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.

Question

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.

Answer 1

To calculate the concentration of SO2 (in ppm) that must be reached in polluted air to produce a pH of 3.2 in raindrops, we need to understand the chemistry involved.

Raindrops become acidic when they dissolve certain gases from the atmosphere, such as SO2. In the presence of water, SO2 dissolves and reacts with water to form sulfurous acid (H2SO3) according to the following equation:

SO2 + H2O -> H2SO3

Sulfurous acid then dissociates into hydrogen ions (H+) and bisulfite ions (HSO3-):

H2SO3 -> H+ + HSO3-

The acidity of the rain is determined by the concentration of hydrogen ions (H+) present, which is measured by pH. A lower pH value indicates a higher concentration of hydrogen ions and a more acidic solution.

In this case, we are given that the raindrops have a pH of 3.2, which indicates a concentration of hydrogen ions [H+] of 10^(-3.2) mol/L.

Now, to calculate the concentration of SO2 (in ppm), we need to understand the relationship between the concentration of dissolved SO2 and the concentration of hydrogen ions.

The equilibrium constant (Ka) for the reaction between dissolved SO2 and water can be expressed as:

Ka = [H+] [HSO3-] / [SO2]

Since we are told that there is no oxidation of the gas and it purely dissolves in water, we can assume that the concentration of HSO3- is negligible compared to the [H+].

Therefore, we can simplify the expression to:

Ka ≈ [H+] / [SO2]

Now, substituting the given pH value into the equation:

Ka ≈ 10^(-3.2) / [SO2]

Finally, using the value of the equilibrium constant for SO2, which is approximately 1.6 x 10^(-2), we can calculate the concentration of SO2 (in ppm):

[SO2] ≈ 10^(-3.2) / (1.6 x 10^(-2))

[SO2] ≈ 10^(-3.2 + 2 + 2)

[SO2] ≈ 10^(-3.2 + 4)

[SO2] ≈ 10^0.8

[SO2] ≈ 6.31 ppm

Therefore, to produce a pH of 3.2 in raindrops without any oxidation of the gas, the concentration of SO2 in polluted air must be approximately 6.31 ppm.