Exercise: Hexachlorobenzene (C6Cl6) is a highly toxic waste product of pesticide manufacturing. It is resistant to biodegradation. Sediments at the bottom of a reservoir in the Upper Mississippi River catchment have been found to contain high C6Cl6 concentrations. The sedimentation rate is largely unknown, but an effective diffusion coefficient had been determined for C6Cl6 from core samples of the reservoir sediments for hexachlorobenzene and these sediments: D=1.2·10-9 m2·s-1. When did the spill occur? (Do a least square fit of the Gaussian distribution to the measured concentrations. The attempt at a solution I am looking for a way to calculate the time difference for when the concentration was 0.1 and when it was at it's maximum level at 2.5 g/m³, like: how long did it take the C6Cl6 to diffuse to reach a level of 2.5.
c(x, t) = (M*/2√(πDt)) ·e-(x2/4Dt).