Formal Definition of Reaction Rate
Consider a typical chemical reaction:
- aA + bB → pP + qQ
The lowercase letters (a, b, p, and q) represent stoichiometric coefficients, while the capital letters represent the reactants (A and B) and the products (P and Q).
According to IUPAC's Gold Book definition the reaction rate r for a chemical reaction occurring in a closed system under constant-volume conditions, without a build-up of reaction intermediates, is defined as:
where denotes the concentration(Molarity, mol/L) of the substance X. (NOTE: Rate of a reaction is always positive. '-' sign is present in the reactant involving terms because the reactant concentration is decreasing.) The IUPAC recommends that the unit of time should always be the second. In such a case the rate of reaction differs from the rate of increase of concentration of a product P by a constant factor (the reciprocal of its stoichiometric number) and for a reactant A by minus the reciprocal of the stoichiometric number. Reaction rate usually has the units of mol L−1 s−1. It is important to bear in mind that the previous definition is only valid for a single reaction, in a closed system of constant volume. This most usually implicit assumption must be stated explicitly, otherwise the definition is incorrect: If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
For any system in general the full mass balance must be taken into account: IN - OUT + GENERATION -CONSUMPTION= ACCUMULATION
When applied to the closed system at constant volume considered previously, this equation reduces to:, where the concentration is related to the number of molecules by . Here is the Avogadro constant.
For a single reaction in a closed system of varying volume the so called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time.
Here is the stoichiometric coefficient for substance, equal to a, b, p, and q in the typical reaction above. Also is the volume of reaction and is the concentration of substance .
When side products or reaction intermediates are formed, the IUPAC recommends the use of the terms rate of appearance and rate of disappearance for products and reactants, properly.
Reaction rates may also be defined on a basis that is not the volume of the reactor. When a catalyst is used the reaction rate may be stated on a catalyst weight (mol g−1 s−1) or surface area (mol m−2 s−1) basis. If the basis is a specific catalyst site that may be rigorously counted by a specified method, the rate is given in units of s−1 and is called a turnover frequency.
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