Answer:
The equilibrium constant for the reaction comes out to be 7.145
Explanation:
Given concentration of all the species at equilibrium are shown below
[tex]\left [ SO_{2} \right ] = 0.42 \textrm{ M}, \left [ O_{2} \right ] = 0.21 \textrm{ M}, \left [ SO_{3} \right ] = 0.072 \textrm{ M}[/tex] \\
Given reaction is shown below
[tex]2\textrm{SO}_{3}\left ( g \right )\rightleftharpoons 2\textrm{SO}_{2}\left ( g \right )+\textrm{O}_{2}\left ( g \right )[/tex]
[tex]K_{eq} = \displaystyle \frac{\left [ SO_{2} \right ]^{2}\times \left [ O_{2} \right ]}{\left [ SO_{3} \right ]^{2}} \\K_{eq} = \displaystyle \frac{\left ( 0.42 \right )^{2}\times 0.21}{\left ( 0.072 \right )^{2}} \\K_{eq} = 7.145[/tex]
[tex]K_{eq}[/tex] for the reaction is 7.145