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Chapter 12: Problem 110

A sample of iron(II) sulfate was heated in an evacuated container to \(920 \mathrm{K},\) where the following reactions occurred:$$\begin{array}{c}2 \mathrm{FeSO}_{4}(s) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{3}(g)+\mathrm{SO}_{2}(g) \\ \mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \end{array}$$.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.

Short Answer

Expert verified
In summary, given the reactions and the partial pressures of the gases involved, we calculated the equilibrium constants: \(K_{p1} = 59.42\) and \(K_{p2} = 0.002037\).

Step by step solution

01

Write the expressions for \(K_{p1}\) and \(K_{p2}\)

For each of the given reactions, write the expressions for the equilibrium constants: \(K_{p1} = \frac{P(\mathrm{SO}_3) \cdot P(\mathrm{SO}_2)}{(P(\mathrm{FeSO}_4))^2}\), \(K_{p2} = \frac{P(\mathrm{SO}_2) \cdot P(\frac{1}{2}\mathrm{O}_2)}{P(\mathrm{SO}_3)}\).
02

Find the partial pressures of other gases

Given the total pressure 0.836 atm and knowing the partial pressure of oxygen gas to be 0.0275 atm, we can find the combined partial pressures of \(\mathrm{SO}_3 (g)\) and \(\mathrm{SO}_2 (g)\) \(P(\mathrm{SO}_3) + P(\mathrm{SO}_2) = 0.836 - 0.0275 = 0.8085\) atm
03

Express the unknown partial pressures in terms of the known value

Let \(x\) be the partial pressure of \(\mathrm{SO}_3 (g)\). Then, the partial pressure of \(\mathrm{SO}_2 (g)\) is \(0.8085 - x\). Now we can write the expression for \(K_{p1}\) in terms of x: \(K_{p1} = \frac{x (0.8085 - x)}{(0.0275)^2}\).
04

Use the second reaction to find the relationship between the partial pressures of \(\mathrm{SO}_3\) and \(\mathrm{SO}_2\)

In the second reaction, we can express the amount of \(\mathrm{SO}_3\) produced in terms of the amount of \(\mathrm{SO}_2\). The mole ratio of the gases in the second reaction is 1:1:\(\frac{1}{2}\). Since twice the amount of \(\mathrm{SO}_2\) is produced for every mole of O2, we get: \(x = 0.8085 - (2 \cdot 0.0275) = 0.8085 - 0.055 = 0.7535\) atm
05

Calculate the partial pressure of \(\mathrm{SO}_2 (g)\)

Now, we can calculate the partial pressure of \(\mathrm{SO}_2 (g)\): \(P(\mathrm{SO}_2) = 0.8085 - 0.7535 = 0.055\) atm
06

Calculate the equilibrium constants \(K_{p1}\) and \(K_{p2}\)

Now that we have the partial pressures of all gases, we can calculate \(K_{p1}\) and \(K_{p2}\): \(K_{p1} = \frac{(0.7535)(0.055)}{(0.0275)^2} = 59.42\) \(K_{p2} = \frac{(0.055)(0.0275)}{0.7535} = 0.002037\) So, the equilibrium constants for the given reactions are: \(K_{p1} = 59.42\) \(K_{p2} = 0.002037\)

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Most popular questions from this chapter

What will happen to the number of moles of \(\mathrm{SO}_{3}\) in equilibrium with \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) in the reaction,$$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$.in each of the following cases? a. Oxygen gas is added. b. The pressure is increased by decreasing the volume of the reaction container. c. In a rigid reaction container, the pressure is increased by adding argon gas. d. The temperature is decreased (the reaction is endothermic). e. Gaseous sulfur dioxide is removed.

At \(25^{\circ} \mathrm{C},\) gaseous \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decomposes to \(\mathrm{SO}_{2}(g)\) and \(\mathrm{Cl}_{2}(g)\) to the extent that \(12.5 \%\) of the original \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) (by moles) has decomposed to reach equilibrium. The total pressure (at equilibrium) is 0.900 atm. Calculate the value of \(K_{\mathrm{p}}\) for this system.

Lexan is a plastic used to make compact discs, eyeglass lenses, and bulletproof glass. One of the compounds used to make Lexan is phosgene \(\left(\mathrm{COCl}_{2}\right),\) an extremely poisonous gas. Phosgene decomposes by the reaction,$$\operatorname{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)$$,for which \(K_{\mathrm{p}}=6.8 \times 10^{-9}\) at \(100^{\circ} \mathrm{C}\). If pure phosgene at an initial pressure of 1.0 atm decomposes, calculate the equilibrium pressures of all species.

Consider the following exothermic reaction at equilibrium: $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$. Predict how the following changes affect the number of moles of each component of the system after equilibrium is reestablished by completing the table below. Complete the table with the terms increase, decrease, or no change.

Consider an equilibrium mixture of four chemicals \((\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D},\) all gases) reacting in a closed flask according to the equation:$$\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)$$. a. You add more \(A\) to the flask. How does the concentration of each chemical compare to its original concentration after equilibrium is reestablished? Justify your answer. b. You have the original setup at equilibrium, and you add more \(\mathrm{D}\) to the flask. How does the concentration of each chemical compare to its original concentration after equilibrium is reestablished? Justify your answer.
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