To determine how the equilibrium of the reaction
[tex]\[ 200 \text{ kJ} + 2 \text{ SO}_3(g) \rightleftharpoons \text{ O}_2(g) + 2 \text{ SO}_2(g) \][/tex]
would be affected if the temperature decreased, we need to analyze the reaction using Le Chatelier's principle.
Le Chatelier's principle states that if a system at equilibrium is subjected to a change in conditions (such as temperature, pressure, or concentration), the system will adjust itself to counteract that change and restore a new equilibrium.
In this specific reaction, [tex]\(200 \text{ kJ}\)[/tex] of heat is absorbed (endothermic reaction) as [tex]\( \text{SO}_3 \)[/tex] decomposes into [tex]\( \text{O}_2 \)[/tex] and [tex]\( \text{SO}_2 \)[/tex].
When the temperature is decreased, the system will try to counteract this change by producing more heat. For an endothermic reaction, this means the system will shift toward the reactants (left side of the equation) to absorb heat.
Therefore, the equilibrium will shift to produce more [tex]\( \text{SO}_3 \)[/tex] and less [tex]\( \text{O}_2 \)[/tex] and [tex]\( \text{SO}_2 \)[/tex].
Hence, the correct answer is:
B. The reaction would shift to produce more [tex]\( \text{SO}_3 \)[/tex].
