Several alternative compounds have been added to gasoline, including methanol, ethanol, an...

Several alternative compounds have been added to gasoline, including methanol, ethanol, and methyl tert-butyl ether (MTBE), to increase the oxygen content of gasoline in order to reduce the formation of CO on combustion. Unfortunately, MTBE has been found in groundwater at concentrations sufficient to cause concern. Persistence of a compound in water can be evaluated from its half-life, t1/2, that is, the time for one-half of the compound to leave the system of interest. The half-life depends on the conditions in the system, of course, but for environmental evaluation can be approximated by

where [OH-]is the concentration of hydroxyl radical in the system that for this problem of the contamination of water is equal to 1.5 × 106 molecules/cm3. The values of k determined from experiment are

Calculate the half-life of each of the three compounds, and order them according to their persistence.