text: Consider a typical balanced chemical reaction:
  The lowercase letters (, , , and ) represent stoichiometric coefficients, while the capital letters represent the reactants ( and ) and the products ( and ).
  According to IUPAC's Gold Book definition
  the reaction rate  for a chemical reaction occurring in a closed system at constant volume, without a build-up of reaction intermediates, is defined as:
  where  denotes the concentration of the substance  or . The reaction rate thus defined has the units of mol/L/s.
  The rate of a reaction is always positive. A negative sign is present to indicate that the reactant concentration is decreasing. The IUPAC recommends that the unit of time should always be the second. 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. The stoichiometric numbers are included so that the defined rate is independent of which reactant or product species is chosen for measurement. For example, if  and  then  is consumed three times more rapidly than , but  is uniquely defined. An additional advantage of this definition is that for an elementary and irreversible reaction,  is equal to the product of the probability of overcoming the transition state activation energy and the number of times per second the transition state is approached by reactant molecules. When so defined, for an elementary and irreversible reaction,  is the rate of successful chemical reaction events leading to the product.
  The above definition is only valid for a single reaction, in a closed system of constant volume. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
  For an open system, the full mass balance must be taken into account:
  where 
  * is the inflow rate of  in molecules per second;
  * the outflow;
  * is the instantaneous reaction rate of  (in number concentration rather than molar) in a given differential volume, integrated over the entire system volume  at a given moment. 
  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 , , , and  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 the rate of increase of concentration and rate of the decrease of concentration 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 s) or surface area (mol m s) 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 and is called a turnover frequency.