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Chapter 12: Problem 37

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

Short Answer

Expert verified
The value of the equilibrium constant (K) for the given reaction is \( 8.0 \times 10^{9} \).

Step by step solution

01

Write the balanced chemical equation

For this problem, we are given the balanced chemical equation: \[ 4 \mathrm{Fe}(s) + 3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \]
02

Calculate the concentrations of Fe, O₂, and Fe₂O₃

We know the amount of each substance and the volume of the container (2.0 L). The concentrations can be calculated as follows: - Fe(s): \(1.0 \,\text{mole} \); \(\frac{1.0 \,\text{mole}}{2.0 \,\text{L}} = 0.5 \,\text{M} \) - O₂(g): \(1.0 \times 10^{-3}\,\text{mole} \); \(\frac{1.0 \times 10^{-3}\,\text{mole}}{2.0 \,\text{L}} = 5.0 \times 10^{-4}\,\text{M} \) - Fe₂O₃(s): \(2.0\,\text{moles}\); \(\frac{2.0\,\text{moles}}{2.0\,\text{L}} = 1.0\,\text{M} \)
03

Apply the equilibrium constant formula

For the reaction equilibrium constant \(K_{c}\), the formula is: \[K_{c} = \frac{[\mathrm{Fe}_{2}\mathrm{O}_{3}]^2}{[\mathrm{Fe}]^4 [\mathrm{O}_{2}]^3}\] However, we don't include solids (Fe and Fe₂O₃) in the equilibrium expression. Hence, the formula becomes: \[K_{c} = \frac{1}{[\mathrm{O}_{2}]^3}\]
04

Substitute the values and calculate K

Now we substitute the concentration of O₂ into the formula and calculate K: \[K_{c} = \frac{1}{(5.0 \times 10^{-4})^3} = \frac{1}{1.25 \times 10^{-10}} = 8.0 \times 10^{9}\] Thus, the value of the equilibrium constant (K) for this reaction is \(8.0 \times 10^{9}\).

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Most popular questions from this chapter

A sample of gaseous nitrosyl bromide (NOBr) was placed in a container fitted with a frictionless, massless piston, where it decomposed at \(25^{\circ} \mathrm{C}\) according to the following equation:$$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ The initial density of the system was recorded as \(4.495 \mathrm{g} / \mathrm{L}\) After equilibrium was reached, the density was noted to be \(4.086 \mathrm{g} / \mathrm{L}\) a. Determine the value of the equilibrium constant \(K\) for the reaction. b. If \(\mathrm{Ar}(g)\) is added to the system at equilibrium at constant temperature, what will happen to the equilibrium position? What happens to the value of \(K ?\) Explain each answer.

At a particular temperature, 12.0 moles of \(\mathrm{SO}_{3}\) is placed into a 3.0-L rigid container, and the \(\mathrm{SO}_{3}\) dissociates by the reaction $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$. At equilibrium, 3.0 moles of \(\mathrm{SO}_{2}\) is present. Calculate \(K\) for this reaction.

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 UO \(_{2}(s)\) is added to the system. b. The reaction is performed in a glass reaction vessel; \(\mathrm{HF}(g)\) attacks and reacts with glass. c. Water vapor is removed.

Consider the following reaction:$$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$.Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},\) and \(\mathrm{CO}_{2}\) are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \(^{14} \mathrm{C},\) will \(^{14} \mathrm{C}\) be found only in CO molecules for an indefinite period of time? 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.)
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