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Chapter 13: Problem 46

The equilibrium constant \(K_{\mathrm{p}}\) is \(2.4 \times 10^{3}\) at a certain temperature for the reaction $$2 \mathrm{NO}(g) \leftrightharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$$ For which of the following sets of conditions is the system at equilibrium? For those not at equilibrium, in which direction will the system shift? a. $P_{\mathrm{NO}}=0.012 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.11 \mathrm{atm}, P_{\mathrm{O}_{2}}=2.0 \mathrm{atm}$ b. $P_{\mathrm{NO}}=0.0078 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.36 \mathrm{atm}, P_{\mathrm{O}_{2}}=0.67 \mathrm{atm}$ c. $P_{\mathrm{NO}}=0.0062 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.51 \mathrm{atm}, P_{\mathrm{O}_{2}}=0.18 \mathrm{atm}$

Short Answer

Expert verified
For the given sets of conditions: a. The reaction will shift to the right. b. The reaction will shift to the left. c. The system is at equilibrium.

Step by step solution

01

Write the expression for Qp

The equation for Qp is given by: $$Q_p = \frac{P_{N_2} \times P_{O_2}}{P_{NO}^2}$$ Now, we will calculate the value of Qp for each set of conditions and compare it to the given equilibrium constant (Kp) to determine if the system is at equilibrium and, if not, in which direction the system will shift.
02

Calculate Qp for condition (a)

Substitute the given values for condition (a) into the Qp expression: $$Q_{p_{a}} = \frac{0.11 \times 2.0}{(0.012)^2} = 1520.8$$ #a. Compare Qp for condition (a) with Kp Since \(Q_{p_{a}} < K_p\) (1520.8 < 2400), the reaction will shift to the right (in favor of the products).
03

Calculate Qp for condition (b)

Substitute the given values for condition (b) into the Qp expression: $$Q_{p_{b}} = \frac{0.36 \times 0.67}{(0.0078)^2} = 3912.3$$ #b. Compare Qp for condition (b) with Kp Since \(Q_{p_{b}} > K_p\) (3912.3 > 2400), the reaction will shift to the left (in favor of the reactants).
04

Calculate Qp for condition (c)

Substitute the given values for condition (c) into the Qp expression: $$Q_{p_{c}} = \frac{0.51 \times 0.18}{(0.0062)^2} = 2396.7$$ #c. Compare Qp for condition (c) with Kp Since \(Q_{p_{c}} \approx K_p\) (2396.7 ≈ 2400), the system is at equilibrium for condition (c). To summarize, only condition (c) is at equilibrium. Condition (a) will shift to the right, and condition (b) will shift to the left.

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Most popular questions from this chapter

Consider the decomposition of the compound $\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}$ as follows: $$\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)+3 \mathrm{CO}(g)$$ When a 5.63 -g sample of pure $\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}(g)\( was sealed into an otherwise empty \)2.50-\mathrm{L}$ flask and heated to \(200 .^{\circ} \mathrm{C},\) the pres- sure in the flask gradually rose to 1.63 \(\mathrm{atm}\) and remained at that value. Calculate \(K\) for this reaction.

At high temperatures, elemental nitrogen and oxygen react with each other to form nitrogen monoxide: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ Suppose the system is analyzed at a particular temperature, and the equilibrium concentrations are found to be \(\left[\mathrm{N}_{2}\right]=\) \(0.041 M,\left[\mathrm{O}_{2}\right]=0.0078 M,\) and $[\mathrm{NO}]=4.7 \times 10^{-4} M .\( Calculate the value of \)K$ for the reaction.

A sample of \(\mathrm{S}_{8}(g)\) is placed in an otherwise empty rigid container at 1325 \(\mathrm{K}\) at an initial pressure of \(1.00 \mathrm{atm},\) where it decomposes to \(\mathrm{S}_{2}(g)\) by the reaction $$\mathrm{S}_{8}(g) \rightleftharpoons 4 \mathrm{S}_{2}(g)$$ At equilibrium, the partial pressure of \(\mathrm{S}_{8}\) is 0.25 atm. Calculate \(K_{\mathrm{p}}\) for this reaction at 1325 \(\mathrm{K}\) .

For the reaction $$\mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{HS}(s)$$ \(K=400\) . at \(35.0^{\circ} \mathrm{C} .\) If 2.00 moles each of \(\mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{S},\) and $\mathrm{NH}_{4} \mathrm{HS}\( are placed in a \)5.00-\mathrm{L}$ vessel, what mass of \(\mathrm{NH}_{4} \mathrm{HS}\) will be present at equilibrium? What is the pressure of \(\mathrm{H}_{2} \mathrm{S}\) at equilibrium?

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.
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