1 s-1. Inevitably the comparison... 

The basicity constants in water and micelles then have the same units (M 1), and values of K and Kb are not very different for arenimidazoles and nitroindoles under a variety of conditions (Table 10). The comparisons suggest that inherent basicities are not very different in water and cationic micelles, but, as with second-order rate constants of bimolecular reactions (Section 5), there is a limited degree of specificity because K /Kb is slightly larger for the nitroindoles than for the arenimidazoles, almost certainly because of interactions between the cationic micellar head groups and the indicator anions. 

Here, the overall absorbance change, A A, has two components, ai and a2, and the two second-order rate constants are k and K".The interpretation of this rate law is that electron injection leads to equal numbers of adsorbed M(III) complexes and injected electrons. Thus, the recombination process is first-order in [M(III)] and [n] where fri is the concentration of injected electrons. The concentration of M(III) is expressed in molecules cm-2 because the M(III) species are surface confined, while the concentration of injected electrons has units of electrons cm-3 these... 

Transient UV-vis absorption spectra showed that theTi02/Ru(II) films yield prompt electron injection upon photolysis ( >108s 1) These same films displayed photoluminescence decays with parallel first- and second-order components, the first-order component having a rate constant of about lxl06s-1. These two sets of results provide further support for the existence of at least two populations of adsorbed Ru(II), one of which injects electrons rapidly and another which does not inject electrons and is thus capable of luminescing on a longer time scale. The second-order component of the luminescence decay is attributed to bimolecular triplet-triplet annihilation of surface-bound Ru(II). (Note that the second-order rate constants reported for luminescence decay have units of s-1 because they are actually values for k2(Asi))... 

Notice that the units of the second-order rate constant k2 are dm3 mol s 1 which are, in effect, (concentration) 1 s-1. 

Fig. 4.4. LFER between exchange rate constants for Mfacacjj and M(H20) + k. at 25 °C. The values are both in s units and the former exchanges are in acac. The data for Mo are second-order rate constants for anation.

Concentrations of gaseous pollutants are often expressed in terms of parts per million (ppm) by volume, and time is expressed in minutes. Use of these concentration units must be reflected in the units used for the rate constants as well for example, second-order rate constants are in units of ppnt-1 min-1. Occasionally, gas concentrations are given in units of mol L-1 or in units of pressure such as Torr, atmospheres, or Pascals these can be converted to the more conventional units... 

Rate Constant. The logarithms of second-order rate constants (expressed as M sec.-1) are given for 25°C. unless otherwise indicated. These are rounded off to the nearest 0.1 unit. The ionic strengths are often 0.1-0.2 M. 

Solution First we evaluate kr, using Equation (32). It is convenient to use cgs units for this calculation therefore we write kr = 4 (1.38 10-16) (293)/(3 )(0.010) = 0.54 10-11 cm3 s 1. Recall that the coefficient of viscosity has units (mass length-1 time-1), so the cgs unit, the poise, is the same as (g cm -1 s -1). As a second-order rate constant, kr has units (concentration -1 time -1), so we recognize that the value calculated for kr gives this quantity per particle, or kr = 0.54 10-11 cm3 particle-1 s-1. Note that multiplication by Avogadro s number of particles per mole and dividing by 103 cm3 per liter gives kr = 3.25 109 liter mole-1 s-1 for the more familiar diffusion-controlled rate constant. 

The units of k2 are M 1 s 1. If [B] is present at unit activity, the rate is /c2[A], a quantity with units of s We can see that the bimolecular, or second-order, rate constant for reaction of A with B may be compared with first-order constants when the second reactant B is present at unit activity. In many real situations, reactant B is present in large excess and in a virtually constant concentration. The reaction is pseudo-first order and the experimentally observed rate constant /c2[B] is an apparent first-order rate constant. The bimolecular rate constant k2 can be obtained by dividing the apparent constant by [B]. 

Energy Levels and Transition Probabilities of Some Atom of Photochemical Interest, 363 Conversion Factors for Absorption Cofficients, 373 Conversion Factors for Second Order Rate Constants, 37 1 Conversion Factors for Third Order Rate Constants, 374 Conversion from Pressure to Concentration Units, 375 Enthalpies of Formation of Atoms at 1 atm and 0°K in 11 . Idea Gas State, 375... 

A detailed study of the kinetics of the Lys 41 reaction by Murdock et al. (124) indicates that the pK of Lys 41 is 8.8 0.1. This value is about 1.4 pH units lower than that for the usual t-amino groups and would account for the apparent enhanced reactivity at lower pH. The second-order rate constant corrected to the free base form is within a factor of 2 of that derived from data on simple peptides. A strongly cationic center was inferred as the reason for this low pXa. In the X-ray structure a number of cationic residues are, in fact, close by, especially Arg 39. 

Significance of the Michaelis Constant, Km. The Michae-lis constant Km has the dimensions of a concentration (molarity), because k x and k2, the two rate constants in the numerator of equation (23), are first-order rate constants with units expressed per second (s 1), whereas the denominator fc is a second-order rate constant with units of m-is-1. To appreciate the meaning of Km, suppose that [S] = Km. The denominator in equation (25) then is equal to 2[S], which makes the velocity v = VmaJ2. Thus, the Km is the substrate concentration at which the velocity is half maximal (fig. 7.6). 

T is the temperature in degrees Kelvin. The units of A, called the pre-exponential factor, are the same as those of kobs for a first-order rate constant, time "1 for a second-order rate constant, l mole-1 time-1. We use the notation A obs to emphasize that the equation applies to the observed rate constant, which may or may not be simply related to the microscopic k s characterizing the individual steps of a reaction sequence. 

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