A rate
law is an equation that relates the rate of disappearance of
reactants,
or appearance of products,
to the reactant concentrations. The simplest type of reaction is
the spontaneous decomposition of isolated molecules or atoms, and
it is encountered most commonly in radioactive decay of unstable
nuclei. The rate law for the breakdown of carbon14 nuclei is
The expression
should be read as "the rate of change
of carbon14 concentration with time." (For any quantity, x,
whose value changes with time, the expression dx/dt
means "the rate of change of x with time.")
The rate
law just given can be translated as: "The rate of disappearance
of carbon14 atoms is proportional to the number of carbon14 atoms
that are present per liter and available for decay."
Since each atom has the same inherent
probability of decaying during a specified time interval, and since
the probability of one atom's decaying is independent of the presence
or absence of other atoms, this is the rate law that would be expected
intuitively. [C14] represents the concentration of carbon14, and
k is the rate
constant.
