This problem is providing a chemical reaction reaction at equilibrium and its pressure-based equilibrium constant, and thus asks for molecules of SO2 at equilibrium. At the end, the answer turns out to be 1.25x10¹² molecules.
In chemistry, when chemical reactions take place, they do not necessarily go to completion, but can reach a constant-concentration point denominated "equilibrium" where the reaction does not proceed any longer.
In such a way, for the given reaction, one can write the equilibrium expression based on the law of mass action, which sets the products on top, reactants on bottom and ignores both solids and liquids:
[tex]Kp=\frac{1}{p_{SO_2}*p_{O_2}^{1/2}}[/tex]
However, in order to calculate this, one needs the partial pressure of O2, defined in similar problems as 0.21 atm for us to find the partial pressure of SO2 first:
[tex]2.38x10^{15}=\frac{1}{p_{SO_2}*(0.21)^{1/2}}\\\\p_{SO_2}=\frac{1}{(2.38x10^{15})(0.21)^{1/2}}\\\\p_{SO_2}=9.17x10^{-16}atm[/tex]
Keep in mind this 0.21 atm may vary depending on the problem you were given.
Thus, we obtain the mole fraction of SO2 as follows:
[tex]x_{SO_2}=\frac{9.17x10^{-16}atm}{9.17x10^{-16}atm+0.21atm}=4.37x10^{-15}\\ \\[/tex]
Finally, we use this mole fraction to calculate the moles of SO2 in 475 moles of the gas mixture, and then use the Avogadro's number to calculate the molecules:
[tex]molecules=475mol*4.37x10^{-15}*\frac{6.022x10^{23}}{1mol} =1.25x10^{12}molecules[/tex]
Learn more about chemical equilibrium: https://brainly.com/question/26453983
