Environmental Engineering

Question 1: Sulfur dioxide (SO₂) is a gas that is released from the burning of fossil fuels (in particular, coal that contains low concentrations of sulfur). The Henry’s law constant for SO₂(g) is 1.23 [with implied units of mol/(L-atm)]. SO2(g) behaves very much like CO₂(g), in that it combines with water to form an acid (sulfurous acid, H₂SO₃) that can release one or two H+ ions to solution. However, H₂SO₃ is a considerably stronger acid than H₂CO₃, as indicated by its Ka values:

H₂SO₃ <----> H⁺ + HSO₃⁻                 K_a1 = 10^−1.85

HSO₃^- <------> H⁺ +SO₃^2-               K_a2 = 10^-7.19

Calculate the pH of water in a cloud that has equilibrated with atmospheric CO₂(g) (370 ppm) plus 1.0 ppm SO₂(g). Compare the result with that shown in your book for equilibration with “pure” air containing CO₂(g) but no SO₂(g).

Question 2: Despite its toxicity, cyanide is used extensively in some industries. Hydrogen cyanide (HCN) and its conjugate base, cyanide ion (CN⁻) are relatively harmless in solution (assuming that none of the workers drink the water!), but HCN can be dangerous if it enters the gas phase and is inhaled. A solution contains 2mg/L total cyanide (TOTCN) and is at pH 8.5. pK_a for HCN is 9.21, and the Henry’s constant for HCN is 25.0 [(mol/L-atm)].

a. What is the concentration of HCN(aq) in the solution?

b. What would the partial pressure of HCN(g) be in the gas phase, if the gas equilibrated with the solution?

Question 3: In that problem, you were told to assume that all the Ba₂₊ in the original solution precipitated. In reality, we know that some Ba²⁺ must remain in solution for the solubility product of BaSO₄(s) (pK_sp = 9.98) to be satisfied. Test the assumption that you made in the original problem by calculating the fraction of Ba²⁺ that is expected to remain dissolved once equilibrium is reached.

Question 4: Phosphorus is a critical nutrient used in fertilizers, and the world’s supply of phosphorus rocks in mines is becoming limited, so phosphorus recovery from wastewater is increasingly attractive. The most common approach for recovering the phosphorus is to precipitate and purify it in a solid called ‘struvite’ with chemical formula MgNH₄PO₄(s). The dissolution reaction for struvite is

MgNH₄PO₄ (s) <-----> Mg²⁺ + NH₄⁺ + PO₄ ³⁻         pK_sp = 13.26

Both NH₄ ⁺ and the PO₄ ³⁻ participate in acid/base reactions, as follows:

NH₄⁺ <--> H⁺ + NH₃         pK_a1 = 9.24

HPO₄²⁻ <----> H⁺ + PO₄³⁻            pK_a2 = 12.19

If a treated wastewater contains 20 mg/L TOTN (the total concentration of N, distributed between NH₄ ⁺ and NH₃) and 2 mg/L TOTP (the total concentration of P, distributed between HPO₄ ²⁻ and PO₄ ³⁻) and is at pH 10.3, what concentration of Mg²⁺ is required for struvite to start precipitating?