15. The Rates of Chemical Reactions   Previous PageNext Page
       Experimental Rate Laws

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 carbon-14 nuclei is

The expression

should be read as "the rate of change of carbon-14 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 carbon-14 atoms is proportional to the number of carbon-14 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. [C-14] represents the concentration of carbon-14, and k is the rate constant.


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