The concept of half-life is used extensively in environmental engineering and science. For example, it is used to describe the decay of radioisotopes, elimination of poisons from people, self-cleaning of lakes, and the disappearance of pesticides from soil. Starting with the mass-balance equation, develop an expression that describes the half-life (t1/2) of a substance in terms of the reaction rate constant, k, assuming the decay reaction takes place in a batch reactor.