Problem 1. The mass transport of "Pollutant A" will be examined in three different compartments (air, water, and soil) in a container closed to the atmosphere. At t = 10 min, the concentration of "Pollutant X" in air (p¹₀ A₁), water (p¹₀ A₂), and soil (w¹₀ A) are given as 3 mg/L, 4 mg/L, and 0.1 mg/g, respectively. Some other information for "Pollutant X" is given in the following table:
Air (Vₐ = 8 L) p¹₀ A₁ = 3 mg/L
Water (Vw = 3 L) p¹₀ A₂ = 4 mg/L
Soil particles (m = 50 g) w¹₀ A = 0.1 mg/g
Additional information for Pollutant X:
Henry's constant (H) = 0.1 Lw/La
Soil-water equilibrium constant (KA₂) = 0.025 Lw/g
One-film air phase mass trans. Const. (KAI) = 0.2 m/min
One-film water phase mass trans. Const. (KA₂) = 0.004 m/min
Physical properties of compartments:
Depth of air (hₐ) = 25 cm
Volume of air (V₂) = 8 liters
Volume of water (VW) = 3 liters
Mass of soil (m) = 50 grams
Based on the information given in the problem:
a) Calculate the total mass of "Pollutant X" in the container as grams. (10p)
b) Determine the direction of mass transport for Pollutant X between "water and air" and "water and soil" at t = 10 min. (10p)
c) Calculate the flux for the mass transport of "Pollutant X" between water and air phases as mg/m².min at 10 min. (15p)
d) Calculate the equilibrium concentrations of Pollutant X in air, water, and soil phases (p A₁, p A₂, and w A) when the whole system reaches equilibrium. (15p)
e) If the water phase concentration at 30 min (p₃₀ A₂) from t = 0 is 5 mg/L, calculate the concentration of "Pollutant X" in air at t = 30 min (p³₀ A₁). (20p)