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Chapter 7: Problem 15

Is the yield of \(\mathrm{SO}_{3}\) at equilibrium favored by a higher or lower pressure? By a higher or lower temperature? $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{SO}_{3}(g) \quad \Delta H=-197 \mathrm{~kJ} / \mathrm{mol} $$

Short Answer

Expert verified
Higher pressure and lower temperature favor the yield of \( \mathrm{SO}_3 \).

Step by step solution

01

Identify the effect of pressure on the equilibrium

Consider the balanced equation for the synthesis of \( \mathrm{SO}_3 \) from \( \mathrm{SO}_2 \) and \( \mathrm{O}_2 \):\[ 2 \mathrm{SO}_2(g) + \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{SO}_3(g) \]. Notice that there are 3 moles of gaseous reactants and 2 moles of gaseous products. According to Le Chatelier's principle, increasing the pressure shifts the equilibrium towards the side with fewer moles of gas. Therefore, the yield of \( \mathrm{SO}_3 \) is favored by an increase in pressure.
02

Analyze the effect of temperature on the equilibrium

The reaction is exothermic (\( \Delta H = -197 \text{ kJ/mol} \)), meaning heat is released during the forward reaction. According to Le Chatelier's principle, increasing the temperature will shift the equilibrium towards the endothermic direction (reactants) to absorb the extra heat. Conversely, lowering the temperature shifts the equilibrium towards the exothermic direction (products), thus favoring the formation of \( \mathrm{SO}_3 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equilibrium
In chemical reactions, equilibrium refers to the state where the rate of the forward reaction equals the rate of the reverse reaction. This balance means the concentrations of reactants and products remain constant over time, although they are not necessarily equal. For the synthesis of \(\mathrm{SO}_3\) from \(\mathrm{SO}_2\) and \(\mathrm{O}_2\), reaching equilibrium implies a specific ratio of reactants and products that stabilizes.
  • Equilibrium is dynamic; molecules are continuously reacting, yet overall composition remains constant.
  • Le Chatelier's Principle predicts how changes in conditions affect equilibrium.
  • If a system at equilibrium is disturbed, it will adjust to counteract the disturbance and establish a new equilibrium.
Understanding equilibrium is key to predicting the yields of desired products in industrial chemical processes. For example, adjusting conditions such as pressure and temperature can significantly impact the amounts of products formed.
Pressure Effects
Pressure has a significant influence on the equilibrium of reactions involving gases. According to Le Chatelier's Principle, if you increase the pressure on a reaction mixture, the equilibrium position will shift towards the side with the fewer moles of gas. This adjustment helps the system relieve some of the increased pressure.
  • In the \(\mathrm{SO}_3\) production: \(2 \mathrm{SO}_2(g) + \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{SO}_3(g)\).
  • There are 3 moles of reactants (2 \(\mathrm{SO}_2\) + 1 \(\mathrm{O}_2\)) and 2 moles of products (\(\mathrm{SO}_3\)).
This means that increasing pressure will favor the formation of \(\mathrm{SO}_3\), thus maximizing its yield. Conversely, reducing pressure would shift the equilibrium toward the reactants, decreasing the production of \(\mathrm{SO}_3\).
Temperature Effects
Temperature changes can impact equilibrium in reactions, significantly altering product yields. Le Chatelier's Principle guides us here too, by stating that if temperature increases, the system will shift in the direction that absorbs heat.
  • Consider the reaction: \(2 \mathrm{SO}_2(g) + \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{SO}_3(g)\).
  • With \(\Delta H = -197 \text{ kJ/mol}\), the reaction releases heat (exothermic reaction).
Thus, increasing the temperature pushes the equilibrium towards the reactants (endo direction), reducing \(\mathrm{SO}_3\) yield. Lowering the temperature will favor forward reactions, as the system seeks to produce more heat, thereby increasing \(\mathrm{SO}_3\) yield.
Exothermic Reactions
Exothermic reactions are characterized by the release of heat energy as products form. This is an important factor in determining reaction direction and conditions for maximum yield.
  • In an exothermic reaction, such as \(2 \mathrm{SO}_2(g) + \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{SO}_3(g)\) with \(\Delta H = -197 \text{ kJ/mol}\), heat is a product of the reaction.
  • The negative sign of \(\Delta H\) indicates that the reaction releases energy.
So, if the temperature is lowered, the reaction "wants" to shift towards more heat production, which means moving forward to produce \(\mathrm{SO}_3\). On the other hand, if the temperature is raised, the reaction will shift in the reverse direction to absorb excess heat by favoring reactants. Understanding these dynamics is crucial for optimizing reactions in industrial applications where maximizing product yield is essential.

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Most popular questions from this chapter

Hydrogen chloride can be made from the reaction of chlorine and hydrogen: $$ \mathrm{Cl}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g) $$ For this reaction, \(K=26 \times 10^{33}\) and \(\Delta H=-184 \mathrm{~kJ} / \mathrm{mol}\) at \(298 \mathrm{~K}\). (a) Is the reaction endothermic or exothermic? (b) Are the reactants or the products favored at equilibrium? (c) Explain the effect on the equilibrium of (1) Increasing pressure by decreasing volume (2) Increasing the concentration of \(\mathrm{HCl}(g)\) (3) Decreasing the concentration of \(\mathrm{Cl}_{2}(g)\) (4) Increasing the concentration of \(\mathrm{H}_{2}(g)\) (5) Adding a catalyst

Classify each of the following as having potential or kinetic energy. For those identified as having potential energy, discuss how the potential energy would be realized by conversion to another form of energy. (a) gunpowder (b) a bullet in flight (c) a cell phone (lithium ion) battery (d) wind (e) a candy bar (f) spinning wind mill blades

Is the total enthalpy \((H)\) of the reactants for an endothermic reaction greater than or less than the total enthalpy of the products?

Methanol, \(\mathrm{CH}_{3} \mathrm{OH},\) is used as race car fuel. (a) Write the balanced equation for the combustion reaction of methanol with \(\mathrm{O}_{2}\) to form \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). (b) \(\Delta H=-728 \mathrm{~kJ} / \mathrm{mol}\) methanol for the process. How many kilojoules are released by burning \(1.85 \mathrm{~mol}\) of methanol? (c) How many kilojoules are released by buming \(50.0 \mathrm{~g}\) of methanol?

Glucose, also known as "blood sugar" when measured in blood, has the formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (a) Write the equation for the combustion of glucose with \(\mathrm{O}_{2}\) to give \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) (b) If \(3.8 \mathrm{kcal}(16 \mathrm{~kJ})\) is released by combustion of each gram of glucose, how many kilojoules are released by the combustion of \(1.50 \mathrm{~mol}\) of glucose? (c) What is the minimum amount of energy (in \(\mathrm{kJ}\) ) a plant must absorb to produce \(15.0 \mathrm{~g}\) of glucose?
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