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Chapter 13: Problem 5

Consider the reaction $\mathrm{A}(g)+2 \mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)\( in a \)1.0-\mathrm{L}$ rigid flask. Answer the following questions for each situation \((\mathrm{a}-\mathrm{d}) :\) 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 \([\mathrm{A}]\) 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 \([\mathrm{B}]\) 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 \([\mathrm{D}]\) once equilibrium is reestablished.

Short Answer

Expert verified
For each situation (a-d), after adding 1 mole of C, the new equilibrium concentrations can be estimated as follows: a. [A'] is estimated using: \[K = \frac{([C]+1)[D]}{[A'][B]^2}\] b. [B'] is estimated using: \[K = \frac{([C]+1)[D]}{[A][B']^2}\] c. [C'] is estimated using: \[K = \frac{([C']+1)[D]}{[A][B]^2}\] d. [D'] is estimated using: \[K = \frac{([C]+1)[D']}{[A][B]^2}\] We cannot give specific ranges without additional information. With more information, the ranges can be narrowed down and compared as explained in the steps above.

Step by step solution

01

Understand the chemical reaction and equilibrium conditions

The given reaction is: \[A(g) + 2B(g) \rightleftharpoons C(g) + D(g)\] Initially, we should understand the concept of the equilibrium constant, K. The equilibrium constant K can be calculated using the concentrations of all substances at equilibrium. For this reaction, K is given by: \[K = \frac{[C][D]}{[A][B]^2}\] where [A], [B], [C], and [D] are the equilibrium concentrations of A, B, C, and D, respectively. Once we have determined K, we will be able to deduce the equilibrium concentrations after a change has been made in one of the concentrations.
02

Calculate K for each situation

For each of the given situations (a-d), we have the concentrations of one of the substances at equilibrium. We should first calculate K using these concentrations. a. If at equilibrium [A]=1M, we have the equation for K as follows: \[K = \frac{[C][D]}{[1][B]^2}\] b. If at equilibrium [B]=1M, we have: \[K = \frac{[C][D]}{[A][1]^2}\] c. If at equilibrium [C]=1M, we have: \[K = \frac{[1][D]}{[A][B]^2}\] d. If at equilibrium [D]=1M, we have: \[K = \frac{[C][1]}{[A][B]^2}\]
03

Calculate the new equilibrium concentrations after the change

For each situation, we will now calculate the requested substance's estimated range after the given change. a. If 1 mole of C is added to the reaction mix with [A]=1M, we can estimate the new equilibrium concentration of A, [A'] as follows: \[K = \frac{([C]+1)[D]}{[A'][B]^2}\] b. If 1 mole of C is added to the reaction mix with [B]=1M, we can estimate the new equilibrium concentration of B, [B'] as follows: \[K = \frac{([C]+1)[D]}{[A][B']^2}\] c. If 1 mole of C is added to the reaction mix with [C]=1M, we can estimate the new equilibrium concentration of C, [C'] as follows: \[K = \frac{([C']+1)[D]}{[A][B]^2}\] d. If 1 mole of C is added to the reaction mix with [D]=1M, we can estimate the new equilibrium concentration of D, [D'] as follows: \[K = \frac{([C]+1)[D']}{[A][B]^2}\]
04

Estimate a range for the requested substance and compare the values

For each situation, we must estimate the range for the requested substance and fulfill the remaining requirements; however, we cannot give a specific range without additional information. The proposed strategies for how the ranges can be found, narrowed, and compared have been explained in the respective sections (Step 3).

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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.

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},\( and 2.0 \)\mathrm{moles}$ of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) all in a 2.0 \(\mathrm{-L}\) container. Calculate the value of \(K\) for this reaction.

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.

The following equilibrium pressures at a certain temperature were observed for the reaction $$\begin{aligned} 2 \mathrm{NO}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \\ P_{\mathrm{NO}_{2}} &=0.55 \mathrm{atm} \\\ P_{\mathrm{NO}} &=6.5 \times 10^{-5} \mathrm{atm} \\ P_{\mathrm{O}_{2}} &=4.5 \times 10^{-5} \mathrm{atm} \end{aligned}$$ Calculate the value for the equilibrium constant \(K_{\mathrm{p}}\) at this temperature.

A sample of \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) is placed in an empty cylinder at \(25^{\circ} \mathrm{C}\) . After equilibrium is reached the total pressure is 1.5 atm and 16\(\%\) (by moles) of the original $\mathrm{N}_{2} \mathrm{O}_{4}(g)\( has dissociated to \)\mathrm{NO}_{2}(g) .$ a. Calculate the value of \(K_{\mathrm{p}}\) for this dissociation reaction at \(25^{\circ} \mathrm{C} .\) b. If the volume of the cylinder is increased until the total pressure is 1.0 atm (the temperature of the system remains constant), calculate the equilibrium pressure of \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) and \(\mathrm{NO}_{2}(g) .\) c. What percentage (by moles) of the original $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ is dissociated at the new equilibrium position (total pressure \(=1.00 \mathrm{atm} ) ?\)
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