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Chapter 15: Problem 47

Consider the equilibrium $$ 2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g) $$ What would be the effect on the position of equilibrium of (a) increasing the total pressure on the system by decreasing its volume, (b) adding \(I_{2}\) to the reaction mixture, (c) decreasing the temperature?

Short Answer

Expert verified
According to Le Chatelier's Principle, (a) increasing pressure will cause the equilibrium to shift towards the side with fewer gaseous molecules鈥攊n this case, the formation of \(I_{2}\), (b) adding \(I_{2}\) will make the equilibrium shift to the left, favoring dissociation into two \(I\) atoms, and (c) lowering the temperature will shift the equilibrium to the right, producing more \(I_{2}\) since the reaction is endothermic.

Step by step solution

01

Effect of Increasing Pressure

According to Le Chatelier's Principle, if pressure is increased, the equilibrium shifts in the direction where fewer gaseous molecules exist, to reduce the pressure. In the equation \(2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g)\), the right-hand side (1 mol of \(I_{2}\)) has fewer molecules than the left-hand side (2 mol of \(I\)). Therefore, when the pressure is increased, the equilibrium will shift to the right to favor the formation of more \(I_{2}\).
02

Effect of Additional Iodine \(I_{2}\)

When more \(I_{2}\) is added to the mixture, the increased concentration of \(I_{2}\) would cause a shift to the side with less \(I_{2}\) to establish a new equilibrium according to Le Chatelier's principle. As a result, the equilibrium will shift to the left, favoring the dissociation into two \(I\) molecules.
03

Effect of Decreasing Temperature

This reaction is endothermic (absorbs heat) because the dissociation of iodine into two separate atoms requires energy. So according to Le Chatelier's principle, if the temperature decreases (heat is removed), the equilibrium will shift in the direction that produces heat. That would be the left hand side, as 2I is converted to \(I_{2}\). So the equilibrium will shift to the right, yielding a significant increase in \(I_{2}\).

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Key Concepts

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

Le Chatelier's Principle
Le Chatelier's Principle is a fundamental concept in chemistry that helps us predict how a change in conditions affects a chemical equilibrium. Simply put, it states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and re-establish equilibrium.
Le Chatelier's Principle can be applied to changes in pressure, temperature, and concentration:
  • **Pressure:** For gaseous reactions, changing pressure by altering volume affects the equilibrium in the direction where fewer or more gas molecules are present.
  • **Temperature:** A decrease in temperature will shift the equilibrium in the direction of the exothermic reaction, while an increase will favor the endothermic reaction.
  • **Concentration:** Adding or removing reactants or products will influence the equilibrium to shift to use up or produce more of the added or removed substances.
By understanding these principles, we can predict the behavior of gases and liquids under various chemical settings, making this principle essential for controlling reactions in industrial and laboratory contexts.
Reaction Shifts
Reaction shifts refer to the change in the position of equilibrium in response to a disturbance in the system. According to Le Chatelier's Principle, equilibrium shifts aim to neutralize changes imposed on the system, striving to reach a new state of balance.For example, in the reaction \[2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g)\]various external changes can cause shifts:
  • **Increased Pressure:** The equilibrium shifts towards fewer moles of gas. In this case, to the right, forming \(I_{2}\).
  • **Added \(I_{2}\):** An increase in \(I_{2}\) concentration causes the equilibrium to shift towards the left, favoring the formation of more \(I\) atoms.
  • **Decreased Temperature:** Since the reaction is endothermic, a temperature drop shifts the equilibrium to the side that releases heat, shifting to the right.
Understanding reaction shifts allows for better manipulation and optimization of chemical processes, crucial for industrial applications.
Gas Phase Reactions
Gas phase reactions are chemical reactions that occur within gases. Due to the fluid nature of gases, reactions in the gas phase can be significantly influenced by changes in pressure and temperature, making them a perfect subject for Le Chatelier's Principle. The key aspects of gas phase reactions include:
  • **Molecular Collisions:** Gas molecules move quickly and collide with each other frequently, which influences the rate of reaction. Higher pressure increases collision frequency.
  • **Volume and Pressure:** According to Boyle's Law, for a fixed amount of gas at constant temperature, the volume of a gas is inversely proportional to its pressure. Therefore, changes in volume greatly impact the behavior of gas phase reactions.
  • **Temperature Dependence:** The reactions are sensitive to temperature changes, with endothermic and exothermic characteristics playing a role in shifts in equilibrium depending on whether the temperature rises or falls.
These characteristics make gas phase reactions particularly dynamic and susceptible to external changes, challenging but also providing opportunities for control in chemical processes.

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Most popular questions from this chapter

What effect does an increase in pressure have on each of these systems at equilibrium? (a) \(\mathrm{A}(s) \rightleftharpoons 2 \mathrm{~B}(s)\) (b) \(2 \mathrm{~A}(l) \rightleftharpoons \mathrm{B}(l)\) (c) \(\mathrm{A}(s) \rightleftharpoons \mathrm{B}(g)\) (d) \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) (e) \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)\) The temperature is kept constant. In each case, the reacting mixture is in a cylinder fitted with a movable piston.

Consider this equilibrium process: $$ \begin{aligned} \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \\\ \Delta H^{\circ} &=92.5 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Predict the direction of the shift in equilibrium when (a) the temperature is raised, (b) more chlorine gas is added to the reaction mixture, \((\mathrm{c})\) some \(\mathrm{PCl}_{3}\) is removed from the mixture, (d) the pressure on the gases is increased, (e) a catalyst is added to the reaction mixture.

About 75 percent of hydrogen for industrial use is produced by the steam- reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at \(800^{\circ} \mathrm{C}\) to give hydrogen and carbon monoxide: $$ \begin{aligned} \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g) &+3 \mathrm{H}_{2}(g) \\ \Delta H^{\circ} &=206 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ The secondary stage is carried out at about \(1000^{\circ} \mathrm{C}\) in the presence of air, to convert the remaining methane to hydrogen: \(\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)\) $$ \Delta H^{\circ}=35.7 \mathrm{~kJ} / \mathrm{mol} $$ (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stages? (b) The equilibrium constant \(K_{\mathrm{c}}\) for the primary stage is 18 at \(800^{\circ} \mathrm{C}\). (i) Calculate \(K_{P}\) for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

The decomposition of ammonium hydrogen sulfide $$ \mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g) $$ is an endothermic process. A \(6.1589-\mathrm{g}\) sample of the solid is placed in an evacuated 4.000 - \(L\) vessel at exactly \(24^{\circ} \mathrm{C}\). After equilibrium has been established, the total pressure inside is \(0.709 \mathrm{~atm}\). Some solid \(\mathrm{NH}_{4} \mathrm{HS}\) remains in the vessel. (a) What is the \(K_{P}\) for the reaction? (b) What percentage of the solid has decomposed? (c) If the volume of the vessel were doubled at constant temperature, what would happen to the amount of solid in the vessel?

When a gas was heated under atmospheric conditions, its color was found to deepen. Heating above \(150^{\circ} \mathrm{C}\) caused the color to fade, and at \(550^{\circ} \mathrm{C}\) the color was barely detectable. However, at \(550^{\circ} \mathrm{C}\), the color was partially restored by increasing the pressure of the system. Which of these best fits this description? Justify your choice. (a) A mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color and nitrogen dioxide is a brown gas. The other gases are colorless.)
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