Acid rain is produced by the emission of various pollutants into the atmosphere by various industries. Coal-burning plants which produce electricity, for example, emit large quantities of sulfur-containing chemicals into the air. These chemicals undergo a series of chemical reactions in the lower atmosphere. The products of these reactions combine with natural rainwater and snow, and are then deposited as acid rain.
A quick overview of acidity might be helpful. There are a number of definitions for an acid, as you know if you have taken first-year chemistry! We'll use a fairly simple definition. An acid is created when a hydrogen ion (a hydrogen atom with a positive charge, written H^{+}) mixes with ordinary water (H_{2}O) to form a hydronium ion (H_{3}O^{+}). The reaction looks like this:
Reactants | Product | |
H^{+} + H_{2}O | -----> | H_{3}O^{+} |
If we know how much of the hydrogen atom we have (that is, if we know its concentration, written as [H^{+}], we can calculate its pH. pH is a measure of the acidity of a liquid solution, and is shown on a scale from 1 to 14:
ACIDIC | NEUTRAL | BASIC |
____________ | ___|______ | ________________ |
1 2 3 4 5 | 6 7 8 9 | 10 11 12 13 14 |
According to the graphic above, an chemical with a pH less than 7 is considered to be an acid, a neutral substance (like pure water) has a pH of 7, and any liquid above a pH of 7 is called basic. We are concerned, of course, with rainwater that has a pH of less than 7!
To build this model, we need to investigate the chemistry of acid rain in a little more detail. The primary pollutant generated by coal-burning plants is sulfuric acid, or H_{2}SO_{4}. When sulfuric acid is deposited into the atmosphere, it dissociates, or breaks apart, into two new products:
Reactant | Products | |
H_{2}SO_{4} | -----> | H^{+ +} HSO_{4-} |
Notice the charges on the right -- a plus charge on the hydrogen and the minus charge on the sulfur compound add up to zero, which is the charge on the sulfuric acid. More importantly, notice that we now have a hydrogen ion (H^{+}) on the loose! This ion can now react with water to form acid rain, but we're not quite done yet!
We need to investigate two "k" numbers: K and k! The letter "K" is called the equilibrium constant. This is a unitless number that measures the tendency of chemical to break apart. Chemists prefer to say: K is a measure of the tendency of a reaction to go to the right, that is, to follow the reaction arrow to form products. The table below shows this tendency:
An example: what is the value of K for these non-chemical situations?
In the reaction above, K is 1,0000. Since this is a number substantially bigger than 1, we can say that it is absolutely true that H_{2}SO_{4} will dissociate into the two products. If sulfuric acid gets into the atmosphere, we can guarantee that it will break apart.
In most books it should be noted that you will generally see the term "K_{a}", where the little "a" stands for acid. K_{a} is called the "dissociation constant of an acid", and you look them up in tables of dissociation constants found in many chemistry books.
The second "k" is the rate constant for a reaction. This "k" tells you not whether or not the reaction will occur (that's the job of K_{a}!), but how fast it will go IF it is allowed to do so! In each of the acid rain reactions, there will be TWO values of k -- one in the forward direction and one in the reverse direction. All of the reactions of interest here are reversible -- the products can recombine to form the original chemical. Basically, a chemical can break apart (dissociate) but then, if conditions are right, connect back together again! We show this with an arrow going in both directions:
k_{-1} | ||
<----- | ||
<----- | ||
H_{2}SO_{4} | -----> | H^{+ +} HSO_{4-} |
k_{1} |
Remember that if K_{a} is large, there is not much of a chance that things will recombine, but it is still a possibility!
Each of the reactions of importance will produce a hydrogen ion, which contributes to the overall acidity of the water. If we know the concentration of the hydrogen ion, written as [H^{+}], we can calculate the pH of the water using this equation:
In this model, we need to study the concentrations of three species: H_{2}SO_{4}, HSO_{4}, and SO_{4}^{+}. For each dissociation reaction, there is a dissociation constant, K_{a}, and a rate constant for the forward and reverse reactions. We will also have a starting concentration for each of the species above.
The dissociation constants are given from a table of dissociation constants:
K_{a} for H_{2}SO_{4}: 1 x 10^{3}
K_{a} for HSO_{4-}: 1.3x 10^{-2}
For the four rate constants (k_{1}, k_{2}, k_{-1}, k_{-2}), you will need to use the algorithms below:
k_{1} = [H_{2}SO_{4}]
k_{2} = [HSO_{4}]
k_{-1} = [HSO_{4}][H] / K_{a1}
k_{-2} = [SO_{4}][H] / K_{a2}
We can calculate [H] using the following algorithm:
[H] = [HSO_{4}] = 2 [SO_{4}]
With the information above, you should be able to construct your basic model of the dissociation reactions of acid rain formation.
Run your model for 8 seconds. You will need to use a fairly small dt to get this model to behave correctly. Experiment with changing the value of dt.
Make sure that you add a converter to convert [H] into pH. You will need to use the built-in function "log10".
Once you are ready to run your model, create a graph of [H_{2}SO_{4}], [HSO_{4}], [SO_{4}], and [H]. Use either a numeric display window or a simple data table to look at how pH changes while the reactions proceed.