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In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. [1]
Graphical rate laws do, however, maintain that intuitive presentation of linearized data, such that visual inspection of the plot can provide mechanistic insight regarding the reaction at hand. The basis for a graphical rate law rests on the rate (v) vs. substrate concentration ([S]) plots
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
As an example, consider the gas-phase reaction NO 2 + CO → NO + CO 2.If this reaction occurred in a single step, its reaction rate (r) would be proportional to the rate of collisions between NO 2 and CO molecules: r = k[NO 2][CO], where k is the reaction rate constant, and square brackets indicate a molar concentration.
The result is equivalent to the Michaelis–Menten kinetics of reactions catalyzed at a site on an enzyme. The rate equation is complex, and the reaction order is not clear. In experimental work, usually two extreme cases are looked for in order to prove the mechanism. In them, the rate-determining step can be: Limiting step: adsorption/desorption
The flux of the diffusive molecules follows Fick's laws of diffusion. For particles in a solution, an example model to calculate the collision frequency and associated coagulation rate is the Smoluchowski coagulation equation proposed by Marian Smoluchowski in a seminal 1916 publication. [4]
Rate 1 is the rate of effusion for the first gas. (volume or number of moles per unit time). Rate 2 is the rate of effusion for the second gas. M 1 is the molar mass of gas 1 M 2 is the molar mass of gas 2. Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight.
The rate of entropy production for the above simple example uses only two entropic forces, and a 2×2 Onsager phenomenological matrix. The expression for the linear approximation to the fluxes and the rate of entropy production can very often be expressed in an analogous way for many more general and complicated systems.