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Diffusion Limit
Diffusion-controlled (or diffusion-limited) reactions are reactions in which the reaction rate is equal to the rate of transport of the reactants through the reaction medium (usually a solution). The process of chemical reaction can be considered as involving the diffusion of reactants until they encounter each other in the right stoichiometry and form an activated complex which can form the product species. The observed rate of chemical reactions is, generally speaking, the rate of the slowest or "rate determining" step. In diffusion controlled reactions the formation of products from the activated complex is much faster than the diffusion of reactants and thus the rate is governed by collision frequency. Diffusion control is rare in the gas phase, where rates of diffusion of molecules are generally very high. Diffusion control is more likely in solution where diffusion of reactants is slower due to the greater number of collisions with solvent molecules. Reactions where the act ...
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Chemical Reaction
A chemical reaction is a process that leads to the chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the Atomic nucleus, nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive Chemical element, elements where both electronic and nuclear changes can occur. The substance (or substances) initially involved in a chemical reaction are called reagent, reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more Product (c ...
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Centipoise
The poise (symbol P; ) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS). It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation). The centipoise (1 cP = 0.01 P) is more commonly used than the poise itself. Dynamic viscosity has dimensions of \mathrm, that is, mathsf^1 \mathsf^ \mathsf^/math>. 1~\text = 0.1~\text^ \text \text^ = 1~\text^ \text \text^ = 1~\text \text \text^. The analogous unit in the International System of Units is the pascal-second (Pa⋅s): 1~\text \text = 1~\text \text \text^ = 1~\text^ \text \text^ = 10~\text. The poise is often used with the metric prefix ''centi-'' because the viscosity of water at 20 °C (standard conditions for temperature and pressure) is almost exactly 1 centipoise. A centipoise is one hundredth of a poise, or one millipascal-second (mPa⋅s) in SI units (1 cP = 10−3 Pa⋅s = 1 mPa⋅s). The CGS symbol f ...
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Chemical Reactions
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur. The substance (or substances) initially involved in a chemical reaction are called reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more products, which usually have properties different from the reactants. Reactio ...
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Diffusion Limited Enzyme
A diffusion-limited enzyme catalyses a reaction so efficiently that the rate limiting step is that of substrate diffusion into the active site, or product diffusion out. This is also known as kinetic perfection or catalytic perfection. Since the rate of catalysis of such enzymes is set by the diffusion-controlled reaction, it therefore represents an intrinsic, physical constraint on evolution (a maximum peak height in the fitness landscape). Diffusion limited perfect enzymes are very rare. Most enzymes catalyse their reactions to a rate that is 1,000-10,000 times slower than this limit. This is due to both the chemical limitations of difficult reactions, and the evolutionary limitations that such high reaction rates do not confer any extra fitness. History The theory of diffusion-controlled reaction was originally utilized by R.A. Alberty, Gordon Hammes, and Manfred Eigen to estimate the upper limit of enzyme-substrate reaction. According to their estimation, the upper l ...
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Toluene
Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon with the chemical formula , often abbreviated as , where Ph stands for the phenyl group. It is a colorless, water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...-insoluble liquid with the odor associated with paint thinners. It is a mono-substituted benzene derivative, consisting of a methyl group (CH3) attached to a phenyl group by a single bond. As such, its systematic IUPAC nomenclature of organic chemistry, IUPAC name is methylbenzene. Toluene is predominantly used as an industrial feedstock and a solvent. As the solvent in some types of paint thinner, permanent markers, contact cement and certain types of glue, toluene is sometimes used as a recreational inhalant and has the potential of causin ...
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Water
Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a solvent). It is vital for all known forms of life, despite not providing food energy or organic micronutrients. Its chemical formula, , indicates that each of its molecules contains one oxygen and two hydrogen atoms, connected by covalent bonds. The hydrogen atoms are attached to the oxygen atom at an angle of 104.45°. In liquid form, is also called "water" at standard temperature and pressure. Because Earth's environment is relatively close to water's triple point, water exists on Earth as a solid, a liquid, and a gas. It forms precipitation in the form of rain and aerosols in the form of fog. Clouds consist of suspended droplets of water and ice, its solid state. When finely divided, crystalline ice ...
