Fick’s first diffusion law states that

Where mass flux = the quantity of mass that passes across a unit area per unit time (g/cm2/s), D = a diffusion coefficient (cm2/s), c = concentration, and x = distance (cm). As environmental engineer measures the following concentration of a pollutant in the sediments underlying a lake (x = 0 at the sediment-water interface and increases downward):

Use the best numerical differentiation technique available to estimate the derivative at x = 0. Employ this estimate in conjunction with Eq. (P24.6) to compute the mass flux of pollutant out of the sediments and into the overlying waters (D = 1.52 x 10^-6 cm²/s). For a lake with 3.6 x 10⁶ m² of sediments, how much pollutant would be transported into the lake over a year’s time?

de D- dx Mass flux %3D