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In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
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.
It breaks down an apparently unimolecular reaction into two elementary steps, with a rate constant for each elementary step. The rate law and rate equation for the entire reaction can be derived from the rate equations and rate constants for the two steps. The Lindemann mechanism is used to model gas phase decomposition or isomerization reactions
Phase reduction is a method used to reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. [1] [2] Many phenomena in our world such as chemical reactions, electric circuits, mechanical vibrations, cardiac cells, and spiking neurons are examples of rhythmic phenomena, and can be considered as nonlinear limit cycle ...
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs
Instead, the slow step involves two molecules of NO 2. A possible mechanism for the overall reaction that explains the rate law is: 2 NO 2 → NO 3 + NO (slow) NO 3 + CO → NO 2 + CO 2 (fast) Each step is called an elementary step, and each has its own rate law and molecularity. The sum of the elementary steps gives the net reaction.
The product-determining step is the step of a chemical reaction that determines the ratio of products formed via differing reaction mechanisms that start from the same reactants. The product determining step is not rate limiting if the rate limiting step of each mechanism is the same.
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .