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Chapter 13: Problem 8

Le Châtelier'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, for the system N2(g) + 3 H2(g) ⇌ 2 NH3(g), when N2 is added at constant volume, the equilibrium shifts to the right, resulting in a decrease in H2 concentration and an increase in NH3 concentration. When N2 is added at constant pressure, the equilibrium shifts towards the side with more moles of gas (N2 and H2), causing a decrease in NH3 concentration and an increase in H2 concentration. Adding an inert gas does not affect the equilibrium position when the pressure is constant, as all concentrations decrease proportionally without affecting their ratios. However, adding an inert gas in a rigid container does not influence the equilibrium position, as both pressure and volume remain constant.

Step by step solution

01

Scenario 1: Constant Volume

When N2 is added at equilibrium with a constant volume, the position of the equilibrium will shift to reduce the effect of increased N2 concentration. Since the forward reaction consumes N2 and H2 to produce NH3, the equilibrium will shift to the right, resulting in a decrease in H2 concentration and an increase in NH3 concentration. This is consistent with Le Châtelier's principle.
02

Scenario 2: Constant Pressure

In this case, N2 is added to the reaction system in a container with a piston so that the pressure can be held constant. When N2 is added, the total pressure of the system increases, causing the volume to expand and the concentration of each reactant and product to decrease. As the system seeks to reestablish equilibrium at constant pressure, the reaction will shift to the side with a larger number of moles of gas. In this case, it is the side with N2 and H2 (4 moles) as opposed to the NH3 side (2 moles). Consequently, the concentration of NH3 decreases, and the concentration of H2 increases, as the equilibrium is reestablished.
03

Scenario 3: Addition of Inert Gas

When an inert gas is added to the system at equilibrium with constant pressure, the volume must expand to accommodate the increased gas, causing the concentration of each reactant and product to decrease without changing their ratio. Since the ratio of the reactants and products remain the same, the equilibrium position is not affected.
04

Scenario 4: Addition of Inert Gas in a Rigid Container

In this case, the addition of an inert gas in a rigid container does not affect the volume or pressure of the system. Since neither the pressure nor the volume changes, the concentrations of the reactants and products remain the same and the equilibrium position is not affected.

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Most popular questions from this chapter

A sample of iron(II) sulfate was heated in an evacuated container to \(920 \mathrm{~K}\), where the following reactions occurred: $$ \begin{array}{l} 2 \mathrm{FeSO}_{4}(s) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{3}(g)+\mathrm{SO}_{2}(g) \\ \mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \end{array} $$ After equilibrium was reached, the total pressure was \(0.836\) atm and the partial pressure of oxygen was \(0.0275\) atm. Calculate \(K_{\mathrm{p}}\) for each of these reactions.

For the reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g), K_{\mathrm{p}}=0.25\) at a cer- tain temperature. If \(0.040\) atm of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is reacted initially, calculate the equilibrium partial pressures of \(\mathrm{NO}_{2}(g)\) and \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\).

At a particular temperature, \(K=3.75\) for the reaction $$ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g) $$ If all four gases had initial concentrations of \(0.800 M\), calculate the equilibrium concentrations of the gases.

An initial mixture of nitrogen gas and hydrogen gas is reacted in a rigid container at a certain temperature by the reaction $$ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ At equilibrium, the concentrations are \(\left[\mathrm{H}_{2}\right]=5.0 \mathrm{M},\left[\mathrm{N}_{2}\right]=\) \(8.0 M\), and \(\left[\mathrm{NH}_{3}\right]=4.0 M .\) What were the concentrations of nitrogen gas and hydrogen gas that were reacted initially?

Predict the shift in the equilibrium position that will occur for each of the following reactions when the volume of the reaction container is increased. a. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) b. \(\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) d. \(\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)
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