A large amount of a heavy oil has been accidentally spilled on a large, elevated parking lot and settled, coating all surfaces, including both flat areas and sloping access ramps. Following the spill, a brief, but intense, storm, lasting 20 min hit the area and we are concerned with contamination of the rain water. The temperature is constant at 10°C and the solubility of the oil in water at this temperature is 1.5 × 10⁻⁵ mol/cm³. The molar volume of the oil at the normal boiling point is estimated to be 200 cm³/mol.

(a) Estimate the diffusion coefficient of the oil in water for these conditions.

(b) In a flat area of the parking lot, the rain water quickly pooled on top of the oil forming a 1.0 cm thick stagnant layer 5 m in diameter.

Determine the concentration of the oil (in mol/cm³) at the top of the water layer and the total amount of oil (in mol) contaminating the pooled water in this area after 48 h.

(c) In a covered sloping access ramp, 3 m wide and 20 m long, the rain water did not pool over the oil but ran over it as a 0.5-cm thick layer at a velocity of 2 m/s. The water flow is turbulent for these conditions and the mass transfer coefficient at the oil–water interface is 5.0

× 10⁻³ cm/s. In this case, there is no significant diffusive resistance in the flowing water. Estimate the average concentration of the oil in the water running off the ramp, and the total amount of oil contaminating the water run-off from this ramp.