The PCB concentration in Lake Michigan is declining according to a first-order rate law having a rate constant of 0.079 per year. If the PCB concentration in Lake Michigan averaged 0.47 ppt in 1991, what will it be in 2005? In what year will the concentration fall to 0.10 ppt? What is the half-life period of PCBs in this lake? (Answer first with PCB concentration of the year 2005, then the year the concentration will be 0.10 ppt, and lastly the half-life).
Because, rate constant k = 0.079 per year
Concentration in 1991 C(1991) = Co = 0.47 ppt
PCB concentration in 2005,
C = Co*exp(-k*t)
t = 2005-1991 = 14 ...
The solution involves a calculation of PCB concentration in a lake given rate constant and average concentration in a previous year. A step-by-step solution is provided.