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Sulfur dioxide ( SO_2 ) plays an important role in the chemistry of our atmosphere, especially when it comes to air pollution and acid rain formation. SO_2 solubility refers to how well SO_2 gas can dissolve in water, such as rainwater. Understanding solubility is crucial when trying to predict chemical behavior in different environmental settings. When SO_2 dissolves in water, it interacts with water molecules to form sulfurous acid ( H_2SO_3 ). The solubility of SO_2 in water at a given temperature indicates how much SO_2 can be held in a liter of water until it is saturated. In this exercise, the solubility given is 1.3653 ext{ moles/L} at 298 ext{ K} , which means that this is the maximum concentration of SO_2 that can exist in the rainwater under these conditions.

• High solubility indicates that a lot of SO_2 can dissolve in water, increasing potential acidity.
• Low solubility means less SO_2 can dissolve, thus less acidity.

The given concentration of 10 ext{ ppm} of SO_2 in the air suggests that enough SO_2 is available to reach the solubility limit when the rain collects this gas. Understanding solubility helps us anticipate and calculate subsequent chemical reactions in natural environmental processes.

Once SO_2 is dissolved in water, it forms sulfurous acid (H_2SO_3). This is where acid dissociation comes into play. Dissociation refers to the splitting of a compound into smaller components, such as ions, in water. In this context, sulfurous acid dissociates into hydrogen ions (H^+) and bisulfite ions (HSO_3^-):\[\mathrm{H_2SO_3} \rightleftharpoons \mathrm{H^+} + \mathrm{HSO_3^-}\]The amount that H_2SO_3 dissociates into these ions depends on the acid's strength, represented by its \mathrm{p}K_a value, which is typically derived from \log ext{-}based measure of how easily an acid gives up its H^+ ion. A low \mathrm{p}K_a value, such as 1.92 here, indicates a stronger tendency for the acid to dissociate.
Knowing the dissociation tendency allows us to calculate the concentration of H^+ ions, which directly affects the acidity (or pH) of the solution. This dissociated H^+ ion concentration can be determined using the equation:\[\mathrm{[H^+]} = \sqrt{K_a \times c_0}\]where K_a is the acid dissociation constant correlating to the given \mathrm{p}K_a, and \(c_0\) is the initial concentration of the acid. Thus, understanding acid dissociation is a key step in determining the pH of the rainwater.

The equilibrium constant (K_a) is a critical concept in chemistry, representing the balance point of a reversible chemical reaction. In the case of H_2SO_3 dissociation, K_a defines how much the sulfurous acid will dissociate into H^+ and HSO_3^- ions at equilibrium. For the reaction:\[\mathrm{H_2SO_3} \rightleftharpoons \mathrm{H^+} + \mathrm{HSO_3^-}\]The equilibrium constant K_a is given as:\[K_a = 10^{-\mathrm{p}K_a}\]In our example, with a \mathrm{p}K_a of 1.92, we calculate K_a to be 10^{-1.92}, describing the tendency of the acid to dissociate.
In general, a large K_a value indicates strong acid dissociation, while a small K_a value indicates weak dissociation. For weak acids like H_2SO_3, understanding this constant helps predict pH changes in the solution. Using K_a and the concentration of undissociated acid, we calculate [H^+] concentration, leading to the subsequent pH.
To find the pH, calculate the hydrogen ion concentration from K_a and the remaining concentration of the initial solution, then use the formula \[pH = -\log{[\mathrm{H^+]}}\]. Thus, the equilibrium constant is essential to understanding and predicting the course of chemical reactions and concentrations in solutions.