\(2 \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \rightleftarrows 2 \mathrm{SO}_{3(\mathrm{~g})}+\mathrm{Q} \mathrm{kJ}\) In the above reaction, how can the yield of product be increased without increasing the pressure? (a) by increasing temperature (b) by decreasing temperature (c) by increasing the volume of the reaction vessel (d) by the addition of the catalyst

Short Answer

Expert verified
Answer: Decrease the temperature.

Step by step solution

01

Analyze each option according to Le Chatelier's Principle

: We will analyze each of the given options (a, b, c, and d) based on the Le Chatelier's principle to determine how the yield of \(\mathrm{SO_3}\) can be increased without affecting pressure: (a) Increasing temperature: Since the reaction is exothermic (releases energy as heat, denoted by positive \(\mathrm{Q}\)), increasing the temperature would shift the equilibrium to the left, favoring the reactants, and thus, decreasing the yield of product. (b) Decreasing temperature: Decreasing the temperature would shift the equilibrium to the right, favoring the formation of products, which in turn, increases the yield of \(\mathrm{SO_3}\). (c) Increasing the volume of the reaction vessel: Increasing the volume of the reaction vessel will lower the pressure in the system. According to Le Chatelier's principle, the equilibrium will shift in the direction of the side with more moles of gas to counteract this change. Since there are \(3\) moles of gas on the reactant side and \(2\) moles of gas on the product side, increasing the volume will shift the reaction to the left, favoring the reactants, and thus, decreasing the yield of the product. (d) Adding a catalyst: A catalyst doesn't affect the position of the equilibrium. It only increases the rate at which the reaction reaches equilibrium. So, adding a catalyst wouldn't have any effect on the yield of \(\mathrm{SO_3}\).
02

Choose the correct answer

: From our analysis in Step 1, we found that the most suitable option to increase the yield of \(\mathrm{SO_3}\) without increasing pressure is: (b) Decreasing temperature.

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