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Chapter 12: Problem 7

Consider the following statements: "Consider the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g),\) for which at equilibrium \([\mathrm{A}]=2 M\) \([\mathrm{B}]=1 M,\) and \([\mathrm{C}]=4 \mathrm{M} .\) To a \(1-\mathrm{L}\) container of the system at equilibrium, you add 3 moles of B. A possible equilibrium condition is \([\mathrm{A}]=1 M,[\mathrm{B}]=3 M,\) and \([\mathrm{C}]=6 \mathrm{M}\) because in both cases \(K=2 . "\) Indicate everything that is correct in these statements and everything that is incorrect. Correct the incorrect statements, and explain.

Short Answer

Expert verified
In the given statements, the fact that "in both cases, \(K = 2\)" is correct, as both equilibrium constants have a value of 2. However, the statement "To a \(1-L\) container of the system at equilibrium, you add 3 moles of B" is incorrect. The correct statement is: "To a \(1-L\) container of the system at equilibrium, you add 2 moles of B. A possible equilibrium condition is \([\mathrm{A}] = 1\:M, [\mathrm{B}] = 3\:M,\) and \([\mathrm{C}] = 6\:M\), because in both cases \(K = 2\)."

Step by step solution

01

Write the reaction equation and equilibrium constant expression

The given reaction is: \(\mathrm{A}(g) + \mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)\) The equilibrium constant expression for this reaction is: \[K = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]}\]
02

Calculate the equilibrium constant for the first condition

Given, at equilibrium: \([\mathrm{A}] = 2\:M\) \([\mathrm{B}] = 1\:M\) \([\mathrm{C}] = 4\:M\) Now, we calculate the equilibrium constant (denoted as \(K_1\)) for this set of concentrations: \[K_1 = \frac{4}{(2)(1)} = 2\]
03

Calculate the equilibrium constant for the second condition

Given, another possible equilibrium condition: \([\mathrm{A}] = 1\:M\) \([\mathrm{B}] = 3\:M\) \([\mathrm{C}] = 6\:M\) Now, we calculate the equilibrium constant (denoted as \(K_2\)) for this set of concentrations: \[K_2 = \frac{6}{(1)(3)} = 2\]
04

Compare the equilibrium constants and find the correct/incorrect statements

Since both equilibrium constants are equal and have a value of 2 (i.e., \(K_1 = K_2 = 2\)), we can conclude that the statement "in both cases, \(K = 2\)" is correct. However, the statement "To a \(1-L\) container of the system at equilibrium, you add 3 moles of B" is incorrect. When we add 3 moles of B, the new concentrations would be: \([\mathrm{A}] = 1\:M\) \([\mathrm{B}] = 4\:M\) (as new concentration would be \(1\:M + 3 \: moles/L\)) \([\mathrm{C}] = 6\:M\) Nevertheless, it doesn't affect the overall conclusion that both conditions result in the same \(K\) value. To correct the statement, we can say: "To a \(1-L\) container of the system at equilibrium, you add 2 moles of B. A possible equilibrium condition is \([\mathrm{A}] = 1\:M, [\mathrm{B}] = 3\:M,\) and \([\mathrm{C}] = 6\:M\), because in both cases \(K = 2\)."

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Most popular questions from this chapter

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.

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.

Consider the reaction \(\mathrm{A}(g)+2 \mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)\) in a 1.0-L rigid flask. Answer the following questions for each situation (a-d): i. Estimate a range (as small as possible) for the requested substance. For example, [A] could be between \(95 M\) and \(100 M\),ii. Explain how you decided on the limits for the estimated range. iii. Indicate what other information would enable you to narrow your estimated range. iv. Compare the estimated concentrations for a through d, and explain any differences. a. If at equilibrium \([\mathrm{A}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for [A] once equilibrium is reestablished. b. If at equilibrium \([\mathrm{B}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for \([\mathbf{B}]\) once equilibrium is reestablished. c. If at equilibrium \([\mathrm{C}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for \([\mathrm{C}]\) once equilibrium is reestablished. d. If at equilibrium \([\mathrm{D}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for [D] once equilibrium is reestablished.

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.

Consider the following reaction at a certain temperature:$$4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$$.An equilibrium mixture contains 1.0 mole of \(\mathrm{Fe}, 1.0 \times 10^{-3}\) mole of \(\mathrm{O}_{2},\) and 2.0 moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) all in a \(2.0-\mathrm{L}\) container. Calculate the value of \(K\) for this reaction.
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