Kinetics Aqa A Level Chemistry

[Bradley Zweig]

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Electrochemical proton-coupled electron transfer (PCET) reactions can proceed via an outer-sphere electron transfer to solution (OS-PCET) or through an inner-sphere mechanism by interfacial polarization of surface-bound active sites (I-PCET). Although OS-PCET has been extensively studied with molecular insight, the inherent heterogeneity of surfaces impedes molecular-level understanding of I-PCET. Herein we employ graphite-conjugated carboxylic acids (GC-COOH) as molecularly well-defined hosts of I-PCET to isolate the intrinsic kinetics of I-PCET. We measure I-PCET rates across the entire pH range, uncovering a V-shaped pH-dependence that lacks the pH-independent regions characteristic of OS-PCET. Accordingly, we develop a mechanistic model for I-PCET that invokes concerted PCET involving hydronium/water or water/hydroxide donor/acceptor pairs, capturing the entire dataset with only four adjustable parameters. We find that I-PCET is fourfold faster with hydronium/water than water/hydroxide, while both reactions display similarly high charge transfer coefficients, indicating late proton transfer transition states. These studies highlight the key mechanistic distinctions between I-PCET and OS-PCET, providing a framework for understanding and modelling more complex multistep I-PCET reactions critical to energy conversion and catalysis.

All data used to support the claims of the main text have been included with this manuscript as a .zip file. Data used to support claims discussed in the Supporting Information can be made available on reasonable request. Source Data are provided with this paper.

We gratefully acknowledge C. Costentin for fruitful discussions. We thank the entire Surendranath laboratory for their support and scientific discussions, with particular acknowledgment towards B. Tang, N. Razdan, S. Weng, A. Chu, M. Pegis and H. Wang for their helpful discussions. This research was supported by the US Department of Energy, Office of Basic Energy Sciences, under award no. DE-SC0020973 (N.B.L. and Y.S.).

N.B.L. and Y.S. conceived the research and developed experiments. N.B.L conducted all experiments and data analysis. N.B.L, Y.S., R.P.B. and A.V.S. developed I-PCET kinetic model. N.B.L., R.P.B. and K.S.W developed scripts for data simulation and fitting. N.B.L. and Y.S. wrote the manuscript with input from all authors.

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The purpose of this study was to examine a level A in vitro-in vivo correlation (IVIVC) for glipizide hydrophilic sustained-release matrices, with an acceptable internal predictability, in the presence of a range of formulation/manufacturing changes. The effect of polymeric blends of ethylcellulose, microcrystalline cellulose, hydroxypropylmethylcellulose, xanthan gum, guar gum, Starch 1500, and lactose on in vitro release profiles was studied and fitted to various release kinetics models. Water uptake kinetics with scanning electron microscopy (SEM) was carried out to support the drug release mechanism. An IVIVC was established by comparing the pharmacokinetic parameters of optimized (M-24) and marketed (Glytop-2.5 SR) formulations after single oral dose studies on white albino rabbits. The matrix M-19 (xanthan:MCC PH301 at 70:40) and M-24 (xanthan:HPMC K4M:Starch 1500 at 70:25:15) showed the glipizide release within the predetermined constraints at all time points with Korsmeyer-Peppas' and zero-order release mechanism, respectively. Kopcha model revealed that the xanthan gum is the major excipient responsible for the diffusional release profile and was further supported by SEM and swelling studies. A significant level A IVIVC with acceptable limits of prediction errors (below 15%) enables the prediction of in vivo performance from their in vitro release profile. It was concluded that proper selection of rate-controlling polymers with release rate modifier excipients will determine overall release profile, duration and mechanism from directly compressed matrices.

Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.

The pioneering work of chemical kinetics was done by German chemist Ludwig Wilhelmy in 1850.[1] He experimentally studied the rate of inversion of sucrose and he used integrated rate law for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later by Wilhelm Ostwald. After Wilhelmy, Peter Waage and Cato Guldberg published 1864 the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.[2][3][4]

Van 't Hoff studied chemical dynamics and in 1884 published his famous "tudes de dynamique chimique".[5] In 1901 he was awarded by the first Nobel Prize in Chemistry "in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions".[6] After van 't Hoff, chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero order reactions (for which reaction rates are independent of concentration), first order reactions, and second order reactions, and can be derived for others. Elementary reactions follow the law of mass action, but the rate law of stepwise reactions has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, the rate-determining step often determines the kinetics. In consecutive first order reactions, a steady state approximation can simplify the rate law. The activation energy for a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

Gorban and Yablonsky have suggested that the history of chemical dynamics can be divided into three eras.[7] The first is the van 't Hoff wave searching for the general laws of chemical reactions and relating kinetics to thermodynamics. The second may be called the Semenov-Hinshelwood wave with emphasis on reaction mechanisms, especially for chain reactions. The third is associated with Aris and the detailed mathematical description of chemical reaction networks.

The reaction rate varies depending upon what substances are reacting. Acid/base reactions, the formation of salts, and ion exchange are usually fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be slower.

In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example, Sherbet (powder) is a mixture of very fine powder of malic acid (a weak organic acid) and sodium hydrogen carbonate. On contact with the saliva in the mouth, these chemicals quickly dissolve and react, releasing carbon dioxide and providing for the fizzy sensation. Also, fireworks manufacturers modify the surface area of solid reactants to control the rate at which the fuels in fireworks are oxidised, using this to create diverse effects. For example, finely divided aluminium confined in a shell explodes violently. If larger pieces of aluminium are used, the reaction is slower and sparks are seen as pieces of burning metal are ejected.

The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their concentrations. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will usually result in the corresponding increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. For example, combustion will occur more rapidly in pure oxygen than in air (21% oxygen).

The rate equation shows the detailed dependence of the reaction rate on the concentrations of reactants and other species present. The mathematical forms depend on the reaction mechanism. The actual rate equation for a given reaction is determined experimentally and provides information about the reaction mechanism. The mathematical expression of the rate equation is often given by

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