See any good textbooks on physical chemistry and chemical reaction engineering, and Perrys Chemical Engineers Handbook part 4 (which also covers
thermodynamics).
Basically, the rate of a chemical reaction in a liquid or gas phase, i.e. the rate of formation of the major product with time is usually (other than
in some autodecompositions and some cases of catalysis) proportional to the product of the remaining concentrations of the reagents. This is derived
from the collision theory of reactions, which are stochastic processes. This leads to a differential equation, e.g. for a normal second-order reaction
between two reagents A and B producing C, which is the most common case,
d[C]/dt = k[A][B] where k is the rate constant at a given temperature (and pressure in the case of a gas-phase reaction).
If the original concentrations of A and B are [Ao] and [Bo], and C is produced proportionately to their consumption,
d[C]/dt = k([Ao] - [C])([Bo] - [C])
which can be integrated to give a second-order exponential function.
In the case of a normal first-order decomposition of a single reagent A to C, it becomes simply d[C]/dt = k([Ao] - [C]), which integrates to a simple
first-order exponential equation.
Some autodecompositions instead are linear (constant-rate, with a definite end-time). Some free-radical composite chain reactions (especially
gas-phase, like reactions of halogens with H2 or alkanes) and autodecompositions have a fractional order. There are third-order reactions, but they
are very rare. In homogenous catalysis, by a gaseous or liquid substance which is mixed or dissolved in the same medium, and which remains unchanged
at the end of the reaction, the rate constant k is replaced by k[D], where [D] is the (constant) concentration of the catalyst.
The rate constant k varies with temperature, usually increasing with temperature T (because the Brownian motion of molecules, essential in the
collision theory of reactions), increases with temperature according to the Arrhenius equation, which has been found to be very accurate:
k = Aexp(-E/RT)
where A is the "frequency factor", E is the energy of activation, and R is the gas constant. which depends on the reaction. A and E depend
on the reaction.
The above applies to homogenous reactions, in which the reagents are rapidly and completely mixed. In heterogenous reactions, the rates are further
(in addition to the ordinary rate constant) affected by the degree and rate of mixing, or of diffusion (and hence mass transfer coefficients) if not
(able to be) physically mixed. Heteogenous reactions also include those in which the catalyst is of another phase, e.g. a solid Pt or Ni or other
catalyst of a liquid- or gas-phase reaction, or a liquid catalyst of a gaseous reaction in which the reagents are insoluble in the liquid. For further
details, see Perry part 4.
John W.
|
![[*]](images/xpblue/default_icon.gif){kind=icon}
