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Chapter 13: Problem 26

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.

Short Answer

Expert verified
The equilibrium constant (K) for the given reaction can be calculated using the expression \[ K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}][\mathrm{O}_{2}]} \]Substituting the given equilibrium concentrations, we get \[ K = \frac{(4.7 \times 10^{-4})^2}{(0.041)(0.0078)} \approx 7.07 \times 10^{-3} \]Thus, the equilibrium constant K for this reaction is approximately \(7.07 \times 10^{-3}\).

Step by step solution

01

Write the equilibrium constant expression

We need to first write the expression for the equilibrium constant (K). For the given reaction: \[ \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2\mathrm{NO}(g) \] The equilibrium constant expression will be: \[ K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}][\mathrm{O}_{2}]} \]
02

Substitute the values of the equilibrium concentrations

Now we substitute the equilibrium concentration values given in the problem into the equilibrium constant expression: \[ K = \frac{(4.7 \times 10^{-4})^2}{(0.041)(0.0078)} \]
03

Solve for K

By solving the expression we will get the value of K: \[ K = \frac{(4.7 \times 10^{-4})^2}{(0.041)(0.0078)} \approx 7.07 \times 10^{-3} \] So the equilibrium constant K for this reaction is approximately \(7.07 \times 10^{-3}\).

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Most popular questions from this chapter

Write the equilibrium expression \((K)\) for each of the following gas-phase reactions. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) b. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) c. \(\mathrm{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g)\) d. \(2 \mathrm{PBr}_{3}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{PCl}_{3}(g)+3 \mathrm{Br}_{2}(g)\)

The synthesis of ammonia gas from nitrogen gas and hydrogen gas represents a classic case in which a knowledge of kinetics and equilibrium was used to make a desired chemical reaction economically feasible. Explain how each of the following conditions helps to maximize the yield of ammonia. a. running the reaction at an elevated temperature b. removing the ammonia from the reaction mixture as it forms c. using a catalyst d. running the reaction at high pressure

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 \(\mathrm{NOBr}\) is \(0.0768\) atm, calculate the partial pressure of \(\mathrm{NO}\) at equilibrium.

Novelty devices for predicting rain contain cobalt(II) chloride and are based on the following equilibrium: $$ \underset{\text { Purple }}{\mathrm{CoCl}_{2}(s)}+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \underset{\text { Pink }}{\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s)} $$ What color will such an indicator be if rain is imminent?

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 \([\mathrm{C}]=4 M .\) To a 1 -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 \([\mathrm{C}]=6 M\) 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.
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