Respuesta :
To determine the pH, we need to find the concentration of hydrogen and hydroxide ions in a solution. It can be calculated with the following formula.
[tex]pH=-\log \lbrack H^+\rbrack[/tex]Givens.
• The concentration of Sulfur Dioxide in the atmosphere is 0.12 ppm.
The chemical equation about the situation is
[tex]SO_2+H_2O\to H+HSO_3[/tex]We can the hydrogen ions products whose concentration we need to find.
We know that 1 ppm is equivalent to 1x10^-6 atm. Let's find the pressure of SO2 in atm.
[tex]0.12\text{ppm}\cdot\frac{1\times10^{-6}\text{atm}}{1\text{ppm}}=1.2\times10^{-7}atm[/tex]Then, determine the equilibrium concentration Ka.
[tex]K_a=\frac{\lbrack H\rbrack\lbrack HSO_3\rbrack}{\lbrack P_{SO2}\rbrack}[/tex]As you can observe, the pressure in the atmosphere is the concentration of SO2. Also, we know that the constant of equilibrium of HSO3 is 1.3x10^-2, so
[tex]1.3\times10^{-2}=\frac{x\cdot x}{1.2\times10^{-7}}[/tex]Then, solve for x.
[tex]\begin{gathered} x^2=1.3\times10^{-2}\cdot1.2\times10^{-7} \\ x=\sqrt[]{1.56\times10^{-9}_{}} \\ x=3\times10^{-5} \end{gathered}[/tex]Where x represents the concentration of hydrogen ions and HSO3. Now, we are able to find the pH.
[tex]pH=-\log \lbrack3\times10^{-5}\rbrack\approx4.5[/tex]Therefore, the pH of the rainwater due to this pollutant is 4.5.
