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Chapter 13: Problem 30

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 reaction \(\mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) can be calculated using the given equilibrium concentrations: \([\mathrm{N}_{2}] = 0.041 M\), \([\mathrm{O}_{2}] = 0.0078 M\), and \([\mathrm{NO}] = 4.7 \times 10^{-4} M\). By plugging these values into the equilibrium expression \(K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}][\mathrm{O}_{2}]}\), we find that K is approximately \(9.13 \times 10^{-4}\).

Step by step solution

01

Write the equilibrium expression

The equilibrium expression for the given reaction is: \(K = \frac{[\mathrm{NO}]^2}{[\mathrm{N}_{2}][\mathrm{O}_{2}]}\)
02

Plug in the given equilibrium concentrations

We are given the equilibrium concentrations as follows: \([\mathrm{N}_{2}] = 0.041 M\) \([\mathrm{O}_{2}] = 0.0078 M\) \([\mathrm{NO}] = 4.7 \times 10^{-4} M\) Now, we plug these values into the equilibrium expression: \(K = \frac{(4.7 \times 10^{-4})^2}{(0.041)(0.0078)}\)
03

Calculate K

Now, let's calculate the value of K: \(K = \frac{(4.7 \times 10^{-4})^2}{(0.041)(0.0078)} \approx 9.13 \times 10^{-4}\) Thus, the equilibrium constant (K) for the given reaction is approximately \(9.13 \times 10^{-4}\).

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Most popular questions from this chapter

Suppose the reaction system $$\mathrm{UO}_{2}(s)+4 \mathrm{HF}(g) \rightleftharpoons \mathrm{UF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ has already reached equilibrium. Predict the effect that each of the following changes will have on the equilibrium position. Tell whether the equilibrium will shift to the right, will shift to the left, or will not be affected. a. Additional \(\mathrm{UO}_{2}(s)\) is added to the system. b. The reaction is performed in a glass reaction vessel; HF \((g)\) attacks and reacts with glass. c. Water vapor is removed.

Consider the following reaction at \(725^{\circ} \mathrm{C} :\) $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \leftrightharpoons 2 \mathrm{CO}(g)$$ At equilibrium, a \(4.50-\mathrm{L}\) container has 2.6 \(\mathrm{g}\) of carbon, \(\mathrm{CO}_{2}\) at a partial pressure of \(0.0020 \mathrm{atm},\) and a total pressure of 0.572 atm. Calculate \(K_{\mathrm{p}}\) for this reaction at \(725^{\circ} \mathrm{C}\)

The reaction to prepare methanol from carbon monoxide and hydrogen $$\mathrm{CO}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$$ is exothermic. If you wanted to use this reaction to produce methanol commercially, would high or low temperatures favor a maximum yield? Explain.

In a study of the reaction $$3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g)$$ at 1200 \(\mathrm{K}\) it was observed that when the equilibrium partial pressure of water vapor is 15.0 torr, the total pressure at equilibrium is 36.3 torr. Calculate the value of \(K_{\mathrm{p}}\) for this reaction at 1200 \(\mathrm{K}\) . Hint: Apply Dalton's law of partial pressures.)

At a particular temperature, \(K_{\mathrm{p}}=0.25\) for the reaction $$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ a. A flask containing only \(\mathrm{N}_{2} \mathrm{O}_{4}\) at an initial pressure of 4.5 \(\mathrm{atm}\) is allowed to reach equilibrium. Calculate the equilibrium partial pressures of the gases. b. A flask containing only \(\mathrm{NO}_{2}\) at an initial pressure of 9.0 \(\mathrm{atm}\) is allowed to reach equilibrium. Calculate the equilibrium partial pressures of the gases. c. From your answers to parts a and b, does it matter from which direction an equilibrium position is reached?
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