Balanced equation
#"Cl"_2("g") + "2O"_3("g")"##rarr##"2ClO(g) + 2O"_2("g")"#
First we need to determine how many moles of ozone will react with #"200.0 g Cl"_2"#. Then we'll use the equation for the ideal gas law to determine the volume of ozone that will be destroyed.
Determine mol #"Cl"_2"# by dividing its given mass by its molar mass #("68.9 g/mol")#. Do this by multiplying by the inverse of the molar mass (mol/g). Then determine mol #"O"_3"# by multiplying by the mol ratio between ozone and chlorine gas in the balanced equation, with ozone in the numerator.
#200.0color(red)cancel(color(black)("g Cl"_2))xx(1color(red)cancel(color(black)("mol Cl"_2)))/(68.9color(red)cancel(color(black)("g Cl"_2)))xx("mol O"_3)/(1color(red)cancel(color(black)("mol Cl"_2)))="5.81 mol O"_3"#
Ideal gas law equation
#PV=nRT#
Known
#P="5.0 kPa"#
#n="5.81 mol O"_3"#
#R="8.31447 L kPa K"^(-1) "mol"^(-1)"#
https://www.katmarsoftware.com/gconvals.htm
#T="220. K"#
Unknown
#V#
Solution
Rearrange the equation to isolate volume, #V#. Plug in the known values and solve.
#V=(nRT)/P#
#V=(5.81color(red)cancel(color(black)("mol"))xx8.31447" L" color(red)cancel(color(black)("kPa"))color(red)cancel(color(black)( "K"))^(-1) color(red)cancel(color(black)("mol"))^(-1)xx220color(red)cancel(color(black)("K")))/(5.0color(red)cancel(color(black)("kPa")))="2100 L"#
(rounded to two significant figures due to #"5.0 kPa"#)
#"200.0 g Cl"_2"# can destroy #"2100 L O"_3"#.
