Revised Michaelis-Menten rate law with time-varying molecular concentrations

Despite over a century's use as a dominant paradigm in the description of biochemical rate processes, the Michaelis-Menten (MM) rate law stands on the restrictive assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium much faster than the molecular concentration changes. The increasingly-appreciated, remedied form of the MM rate law is also based on this quasi-steady state assumption. Although this assumption may be valid for a range of biochemical systems, the exact extent of such systems is not clear. In this study, we relax the quasi-steady state requirement and propose the revised MM rate law for the interactions of molecules with active concentration changes over time. Our revised rate law, characterized by rigorously-derived time delay effects in molecular complex formation, improves the accuracy of models especially for protein-protein and protein-DNA interactions. Our simulation and empirical data analysis show that the improvement is not limited to the quantitatively better characterization of the dynamics, but also allows the prediction for qualitatively new patterns in the systems of interest. The latter include the oscillation condition and period patterns of the mammalian circadian clock and the spontaneous rhythmicity in the degradation rates of circadian proteins, both not properly captured by the previous approaches. Moreover, our revised rate law is capable of more accurate parameter estimation. This work offers an analytical framework for understanding rich dynamics of biomolecular systems, which goes beyond the quasi-steady state assumption.

Modified Rate Law for Bimolecular Reactions: Applicable to Surface as well as Non-surface Reactions

The rate equations in kinematics are expressed through basic laws under surface reaction as well as non-surface reaction. Rate law is center theme of non-surface reaction whereas Langmuir adsorption isotherms are basis of surface reaction rate expressions. A modified rate equation for bimolecular reaction is presented which considers both catalyst surface affairs as well as fraction of successful collision of different reactant for cracking and forming bonds. The modified rate law for bimolecular reaction for surface as well as non-surface reaction is stated as “Rate of a reaction is directly proportional to concentration as well as catalyst surface affair of each reactant” as r = k ΩA[A] ΩB[B] where catalyst surface affair of ith species is defined as Ωi = Ki/(1+Ki[i] + Kj[j] + …). Here, Ki is the equilibrium constant of “i” species for adsorption-desorption processes over catalyst. i, j,… indicates the different adsorbed chemical species at uniform catalyst sites and the same [i], [j], … indicates the concentration of different adsorbed chemical species at uniform catalyst sites.

Kinetics of the Oxidation of Hydrogen Sulfide by Atmospheric Oxygen in an Aqueous Medium

Hydrogen sulfide is an important acid rain precursor and this led us to investigate the kinetics of its oxidation in aqueous phase by atmospheric oxygen. The kinetics was followed by measuring the depletion of oxygen in a reactor. The reaction was studied under pseudo order conditions with [H2S] in excess. The kinetics followed the rate law: -d[O2]/dt = k[S][O2]t (A) Where [S] represents the total concentration of hydrogen sulfide, [O2]t is the concentration of oxygen at time t and k is the second order rate constant. The equilibria (B - C) govern the dissolution of H2S; the sulfide ion in water forms different species: H2S K1 HS- + H+ (B) HS- K2 S2- + H+ (C) Where K1 and K2 are first and second dissociation constants of H2S. Although, H2S is present as undissociated H2S, HS- and S2- ions, nature of [H+ ] dependence of reaction rate required only HS- to be reactive and dominant. The rate law (A) on including [H+ ] dependence became Equation (D). -d[O2]/dt = k1K1[H+ ][S][O2]t / ([H+ ] 2 + K1[H+ ] + K1K2) (D) Our results indicate anthropogenic VOCs such as acetanilide, benzene, ethanol, aniline, toluene, benzamide, o-xylene, m-xylene, p-xylene and anisole to have no significant effect on the reaction rate and any observed small effect is within the uncertainty of the rate measurements.

Anionic Methyl Orange Removal from Aqueous Solutions by Activated Carbon Reinforced Conducting Polyaniline as Adsorbent: Synthesis, Characterization, Adsorption Behavior, Regeneration and Kinetics Study

This work investigated the elimination of Methyl Orange (MO) using a new adsorbent prepared from Activated Carbon (AC) with polyaniline reinforced by a simple oxidation chemical method. The prepared materials were characterized using XRD, TGA, FTIR and nitrogen adsorption isotherms. Furthermore, PANI@CA highest specific surface area values (near 332 m2.g− 1) and total mesoporous volume (near 0.038 cm3.g− 1) displayed the better MO removal capacity (192.52 mg.g− 1 at 298 K and pH 6.0), which is outstandingly higher than that of PANI (46.82 mg.g− 1). Besides, the process's adsorption, kinetics, and isothermal analysis were examined using various variables such as pH, MO concentration and contact time. To pretend the adsorption kinetics, various kinetics models, the pseudo first- and pseudo second- orders, were exercised to the experimental results. The kinetic analysis revealed that the pseudo second order rate law performed better than the pseudo first order rate law in promoting the formation of the chemisorption phase. In the case of isothermal studies, an analysis of measured correlation coefficient (R2) values showed that the Langmuir model was a better match to experimental results than the Freundlich model. By regeneration experiments after five cycles, acceptable results were observed.