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Methanol
Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical compound and the simplest aliphatic Alcohol (chemistry), alcohol, with the chemical formula (a methyl group linked to a hydroxyl group, often abbreviated as MeOH). It is a light, Volatility (chemistry), volatile, colorless and flammable liquid with a distinctive alcoholic odor similar to that of ethanol (potable alcohol), but is more acutely toxic than the latter. Methanol acquired the name wood alcohol because it was once produced through destructive distillation of wood. Today, methanol is mainly produced industrially by hydrogenation of carbon monoxide. Methanol consists of a methyl group linked to a polar hydroxyl group. With more than 20 million tons produced annually, it is used as a Precursor (chemistry), precursor to other commodity chemicals, including formaldehyde, acetic acid, methyl tert-butyl ether, methyl ''tert''-butyl ether, methyl benzoate, anisole, peroxyacids, ...
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N-Pentane
Pentane is an organic compound with the formula C5H12—that is, an alkane with five carbon atoms. The term may refer to any of three structural isomers, or to a mixture of them: in the IUPAC nomenclature, however, pentane means exclusively the ''n''-pentane isomer, in which case pentanes refers to a mixture of them; the other two are called isopentane (methylbutane) and neopentane (dimethylpropane). Cyclopentane is not an isomer of pentane because it has only 10 hydrogen atoms where pentane has 12. Pentanes are components of some fuels and are employed as specialty solvents in the laboratory. Their properties are very similar to those of butanes and hexanes. History Normal pentane was discovered in 1862 by Carl Schorlemmer, who, while analyzing pyrolysis products of the cannel coal mined in Wigan, identified, separated by fractional distillation and studied a series of liquid hydrocarbons inert to Nitric acid, nitric and Sulfuric acid, sulfuric acids. The lightest of them, whi ...
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Stokes-Einstein
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is D = \mu \, k_\text T, where * is the diffusion coefficient; * is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; * is the Boltzmann constant; * is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Note that the equation above describes the classical case and should be modified when quantum effects are relevant. Two frequently used important special forms of the relation are: * Einstein–Smoluchowski equation, for diffusion of charged particles: D = \frac * Stokes–Einstein–Sutherland equation, for diffusion of spherical particles through a liquid with ...
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Activated Complex
In chemistry, an activated complex represents a collection of intermediate structures in a chemical reaction when bonds are breaking and forming. The activated complex is an arrangement of atoms in an arbitrary region near the saddle point In mathematics, a saddle point or minimax point is a Point (geometry), point on the surface (mathematics), surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a Critical point (mathematics), ... of a potential energy surface. The region represents not one defined state, but a range of unstable configurations that a collection of atoms pass through between the reactants and Product (chemistry), products of a reaction. Activated complexes have partial reactant and product character, which can significantly impact their behaviour in chemical reactions. The terms activated complex and transition state are often used interchangeably, but they represent different concepts. Transition state ...
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Stokes-Einstein Equation
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is D = \mu \, k_\text T, where * is the diffusion coefficient; * is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; * is the Boltzmann constant; * is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Note that the equation above describes the classical case and should be modified when quantum effects are relevant. Two frequently used important special forms of the relation are: * Einstein–Smoluchowski equation, for diffusion of charged particles: D = \frac * Stokes–Einstein–Sutherland equation, for diffusion of spherical particles through a liquid with ...
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Fick's Law Of Diffusion
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the Mass diffusivity, diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. ''Fick's first law'': Movement of particles from high to low concentration (diffusive flux) is directly proportional to the particle's concentration gradient. ''Fick's second law'': Prediction of change in concentration gradient with time due to diffusion. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion. History In 1855, physiologist Adolf Fick first reported* * his now well-known laws governing the transport of mass through diffusive means. Fick's work was inspired by the earlier experiments of Thomas Graham (chemist), Thomas Graham, which fell short of p ...
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