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Chemical Kinetics
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
A bimolecular elementary chemical reaction proceeds via a collision between the two reacting molecules, under the action of their mutual interaction forces (of electromagnetic origin). The treatment of the collision process is sufficiently complex, however it is treated, either classically or quantum-mechanically.3 The complication arises from the fact that for an accurate solution of the dynamical problem, it is necessary to accurately know the interaction potential energy between the two molecules; this, in turn, is a function of the electronic and nuclear coordinates of the colliding species. Determining the interaction potential energy is a quantum chemistry problem that, even assuming the Born–Oppenheimer approximation to be valid (see Chapter 6), is impossible to solve with the needed accuracy for molecules of real practical interest.
Oragnic Chemicals in the Environment
Published in Richard A. Larson, Eric J. Weber, Reaction Mechanisms in Environmental Organic Chemistry, 2018
Richard A. Larson, Eric J. Weber
It is useful to classify elementary reactions according to their molecularity, which is defined as the sum of the exponents appearing in a rate equation for a single elementary reaction. The term unimolecular reaction is used to describe an elementary reaction involving one chemical species. A bimolecular reaction involves the interaction of two chemical species. The interaction of three chemical species, or a termolecular reaction, is quite rare and will not be considered for further discussion. Molecularity is often confused with the order of a reaction, which refers to the sum of the exponents appearing in an experimental rate equation.
Transformations of Solid Polyamic Acids at Thermal Treatment
Published in Michael I. Bessonov, Vladimir A. Zubkov, Polyamic Acids and Polyimides, 2020
L. A. Laius, M. I. Tsapovetsky
The rate constant for such a reaction can be estimated from Smolukhov-sky’s equation k = 8πr0D, where r0 is the cage radius, and D is the diffusion constant for the macro molecules.68 We usually have r0 ~ 5 Å. For solid polymers the coefficient of self-diffusion is extremely low. For polystyrene, D = 10-21 cm2/s near Ts and 10-27 cm2/s at 20°C.66 Hence, k = 1.2 ⋅ 10-33 cm3/s ÷ 1.2 ⋅ 10-27 cm3/s. The rate of the bimolecular reaction is determined by the equation -dc/dt = kc.2 Then, the time for attaining the given concentration c1 is t = (c0 — c1)/(c0c1Δ), where c0 is the initial concentration of functional groups. Let us calculate the time needed to restore 80% of the decomposed AAG groups when the initial degree of decomposition is 3% and the diffusion constant of macrochains is similar to that for polystyrene near Ts. In this case, 1 amine or anhydride end group per 30 repeating units is present, and the initial concentration is equal (for polymer PM) to c0 = Na/(V ⋅ 30) = 0.7 ⋅ 1020 cm-3. Here V is the molar volume and Na is Avogadro’s number. The given final concentration is equal to c1=(1−0.8)c0=0.2⋅c0
Insertion products in the reaction of carbonyl oxide Criegee intermediates with acids: Chloro(hydroperoxy)methane formation from reaction of CH2OO with HCl and DCl
Published in Molecular Physics, 2021
Craig A. Taatjes, Rebecca L. Caravan, Frank A. F. Winiberg, Kristen Zuraski, Kendrew Au, Leonid Sheps, David L. Osborn, Luc Vereecken, Carl J. Percival
The reaction of DCl with CH2OO was investigated using the same methodologies as used for HCl + CH2OO earlier [9], and we refer the reader to this publication for details. Briefly, the potential energy scheme (see Figure 2) is based on M06-2X/aug-cc-pVTZ geometries and rovibrational characteristics combined with CCSD(T)/aug-cc-pVTZ energies [22]. The fate of the energised chloro(hydroperoxy)methane adduct was investigated using RRKM-derived energy-specific unimolecular rate coefficients in a master equation analysis [23] assuming identical collisional energy loss in both deuterated and non-deuterated adducts. The (near-)barrierless reactions between CH2OO and HCl/DCl, and dissociation of ClCH2OOD/H to ClCH2O + OD/OH are characterised by a series of constrained M06-2X geometry optimizations, frequency analyses and CCSD(T) energy calculations along the lowest-energy approach pathway. The bimolecular rate is then obtained by E,J,K-microvariational transition state theory [24], and the unimolecular dissociation rate is given by microvariational RRKM theory. Vertical and adiabatic ionisation energies for the reaction products are calculated at the CCSD(T)/aug-cc-pVQZ//M06-2X-D3/aug-cc-pVQZ level of theory [22]. All quantum chemical calculations were done with the Gaussian-16 program suite [25].
Statistical Modeling of Multivariate Destructive Degradation Tests With Blocking
Published in Technometrics, 2020
Qiuzhuang Sun, Zhi-Sheng Ye, Yili Hong
The (transformed) DDT data can be used for risk assessment of the contaminants in terms of their environmental persistence. A standard measure of persistence is the bimolecular rate constant (Xu et al. 2011). Let rl and μl be the respective bimolecular rate constant and the (transformed) mean degradation rate of the lth contaminant. The bimolecular rate constant rl is defined to be μl divided by the concentration of hydroxyl radicals. Since the concentration of hydroxyl radicals is difficult to measure, computing rl is not straightforward. It is customary to use a reference contaminant with known bimolecular rate constant, which is pCBA in the above DDT, to facilitate the estimation of rl of the other contaminants (Buxton et al. 1988). For convenience, let the third contaminant be pCBA in the DDT above. Then the bimolecular rate constants of the other two contaminants can be calculated as
Gamma irradiation-induced degradation and mineralization of methocarbamol in aqueous solution
Published in Environmental Technology, 2023
Amira Zaouak, Habib Chouchane, Haikel Jelassi
Thus the increase of e-aq concentration at elevated pH scavenges OH–. due to their high bimolecular rate constant and consequently reduces the concentration of hydroxyl radicals [43,46]. Therefore, e-aq plays a significant role in the removal of MET as compared to hydroxyl radicals at high pH. However, at pH = 6.2, all reactive radicals are free to react with MET and consequently caused higher removal efficiency of MET as compared to pH = 3 and 10 experiments. It is worth nothing that efficiencies at 4 kGy irradiation dose at both pH 6.2 and 10 are almost similar.