Kinetic Study of Iodination of Propanone in Different Acidic Medium by using Colorimeter

Aims: This study aims at the Kinetic Study of Iodination of Propanone in Different Acidic Medium by using Colorimeter. Background: The kinetic experimentation of iodination of propanone has been performed in presence of different acids such as sulphuric acid, hydrochloric acid and acetic acid. The rate law of the iodination of propanone in acidic medium is determined by observing the disappearance of the brownish yellow colour of iodine in aqueous solution. Objective: The objective of this study is the preparation of standard solution, determination of absorbance of iodine solution at λmax= 480 nm, Kinetic study of iodination of propanone with different acidic medium. Method: The kinetic analysis of this reaction has been carried out by colorimetry. The extent of the reaction has been monitored by measuring the absorbance of the reaction mixture after a suitable time interval. Result: The rate law expression is determined to be rate = k [〖"propanone]" 〗_0^0.728 [acid]0. The rates of iodination of propanone in presence of different acidic medium are H2SO4 > HCl > CH3COOH. Conclusion: The rate of the reaction is found to be independent of the concentration of iodine i.e. it is zero order reaction with respect to iodine. However, it depends on the concentration of propanone and acid catalyst. Other: By using this experimental technique, the consumption of chemicals is very less.

Removal of methyl orange from from aqueous solutions using of PANI and PANI@Activated Carbon: Preparation, characterization, regeneration and comparative study

This work investigated the elimination of Methyl Orange (MO) using a new adsorbent prepared from Activated Carbon (AC) with polyaniline reinforced by a simple oxidation chemical method. The prepared materials were characterized using XRD, TGA, FTIR and nitrogen adsorption isotherms. Furthermore, PANI@CA highest specific surface area values (near 332 m2.g− 1) and total mesoporous volume (near 0.038 cm3.g− 1) displayed the better MO removal capacity (192.52 mg.g− 1 at 298 K and pH 6.0), which is outstandingly higher than that of PANI (46.82 mg.g− 1). Besides, the process's adsorption, kinetics, and isothermal analysis were examined using various variables such as pH, MO concentration and contact time. To pretend the adsorption kinetics, various kinetics models, the pseudo first- and pseudo second- orders, were exercised to the experimental results. The kinetic analysis revealed that the pseudo second order rate law performed better than the pseudo first order rate law in promoting the formation of the chemisorption phase. In the case of isothermal studies, an analysis of measured correlation coefficient (R2) values showed that the Langmuir model was a better match to experimental results than the Freundlich model. By regeneration experiments after five cycles, acceptable results were observed.

Variations and Control of Thrust and Mixture Ratio in Hybrid Rocket Motors

Hybrid rocket motors have several attracting characteristics such as simplicity, low cost, safety, reliability, environmental friendliness. In particular, hybrid rockets can provide complex and flexible thrust profiles not possible with solid rockets in a simpler way than liquid rockets, controlling only a single fluid. Unfortunately, the drawback of this feature is that the mixture ratio cannot be directly controlled but depends on the specific regression rate law. Therefore, in the general case the mixture ratio changes with time and with throttling. Thrust could also change with time for a fixed oxidizer flow. Moreover, propellant residuals are generated by the mixture ratio shift if the throttling profile is not known in advance. The penalties incurred could be more or less significant depending on the mission profile and requirements. In this paper, some proposed ways to mitigate or eliminate these issues are recalled, quantitatively analysed and compared with the standard case. In particular, the addition of energetic additives to influence the regression rate law, the injection of oxidizer in the post-chamber and the altering-intensity swirling-oxidizer-flow injection are discussed. The first option exploits the pressure dependency of the fuel regression to mitigate the shift during throttling. The other two techniques can control both the mixture ratio and thrust, at least in a certain range, at the expense of an increase of the architecture complexity. Moreover, some other options like pulse width modulation or multi-chamber configuration are also presented. Finally, a review of the techniques to achieve high throttling ratios keeping motor stability and efficiency is also discussed.