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The use of k atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations. [19] The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation:, [24]
Equations should be balanced according to the stoichiometry, the number of atoms of each species should be the same on both sides of the equation. This is achieved by scaling the number of involved molecules (A, B, C and D in a schematic example below) by the appropriate integers a, b, c and d .
Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [ 1 ] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution , [ 10 ] [ 11 ] but Gelenbe 's G-network model showed this not to be the case.
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas.The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. [1]
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
This is illustrated in the image here, where the balanced equation is: CH 4 + 2 O 2 → CO 2 + 2 H 2 O. Here, one molecule of methane reacts with two molecules of oxygen gas to yield one molecule of carbon dioxide and two molecules of water. This particular chemical equation is an example of complete combustion. Stoichiometry measures these ...
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[10] [11] A consistent solution that balances two equation terms may generate an accurate approximation to the full equation's solution for values approaching . [ 11 ] [ 12 ] Approximate solutions arising from balancing different terms of an equation may generate distinct approximate solutions e.g. inner and outer layer solutions .