Question

For the following endothermic reaction at equilibrium: $$ 2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) $$ which of the following changes will increase the value of \(K ?\) a. increasing the temperature b. decreasing the temperature c. removing \(\mathrm{SO}_{3}(g)\) (constant \(T\) ) d. decreasing the volume (constant \(T\) ) e. adding \(\operatorname{Ne}(g)\) (constant \(T\) ) f. adding \(\mathrm{SO}_{2}(g)\) (constant \(T\) ) g. adding a catalyst (constant \(T\) )

Short answer

The short answer based on the step-by-step solution is: Increasing the temperature (option a) will increase the value of K for this endothermic reaction at equilibrium, as it favors the forward reaction (formation of SO2 and O2).

Step-by-step solution

Understand Le Chatelier's Principle

Le Chatelier's Principle states that if a change is applied to a system at equilibrium, the system will adjust its position to counteract the change while maintaining equilibrium. In other words, the system will try to minimize the impact of the change and restore its balance.

Evaluate the effect of temperature on K

Recall that an endothermic reaction requires heat to proceed, so increasing the temperature will favor the forward reaction (formation of SO2 and O2), leading to a higher equilibrium constant, K. Therefore, the correct answer is (a).

Evaluate the effect of removing SO3 on K

According to Le Chatelier's Principle, the removal of SO3 will cause the reaction to shift toward the left to compensate for the change. However, this shift does not change the value of the equilibrium constant K, so (c) is not correct.

Evaluate the effect of decreasing volume on K

Decreasing the volume will increase the pressure, which will cause the system to shift toward the side with fewer moles of gas. In this case, the reaction will shift to the left (formation of SO3). However, this shift also does not change the value of K, so (d) is not correct.

Evaluate the effect of adding Ne on K

Since Ne is an inert gas and doesn't participate in the reaction taking place, its addition will not affect the equilibrium constant, K. So, (e) is not correct.

Evaluate the effect of adding SO2 on K

Adding SO2 will shift the reaction toward the left (formation of SO3) to compensate for the change, but it will not change the value of K. Hence, (f) is not correct.

Evaluate the effect of adding a catalyst on K

A catalyst increases the rate of both the forward and reverse reactions, but it does not change the position of the equilibrium nor the value of the equilibrium constant, K. Therefore, (g) is not correct. In summary, the correct answer is (a) increasing the temperature. It is the only change that will increase the value of K for this endothermic reaction.