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Thermal behavior of sodium salt of calf thymus DNA
Published in A. K. Haghi, Lionello Pogliani, Eduardo A. Castro, Devrim Balköse, Omari V. Mukbaniani, Chin Hua Chia, Applied Chemistry and Chemical Engineering, 2017
Aysun TopaloĞlu, GÜler Narin, Devrim BalkÖse
The linearity of the Kissinger plot for the sealed cell DSC data was extremely low indicating that the reactions taking place in these cells are not kinetics limited.18 Furthermore, if multiple reactions having different activation energies occur simultaneously, the temperature dependence of the overall rate (observed as a single transition in the DSC curve) cannot be fit by a single kinetic equation. Also if the transition has several steps comprising the chemical reaction step, heat, and mass transfer steps, and so on, depending on the experimental conditions, one of these steps can be the rate limiting step. Moreover, for our case, the static atmosphere and high water vapor pressure in the sealed cells might lead to diffusion hindrance and back reactions further complicating the problem. Besides, the Kissinger method assumes that the reaction rate is maximum at the peak maximum temperature (Tp). Thus, the Kissinger plot is linear only if the reacted fraction at the maximum reaction rate is independent of the heating rate.51 However, there is no evidence for the Tp values in the sealed cell DSC thermograms to be the temperatures where the reaction rate is maximum. Also from the sealed cell DSC data, the reacted fractions at the peak maxima are 0.42-0.46, that is, not independent of the heating rate.
Rate Processes
Published in Danny D. Reible, Fundamentals of Environmental Engineering, 2017
The kinetics of sorption or reaction are defined by the form of the rate equation and the value of the rate constants that arise. In general, both the form and the rate constants of a reaction are defined by experimental measurements. Often one or more steps may control the overall rate of reaction and be referred to as the rate-limiting step. The stoichiometry of this rate-limiting step, which may not correspond to the stoichiometry of the overall reaction, typically controls the form of the kinetic relationship that governs the overall reaction. In particular, consider the reaction () A+B→CIf this were the fundamental, rate-limiting step in an overall reaction, it would be expected that the rate of the reaction would be proportional to the probability of a collision between a molecule of A and a molecule of B. The probability of a molecule of A being present in a particular location is proportional to its concentration, CA, and similarly the probability of a molecule B being in a particular location is proportional to its concentration, CB. The probability of both being in the same location at the same time is then proportional to the product of the concentrations of A and B.This is a statement of the principle of mass action which implies in this case that the rate of formation of compound C is given by () RC=krCACB
Synthesis of Solids
Published in Elaine A. Moore, Lesley E. Smart, Solid State Chemistry, 2020
Elaine A. Moore, Lesley E. Smart
To use microwave heating in solid-state synthesis, at least one component of the reaction mixture must absorb microwave radiation. The speed of the reaction process is then increased by increasing both the rate of the solid-state reaction and the rate of diffusion, which, as we mentioned earlier, is often the rate-limiting step.
Uptake/release of organic contaminants by microplastics: A critical review of influencing factors, mechanistic modeling, and thermodynamic prediction methods
Published in Critical Reviews in Environmental Science and Technology, 2022
Domenica Mosca Angelucci, M. Concetta Tomei
The uptake process of a solute onto a solid particle as MPs involves different steps: (i) the transport of the solute in the bulk solution, (ii) the diffusion of the solute through the aqueous boundary layer around the sorbent, (iii) the diffusion of the solute inside the solid sorbent and (iv) the sorption on the active sites on the solid surface. In the release process, a reverse sequence of steps takes place starting with the desorption from the active sites. The overall process rate is controlled by the slowest of these steps and their relative contributions can be determined by comparing the related kinetics to identify the rate-limiting step. However, it is worth noting that the effect of each single step depends, besides the properties of MPs and chemicals, also on the surface-to-volume ratio of the solid particle and the environmental conditions (e.g., temperature, initial solute concentration, fluid dynamics, etc.).
Adsorption of leather dyes on activated carbon from leather shaving wastes: kinetics, equilibrium and thermodynamics studies
Published in Environmental Technology, 2019
Christian Manera, Andrezza Piroli Tonello, Daniele Perondi, Marcelo Godinho
The prediction of the rate-limiting step and the interpretation of the mechanisms are required for design purposes. The adsorption process takes place through three sequential steps comprising (i) external diffusion (film diffusion) of the adsorbate through the boundary layer from the adsorbent surface, (ii) intraparticle diffusion and (iii) interaction between the adsorbate and the surface active sites [30,40]. Of the three steps, the third step is assumed to be rapid and considered to be negligible [44]. In order to elucidate the mechanisms and rate controlling steps, the intraparticle diffusion model was applied to experimental data. The model, proposed by Weber and Morris [45], is based on the following equation:where ki is the for intraparticle diffusion rate constant (mg/g min0.5) and C is the intercept, which is related to boundary layer thickness; the higher the C value, the greater is the boundary layer effect [39,46]. The constant ki is the slope of the strait-line portion of the plot of qt against t0.5. According to this model, the amount of dye adsorbed plot against the square root of the contact time should present a linear portion if intraparticle diffusion is involved in the adsorption process, and it should cross the origin if intraparticle diffusion is the sole rate-limiting step [45,47]. Figure 7(a) shows the corresponding plot of qt against t0.5 for AB210 and AR357.
Dephosphorisation of steel slags by leaching with sulphuric acid
Published in Mineral Processing and Extractive Metallurgy, 2018
Yong Qiao, Jiang Diao, Deman Liu, Jianfeng Yang, Dongwei Guo, Siyu Gong, Bing Xie
Based on the unreacted shrinking core model, if we assume the steel slag is round particles, the reactions occur on the outer surface of the particle. As the reaction goes on, the response surface slowly shrank to the centre of the particle and the unreacted residue around the core is considered to be ash layer. Liquid/solid reaction continuously goes on in the whole process. The procedure contains the fluid layer diffusion, product layer diffusion and surface chemical reaction. The overall reaction rate depends on the slowest step, which is called rate-limiting step. According to the unreacted shrinking core model (Qiao et al. 2015): (i)If the rate of leaching process was controlled by the step of diffusion through solid layer around the unreacted core, the integral rate equation was expressed as (ii) If the leaching rate was controlled by the surface chemical reaction, the integral rate equation was(iii)If the leaching rate was controlled by the liquid film diffusion, the integral rate equation waswhere x is the leaching ratio of phosphorus; kd is the pore diffusion rate constant; kr is the apparent rate constant for the surface chemical reaction; kl is the apparent rate constant for diffusion through the fluid film and t is the leaching time.