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Chapter 13: Problem 50

The reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ has \(K_{\mathrm{p}}=109\) at \(25^{\circ} \mathrm{C}\) . If the equilibrium partial pressure of \(\mathrm{Br}_{2}\) is 0.0159 atm and the equilibrium partial pressure of NOBr is 0.0768 atm, calculate the partial pressure of \(\mathrm{NO}\) at equilibrium.

Short Answer

Expert verified
The partial pressure of NO at equilibrium is approximately 0.0302 atm.

Step by step solution

01

Write the equilibrium expression

The equilibrium expression for this reaction is \[K_p = \frac{(P_{\mathrm{NOBr}})^2}{(P_{\mathrm{NO}})^2 \times (P_{\mathrm{Br}_{2}})}\] where \(K_p\) is the equilibrium constant, and \(P_{\mathrm{NO}}\), \(P_{\mathrm{Br}_{2}}\), and \(P_{\mathrm{NOBr}}\) represent the partial pressures of NO, Br2, and NOBr, respectively, at equilibrium.
02

Plug in the given values

We are given \(K_p = 109\), \(P_{\mathrm{Br}_{2}} = 0.0159\), and \(P_{\mathrm{NOBr}} = 0.0768\). Plugging these values into the equilibrium expression, we get: \[109 = \frac{(0.0768)^2}{(P_{\mathrm{NO}})^2 \times (0.0159)}\]
03

Solve for the partial pressure of NO

To solve for \(P_{\mathrm{NO}}\), we will first multiply both sides of the equation by \((P_{\mathrm{NO}})^2 \times (0.0159)\). Then, we will take the square root of both sides to solve for \(P_{\mathrm{NO}}\). \[(P_{\mathrm{NO}})^2 \times (0.0159) \times 109 = (0.0768)^2\] \[(P_{\mathrm{NO}})^2 = \frac{(0.0768)^2}{(0.0159) \times 109}\] \[P_{\mathrm{NO}} = \sqrt{\frac{(0.0768)^2}{(0.0159) \times 109}}\] Calculating the value, we get: \[P_{\mathrm{NO}} \approx 0.0302\] So, the partial pressure of NO at equilibrium is approximately 0.0302 atm.

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Most popular questions from this chapter

In Section 13.1 of your text, it is mentioned that equilibrium is reached in a "closed system." What is meant by the term "closed system," and why is it necessary to have a closed system in order for a system to reach equilibrium? Explain why equilibrium is not reached in an open system.

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.

Nitric oxide and bromine at initial partial pressures of 98.4 and 41.3 torr, respectively, were allowed to react at \(300 .\) K. At equilibrium the total pressure was 110.5 torr. The reaction is $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ a. Calculate the value of \(K_{\mathrm{p}}\) . b. What would be the partial pressures of all species if NO and \(\mathrm{Br}_{2},\) both at an initial partial pressure of \(0.30 \mathrm{atm},\) were allowed to come to equilibrium at this temperature?

For the reaction $$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ it is determined that, at equilibrium at a particular temperature, the concentrations are as follows: $[\mathrm{NO}(g)]=8.1 \times 10^{-3} \mathrm{M}\( \)\left[\mathrm{H}_{2}(g)\right]=4.1 \times 10^{-5} M,\left[\mathrm{N}_{2}(g)\right]=5.3 \times 10^{-2} M,$ and \(\left[\mathrm{H}_{2} \mathrm{O}(g)\right]-2.9 \times 10^{-3} \mathrm{M} .\) Calculate the value of \(K\) for the reaction at this temperature.

An initial mixture of nitrogen gas and hydrogen gas is reacted in a rigid container at a certain temperature by the reaction $$3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ At equilibrium, the concentrations are $\left[\mathrm{H}_{2}\right]=5.0 M,\left[\mathrm{N}_{2}\right]=$ \(8.0 M,\) and \(\left[\mathrm{NH}_{3}\right]=4.0 \mathrm{M} .\) What were the concentrations of nitrogen gas and hydrogen gas that were reacted initially?
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