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Chapter 14: Problem 55

Consider the following equilibrium systems: (a) \(A \Longrightarrow 2 B\) \(\Delta H^{\circ}=20.0 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}\) \(\Delta H^{\circ}=-5.4 \mathrm{~kJ} / \mathrm{mol}\) (c) \(A \Longrightarrow B\) \(\Delta H^{\circ}=0.0 \mathrm{~kJ} / \mathrm{mol}\) Predict the change in the equilibrium constant \(K_{\mathrm{c}}\) that would occur in each case if the temperature of the reacting system were raised.

Short Answer

Expert verified
For system (a), \(K_c\) increases. For system (b), \(K_c\) decreases. For system (c), \(K_c\) remains the same.

Step by step solution

01

System (a)

In this equilibrium system, the reaction is endothermic because \(\Delta H^{\circ} = +20.0 \, kJ/mol\). This means heat is absorbed, thus it can be written as \(A + Heat \Longrightarrow 2 B\). If the temperature is increased, the heat is increased. By Le Chatelier's principle, the system will try to use up this extra heat by shifting the equilibrium to the right, hence, increasing the equilibrium constant \(K_c\). When the equilibrium shifts to the right, more products (B) are formed, thus \(K_c\) (which is determined by the ratio of the product over the reactant concentrations) would increase.
02

System (b)

In this equilibrium system, the reaction is exothermic because the \(\Delta H^{\circ} = -5.4 \, kJ/mol\). This means heat is released, hence it can be written as \(A+B \Longrightarrow C + Heat\). When the temperature is increased, by Le Chatelier's principle, the reaction will work to reduce this extra heat and shifts the equilibrium to the left. Therefore, less product C is formed and the equilibrium constant \(K_c\) decreases.
03

System (c)

In this equilibrium system, the reaction is neither exothermic nor endothermic because \(\Delta H^{\circ}=0.0 \, kJ/mol\). This means that energy is neither absorbed nor released, hence an increase in temperature will not affect the equilibrium and thus, \(K_c\) does not change.

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Most popular questions from this chapter

Explain the difference between physical equilibrium and chemical equilibrium. Give two examples of each.

Pure phosgene gas \(\left(\mathrm{COCl}_{2}\right), 3.00 \times 10^{-2} \mathrm{~mol},\) was placed in a 1.50-L container. It was heated to \(800 \mathrm{~K}\), and at equilibrium the pressure of \(\mathrm{CO}\) was found to be 0.497 atm. Calculate the equilibrium constant \(K_{P}\) for the reaction $$\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)$$

A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$$ Under these conditions, the average molar mass of the gases was \(35 \mathrm{~g} / \mathrm{mol}\). (a) Calculate the mole fractions of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\). (b) What is \(K_{P}\) if the total pressure is 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.

A mixture of 0.47 mole of \(\mathrm{H}_{2}\) and 3.59 moles of \(\mathrm{HCl}\) is heated to \(2800^{\circ} \mathrm{C}\). Calculate the equilibrium partial pressures of \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) if the total pressure is 2.00 atm. For the reaction $$\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)$$ \(K_{P}\) is 193 at \(2800^{\circ} \mathrm{C}\)

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 -g sample of the solid is placed in an evacuated \(4.000-\mathrm{L}\) vessel at exactly \(24^{\circ} \mathrm{C}\). After equilibrium has been established, the total pressure inside is 0.709 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?
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