Global Environmental Problems

Spring 2006

Problem Set #11 (the last one!)

Due: 3 May

1.

In chapter III of Harte, read problem 1 ("Acid Rain"). Compare this to the lecture slides in which I derive a rough estimate of the pH of rainfall based on the density of wet sulfate deposition. Note that Harte solves the coupled chemical equations that describe the dissociation of sulfuric acid and water, while I simply assume that the sulfuric acid completely dissociates and that each mole of sulfuric acid produces two moles of H⁺. Show that doing it my way produces the same answer given by Harte.

2.

In the late 1990s, deposition of sulfate in Beijing was about 6 grams of sulfate (SO₄^2–) per square meter per year. Rainfall in Beijing averages about 25 inches per year.

A.

What is the average pH of precipitation? Assume that all the sulfate is wet deposited, and that sulfate is the only source of acidity in precipitation.

B.

In preparation for the 2008 Olympics, China is making major efforts to reduce sulfur emissions in the Beijing area. This is especially challenging in an economy that is growing at a rate of 10 percent per year. If total deposition of sulfur is reducted by half, what effect will this have on the pH of rainfall in Beijing?

3.

Acid mine drainage (AMD) is a major environmental problem in many areas. AMD results primarily from the oxidation of iron pyrite (FeS₂) contained in the ores from which minerals are extracted, by groundwater flowing through abandoned mines:

FeS₂ + 7/2 H₂O + 15/4 O₂  →  Fe(OH)₃ + 4H⁺ + 2SO₄^2–

A.

AMD from a mine has an average sulfate concentration of 150 milligrams per liter. Considering only the reaction above, what is the pH?

B.

Precipitation in the area averages 100 cm/y; of this, 35 cm goes into the groundwater. The abandoned mine covers an area of 100 ha. All groundwater percolating through this area is AMD. Based on your answer to part A, what is the total outflow of [H⁺] in the AMD, in moles per year?

C.

The AMD drains into a lake with a volume of 20 billion liters. The residence time of water in the lake is 2 years. If AMD is the only source of [H+], what is the pH of the lake water?

4.

Flue-gas desulfurization (FGD) removes sulfur by passing exhaust gases through a spray of lime and water, which react with SO₂ to form calcium sulfate, CaSO₄ (gypsum), which is removed as a solid. 

A.

If the 10-Mt/y reduction in sulfur dioxide emissions mandated by the 1990 amendments to the Clean Air Act were achieved entirely by FGD, how much dry calcium sulfate would be produced?

B.

The calcium sulfate produced by early scrubbers was contaminated by heavy metals in the coal, rendering it hazardous waste. The transport and disposal of such waste costs about $50/t. What is the contribution of this disposal cost to the cost of FGD, per metric ton of SO₂ removed?