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Chapter 13: Problem 8

Le Chatelier's principle is stated (Section 13.7\()\) as follows: "If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change." The system $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$ is used as an example in which the addition of nitrogen gas at equilibrium results in a decrease in \(\mathrm{H}_{2}\) concentration and an increase in \(\mathrm{NH}_{3}\) concentration. In the experiment the volume is assumed to be constant. On the other hand, if \(\mathrm{N}_{2}\) is added to the reaction system in a container with a piston so that the pressure can be held constant, the amount of \(\mathrm{NH}_{3}\) actually could decrease and the concentration of \(\mathrm{H}_{2}\) would increase as equilibrium is reestablished. Explain how this can happen. Also, if you consider this same system at equilibrium, the addition of an inert gas, holding the pressure constant, does affect the equilibrium position. Explain why the addition of an inert gas to this system in a rigid container does not affect the equilibrium position.

Short Answer

Expert verified
In summary, the addition of N₂ to the equilibrium reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) affects the equilibrium position based on whether the volume or pressure is held constant. When the volume is constant, adding N₂ shifts the equilibrium to the right, increasing NH₃ concentration and decreasing H₂ concentration. When the pressure is held constant using a piston, adding N₂ causes the equilibrium to shift left, decreasing NH₃ concentration and increasing H₂ concentration. Adding an inert gas to the system does not affect the equilibrium position because it does not change the partial pressures or concentrations of the reacting species. These observations are consistent with Le Chatelier's principle, which states that the equilibrium will shift in a direction that tends to reduce the imposed change in the system.

Step by step solution

01

1. Identifying the Reaction and Components

First, let's write the balanced chemical equation for the reaction: \[N_{2}(g) + 3 H_{2}(g) \rightleftharpoons 2 NH_{3}(g) \] With this reaction, adding N₂ can cause two possible behaviors: the equilibrium could shift to the right (toward the production of more NH₃) or shift to the left (toward the consumption of NH₃). We will analyze each scenario as we progress through the solution.
02

2. Scenario 1: Adding N₂ at constant volume

According to Le Chatelier's principle, when we introduce more N₂ into the system, the pressure will temporarily increase, causing the equilibrium to shift in a direction that reduces this increase. Since the volume is constant, the shift will be towards the side with fewer moles of gas. In this case, the reaction shows that 4 moles of gas (1 mole N₂ and 3 moles H₂) are on the left side, and 2 moles of NH₃ gas are on the right side. Thus, the equilibrium will shift to the right, increasing the concentration of NH₃ and decreasing the concentration of H₂, as mentioned in the example.
03

3. Scenario 2: Adding N₂ with a piston and keeping the pressure constant

When we add more N₂ into the system, the increase in gas will cause the pressure to rise as well. However, since the pressure is held constant by adjusting the piston, the increase in N₂ will be accompanied by an increase in volume to maintain the pressure. As the volume increases, the gas concentrations decrease. In this case, the equilibrium will attempt to shift to counteract the decrease in pressure by moving towards the side with more moles of gases. Thus, the equilibrium will shift to the left, decreasing the concentration of NH₃ and increasing the concentration of H₂. This behavior is consistent with Le Chatelier's principle since the equilibrium adjusts itself in response to the added N₂.
04

4. Effect of adding an inert gas

If we add an inert gas into the reaction mixture at constant pressure, the total pressure of the system will increase, but the individual partial pressures of N₂, H₂, and NH₃ will not change. Since the equilibrium position is dependent on the concentrations (or partial pressure) of the reactants and products, adding an inert gas at constant pressure will not affect the equilibrium position because it does not change the partial pressures of the reacting species. However, if we add an inert gas to the system in a rigid container (constant volume), the total pressure of the system will increase, but the relative concentrations of N₂, H₂, and NH₃ will also remain unchanged. In this case, the addition of an inert gas does not affect the equilibrium position because the ratio of the concentrations of the reactants and products does not change. This observation is also consistent with Le Chatelier's principle, as there is no change in concentration to counteract.

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Most popular questions from this chapter

In a given experiment, 5.2 moles of pure NOCl were placed in an otherwise empty \(2.0-\mathrm{L}\) container. Equilibrium was established by the following reaction: $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \quad K=1.6 \times 10^{-5}$$ a. Using numerical values for the concentrations in the Initial row and expressions containing the variable \(x\) in both the Change and Equilibrium rows, complete the following table summarizing what happens as this reaction reaches equilibrium. Let \(x=\) the concentration of \(\mathrm{Cl}_{2}\) that is present at equilibrium. b. Calculate the equilibrium concentrations for all species.

Which of the following statements is(are) true? Correct the false statement(s). a. When a reactant is added to a system at equilibrium at a given temperature, the reaction will shift right to reestablish equilibrium. b. When a product is added to a system at equilibrium at a given temperature, the value of K for the reaction will increase when equilibrium is reestablished. c. When temperature is increased for a reaction at equilibrium, the value of K for the reaction will increase. d. When the volume of a reaction container is increased for a system at equilibrium at a given temperature, the reaction will shift left to reestablish equilibrium. e. Addition of a catalyst (a substance that increases the speed of the reaction) has no effect on the equilibrium position.

For the reaction $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g),$ consider two possibilities: (a) you mix 0.5 mole of each reactant, allow the system to come to equilibrium, and then add another mole of \(\mathrm{H}_{2}\) and allow the system to reach equilibrium again, or \((b)\) you \(\operatorname{mix} 1.5\) moles of \(\mathrm{H}_{2}\) and 0.5 mole of \(\mathrm{I}_{2}\) and allow the system to reach equilibrium. Will the final equilibrium mixture be different for the two procedures? Explain.

The reaction $$\mathrm{NH}_{4} \mathrm{SH}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g)$$ has \(K_{\mathrm{p}}=0.10\) at \(27^{\circ} \mathrm{C} .\) What is the minimum amount of \(\mathrm{NH}_{4} \mathrm{SH}\) that must be present for this reaction to be at equilibrium in a 10.0 \(\mathrm{-L}\) container?

The hydrocarbon naphthalene was frequently used in mothballs until recently, when it was discovered that human inhalation of naphthalene vapors can lead to hemolytic anemia. Naphthalene is 93.71% carbon by mass, and a 0.256-mole sample of naphthalene has a mass of 32.8 g. What is the molecular formula of naphthalene? This compound works as a pesticide in mothballs by sublimation of the solid so that it fumigates enclosed spaces with its vapors according to the equation Naphthalene \((s) \rightleftharpoons\) naphthalene \((g)\) $K=4.29 \times 10^{-6}(\( at \)298 \mathrm{~K})\( If \)3.00 \mathrm{~g}$ solid naphthalene is placed into an en with a volume of \(5.00 \mathrm{~L}\) at $25^{\circ} \mathrm{C},$ what percentage thalene will have sublimed once equilibriur estahlished?
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