Chemical And Ionic Equilibrium

Chemical And Ionic Equilibrium Result Question 55

55. The average concentration of $\mathrm{SO} _2$ in the atmosphere over a city on a certain day is $10 \mathrm{~ppm}$, when the average temperature is $298 \mathrm{~K}$. Given that the solubility of $\mathrm{SO} _2$ in water at $298 \mathrm{~K}$ is $1.3653 \mathrm{~mol} / \mathrm{L}$ and $\mathrm{p} K _a$ of $\mathrm{H} _2 \mathrm{SO} _3$ is 1.92 , estimate the $\mathrm{pH}$ of rain on that day.

$(2000,5 M)$

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Answer:

Correct Answer: 55. $( 4.86 )$

Solution:

Partial pressure of $\mathrm{SO}_2$ in air $=10^{-5} \mathrm{~atm}$

$ \left[\mathrm{SO}2\right]{a q}=1.3653 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} $

$\because \mathrm{p} K_a=1.92$ and concentration of $\mathrm{H}_2 \mathrm{SO}_3$ is very low, it is almost completely ionised as

$ \begin{gathered} \mathrm{H}_2 \mathrm{SO}_3 \rightleftharpoons \mathrm{H}^{+}+\mathrm{HSO}_3^{-} \\ {\left[\mathrm{H}^{+}\right]=1.3653 \times 10^{-5} \mathrm{M}} \\ \mathrm{pH}=-\log \left(1.3653 \times 10^{-5}\right)=4.86 \end{gathered} $