Rate Equation

The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders). To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system. For a generic reaction aA + bB → C with no intermediate steps in its reaction mechanism (that is, an elementary reaction), the rate is given by

where and express the concentration of the species A and B, respectively (usually in moles per liter (molarity, M)); x and y are the respective stoichiometric coefficients of the balanced equation; they must be determined experimentally. k is the rate coefficient or rate constant of the reaction. The value of this coefficient k depends on conditions such as temperature, ionic strength, surface area of the adsorbent or light irradiation. For elementary reactions, the rate equation can be derived from first principles using collision theory. Again, x and y are not always derived from the balanced equation.

The rate equation of a reaction with a multi-step mechanism cannot, in general, be deduced from the stoichiometric coefficients of the overall reaction; it must be determined experimentally. The equation may involve fractional exponential coefficients, or it may depend on the concentration of an intermediate species.

The rate equation is a differential equation, and it can be integrated to obtain an integrated rate equation that links concentrations of reactants or products with time.

If the concentration of one of the reactants remains constant (because it is a catalyst or it is in great excess with respect to the other reactants), its concentration can be grouped with the rate constant, obtaining a pseudo constant: If B is the reactant whose concentration is constant, then . The second-order rate equation has been reduced to a pseudo-first-order rate equation. This makes the treatment to obtain an integrated rate equation much easier.

Read more about Rate Equation:  Stoichiometric Reaction Networks, Zero-order Reactions, First-order Reactions, Second-order Reactions, Summary For Reaction Orders 0, 1, 2, and n, Equilibrium Reactions or Opposed Reactions, Consecutive Reactions, Parallel or Competitive Reactions, General Dynamics of Unimolecular Conversion

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... NO3 Using the quasi steady-state approximation, the rate equation is calculated to be Rate = k2 * = k1k2 2 / (k-1 + k2) Experiment has shown that the rate is observed as first-order in the ... If k2 >> k-1 (>> means "much larger than"), then the rate equation may be simplified by assuming that k-1 ~= 0 ... Then the rate equation is Rate = k12 which is second order ...
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... Let the rate constant of conversion from species to species be denoted as, and construct a rate-constant matrix whose entries are the ...
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... or product) is defined as the index, or exponent, to which its concentration term in the rate equation is raised ... For the typical rate equation of form, where.. ... ion 2 HgCl2(aq) + C2O42-(aq) → 2 Cl-(aq) + 2 CO2(g) + Hg2Cl2(s) has the observed rate equation r = k12 In this case, the reaction order with respect to the reactant HgCl2 is 1 ...
Dissociative Substitution - Kinetics
... Dissociative pathways are characterized by a rate determining step that involves release of a ligand from the coordination sphere of the metal undergoing substitution ... of the substituting nucleophile has no influence on this rate, and an intermediate of reduced coordination number can be detected ... The reaction can be described with k1, k-1 and k2, which are the rate constants of their corresponding intermediate reaction steps Normally the rate determining step is the ...

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