First-order rate constant, temperature

The behavior of the reaction rate as a function of temperature dispels any notion that the reaction is simple. Figure 3 shows that there is a maximum in the first-order rate constant-temperature curve at approximately 80 °C. At such a low temperature, the rate-temperature maximum cannot be explained by depolymerization, nor can it be explained by deactivation of the catalyst as a result of more rapid polymer accumulation on the catalyst at higher temperatures since the maximum is obtained for initial rates measured as a function of temperature. Theoretical considerations predict that a maximum in the rate-temperature curve may be expected from the Langmuir-Hinshelwood model for polymerization on solid surfaces but not from the Rideal model (5). The rate of reaction for the Langmuir-Hinshelwood model is given by ... 

The first order rate constant for ethanolysis of the allylic chloride 3 chloro 3 methyl 1 butene is over 100 times greater than that of tert butyl chloride at the same temperature... 

At ordinary temperatures, formaldehyde gas is readily soluble in water, alcohols, and other polar solvents. Its heat of solution in water and the lower ahphatic alcohols is approximately 63 kJ/mol (15 kcal/mol). The reaction of unhydrated formaldehyde with water is very fast the first-order rate constant... 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

First order rate constant k, for the rotation about the C-N bond in N, N-dimediylnicotinamide (3) measured at different temperatures by nuclear magnetic resonance (NMR) are ... 

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

Since a first-order rate constant does not depend on [A]o, one need not know either the initial concentration or the exact instant at which the reaction began. This characteristic should not be used to rationalize experimentation on impure materials. These features do allow, however, a procedure in which measurements of slower reactions are not taken until the sample has reached temperature equilibrium with the thermostating bath. The first sample is simply designated as t = 0. Likewise, for rapidly decaying reaction transients, knowing the true zero time is immaterial. 

Composite temperature dependence. Show that a plot of the apparent first-order rate constant of Eq. (7-34) as ln(/tapp/r) versus lIT will always be curved downward, corresponding to an apparent AW that decreases with increasing temperature. What will the shape of the plot be if by chance AW = AHif ... 

It is of substantial interest to note that, c.s the temperature of the reaction mixture is increased to —33-5°, ion 19 is converted quantitatively back to 18. At that temperature the first-order rate constant for the reversion has been calculated to be 8-0 x 10 sec , which corresponds to a free enthalpy barrier AG ) of 17-4 kcal/mol. 

The solution for Ya is simple, even elegant, but what is the value of F It is equal to the mass holdup divided by the mass throughput. Equation (1.41), but there is no simple formula for the holdup when the density is variable. The same gas-phase reactor will give different conversions for A when the reactions are A 2B and A —> B, even though it is operated at the same temperature and pressure and the first-order rate constants are identical. 

The rates of each of the environmentally important chemical processes are influenced by numerous parameters, but most processes are described mathematically by only one or two variables. For example, the rate of biodegradation varies for each chemical with time, microbial population characteristics, temperature, pH, and other reactants. In modeling efforts, however, this rate can be approximated by a first-order rate constant (in units of time). 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

SAQ 8.21 Potassium hexacyanoferrate(III) in excess oxidizes an alcohol at a temperature of 298 K. The concentration of Ks[Fe(CN)6] is 0.05 mol dm 3. The concentration of the alcohol drops to 45 per cent of its t= 0 value after 20 min. Calculate first the pseudo first-order rate constant k , and thence the second-order rate constant /c2. 

One of the most important redox reactions of this class of compounds is the oxidation of Pt(2.0+)2 by 02, for this is the main cause of the appearance of the blue, purple, or dark red colors of the mixed-valence species. Although no detailed examination has been performed, the kinetics of the 02 oxidation of I Pt,1 (NHo)4(a-pyrrolido-nato)2]2+ into I Pt1 VNH3)4(a-pyrrolidonato)2(H20)2 I41 (Eq. (7)) was spec-trophotometrically examined (117). The study showed that the reaction proceeds over several days at room temperature. The first-order rate constants in acidic media were in the range of kobs = 4.2 x KT6 s 1 (pH = 0.23) - 1.13 x lO6 s"1 (pH = 2.1) (at 25°C, in air, I = 1.5 M) (117). 

Provided that the time-temperature curve obtained from the calorimetric experiments is wholly of first-order, or comprises a first-order section, usually after the inflection point of sigmoid reaction curves, a conventional analysis yields a first-order rate constant ku which is related to the concentration of monomer, m, and the initial concentration of initiator, c0, by the equations... 

The polymerisation of styrene by HC104 in CH2C12 at ambient temperature is internally of first order (rate-constant kf) if the system is reasonably pure [3, 27], but shows marked acceleration if it is extremely pure (9). 

Fast spectroscopy was also used to probe the reactivity of PBN +. The 266 nm laser excitation of peroxydisulfate ion in aqueous solution at room temperature gives the powerful oxidant SOr, which oxidizes PBN in an exergonic reaction (by about 0.8 eV, see Tables 1 and 5) with k = 3 X 109 dm3 mol-1 s 1. The pseudo-first-order rate constant for the decay of PBN + by reaction with water to give HO-PBN" was 2 x 106 s 1, a relatively slow reaction (k = 3.6 x 104 dm3 mol-1 s-1 at ambient temperature). 

Table 4. First order rate constants (k x 10 s t, 10%) for the decay of transients from various nitrostilbcnes in solution at room temperature 133)...

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

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