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Chapter 12: Problem 49

Consider the system $$ \mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta H=98.9 \mathrm{~kJ} $$ (a) Predict whether the forward or reverse reaction will occur when the equilibrium is disturbed by 1\. adding oxygen gas. 2\. compressing the system at constant temperature. 3\. adding argon gas. 4\. removing \(\mathrm{SO}_{2}(g)\). 5\. decreasing the temperature. (b) Which of the above factors will increase the value of K? Which will decrease it?

Short Answer

Expert verified
Answer: When the temperature is decreased, the reaction will proceed more in the forward direction and the equilibrium constant K will increase.

Step by step solution

01

(a) Analyzing the effect of disturbances on the equilibrium

We will use Le Chatelier's principle to analyze the different disturbances and predict the shift in the reaction. 1. Adding oxygen gas: When more O2 is added, the system will try to counteract this change by consuming the added O2, so the reaction will proceed more in the reverse direction. 2. Compressing the system at constant temperature: By compressing the system, the total pressure will increase. The reaction will favor the side with fewer moles of gas to decrease the pressure. Since there is 1 mole of gas in the reactants and \(\frac{3}{2}\) moles of gas in the products, the reaction will proceed more in the forward direction. 3. Adding argon gas: Argon is an inert gas and doesn't participate in the reaction; it will not affect the equilibrium. 4. Removing SO2(g): When SO2 is removed, the system will try to counteract this change by producing more SO2, so the reaction will proceed more in the forward direction. 5. Decreasing the temperature: Since the reaction has a positive \(\Delta H\), it's an endothermic reaction (absorbs heat). As per Le Chatelier's principle, when the temperature is decreased, the system will try to produce heat; thus, the reaction will proceed more in the forward (endothermic) direction.
02

(b) Analyzing the effect of disturbances on the value of K

Out of the 5 disturbances discussed in (a), only temperature change has an effect on the value of K. 1. Adding oxygen gas has no effect on K. 2. Compressing the system at constant temperature has no effect on K. 3. Adding argon gas has no effect on K. 4. Removing SO2(g) has no effect on K. 5. Decreasing the temperature: As the forward reaction is endothermic (positive \(\Delta H\)), when the temperature is decreased, the equilibrium constant K will increase (favoring the forward reaction).

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Most popular questions from this chapter

A compound, X, decomposes at \(131^{\circ} \mathrm{C}\) according to the following equation: $$ 2 \mathrm{X}(g) \rightleftharpoons \mathrm{A}(g)+3 \mathrm{C}(g) \quad K=1.1 \times 10^{-3} $$ If a flask initially contains \(\mathrm{X}, \mathrm{A},\) and \(\mathrm{C},\) all at partial pressures of \(0.250 \mathrm{~atm}\), in which direction will the reaction proceed?

Given the following descriptions of reversible reactions, write a balanced equation (smallest whole-number coefficients) and the equilibrium constant expression for each. (a) Nickel metal reacts with carbon monoxide to form nickel tetracarbonyl \(\left(\mathrm{Ni}(\mathrm{CO})_{4}\right)\) gas. (b) Aqueous nitrous acid in equilibrium with hydrogen and nitrite ions. (c) Chlorine gas and bromide ions in equilibrium with liquid bromine and chloride ions.

When one mole of carbon disulfide gas reacts with hydrogen gas, methane and hydrogen sulfide gases are formed. When equilibrium is reached at \(900^{\circ} \mathrm{C}\), analysis shows that \(P_{\mathrm{CH}_{4}}=0.0833 \mathrm{~atm}, P_{\mathrm{H}_{2} \mathrm{~s}}=0.163 \mathrm{~atm}, P_{\mathrm{CS}_{2}}=\) \(1.27 \mathrm{~atm},\) and \(P_{\mathrm{H}_{2}}=0.873 \mathrm{~atm}\) (a) Write a balanced equation (smallest whole-number coefficients) for the reaction. (b) Find \(K\) at \(900^{\circ} \mathrm{C}\).

Given the following data at a certain temperature, $$ \begin{array}{cl} 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{~N}_{2} \mathrm{O}(g) & K=1.2 \times 10^{-35} \\ \mathrm{~N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) & K=4.6 \times 10^{-3} \\ \frac{1}{2} \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g) & K=4.1 \times 10^{-9} \end{array} $$ calculate \(K\) for the reaction between one mole of dinitrogen oxide gas and oxygen gas to give dinitrogen tetroxide gas.

Write a chemical equation for an equilibrium system that would lead to the following expressions \((\mathrm{a}-\mathrm{d})\) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{H}_{2} \mathrm{~S}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}\) (b) \(K=\frac{\left(P_{\mathrm{F}_{2}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}\) (c) \(K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{Cl}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}\) (d) \(K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}\)
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