Calculate the concentration of SO2(ppm) that must be reached in polluted air (in ppm) if the dissolved gas is to produce a pH of 3.2 in raindrops without any oxidation of the gas.

To calculate the concentration of SO2 (ppm) required to produce a pH of 3.2 in raindrops without oxidation, you need to consider the relationship between the concentration of SO2 and the resulting concentration of sulfuric acid (H2SO4) in the raindrops.

The acidity of rainwater is primarily due to the presence of dissolved carbon dioxide (CO2) and sulfur dioxide (SO2), which react with H2O to form carbonic acid (H2CO3) and sulfurous acid (H2SO3), respectively. Sulfurous acid then dissociates to form hydrogen ions (H+) and bisulfite ions (HSO3-):

SO2 + H2O → H2SO3
H2SO3 → H+ + HSO3-

The concentration of hydrogen ions (H+) determines the pH of the raindrops. A pH of 3.2 indicates an H+ concentration of 10^(-3.2) moles per liter.

To find the concentration of SO2 needed to achieve this pH, we can set up an equilibrium expression for the dissociation of sulfurous acid:

[H+] * [HSO3-] / [H2SO3]

Since the concentration of H2SO3 is directly proportional to the concentration of SO2, we can express it as [H2SO3] = k * [SO2], where k is a constant.

Substituting this into the equilibrium expression and rearranging, we get:

[H+] * [HSO3-] = k * [SO2]

Now, let's assume that the concentration of bisulfite ions (HSO3-) is much larger than the concentration of hydrogen ions (H+). This assumption is typically valid for weak acids like sulfurous acid.

Since [HSO3-] is much greater than [H+], we can approximate [HSO3-] ≈ [H2SO3] ≈ k * [SO2].

Now, rearrange the equation:

[H+] ≈ k * [SO2]

Since [H+] = 10^(-3.2) moles per liter, we can rewrite the equation:

10^(-3.2) ≈ k * [SO2]

Solve for [SO2]:

[SO2] = 10^(-3.2) / k

The constant k depends on temperature and pressure, but at room temperature (~25°C), it is approximately 100. Hence, substituting the value of k:

[SO2] = 10^(-3.2) / 100

Using a scientific calculator, calculate the value of 10^(-3.2) / 100 to find the concentration of SO2 required to produce a pH of 3.2 in raindrops without oxidation.