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Chapter 1: Problem 6

The following reaction is found to be at equilibrium at 25°C: \(2 \mathrm{SO}_{3}(g) \leftrightarrow \mathrm{O}_{2}(g)+2 \mathrm{SO}_{2}(g) \quad \Delta H=-198 \mathrm{kJ} / \mathrm{mol}\) What is the expression for the equilibrium constant, \(K_{\mathrm{c}} ?\) (A) \(\frac{\left[\mathrm{SO}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]\left[\mathrm{SO}_{2}\right]^{2}}\) (B) \(\frac{2\left[\mathrm{SO}_{3}\right]}{\left[\mathrm{O}_{2}\right] 2\left[\mathrm{SO}_{2}\right]}\) (C) \(\frac{\left[\mathrm{O}_{2}\right]\left[\mathrm{SO}_{2}\right]^{2}}{\left[\mathrm{SO}_{3}\right]^{2}}\) (D) \(\frac{\left[\mathrm{O}_{2}\right] 2\left[\mathrm{SO}_{2}\right]}{2\left[\mathrm{SO}_{3}\right]}\)

Short Answer

Expert verified
Option (C), \(K_{c} = \frac{{[O_{2}] \cdot [SO_{2}]^{2}}}{{[SO_{3}]^{2}}}\), is the expression for the equilibrium constant for the given reaction.

Step by step solution

01

Analyze the Balanced Reaction

We have the balanced reaction: \(2 \mathrm{SO}_{3}(g) \leftrightarrow \mathrm{O}_{2}(g) + 2 \mathrm{SO}_{2}(g)\). The reactant is \(SO_{3}\) with stoichiometric coefficient 2 and the products are \(O_{2}\) with stoichiometric coefficient 1 and \(SO_{2}\) with stoichiometric coefficient 2.
02

Apply the Law of Mass Action

According to the law of mass action, the equilibrium constant, \(K_{\mathrm{c}}\), is given by the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient in the balanced chemical equation. Applying this to our reaction, we get: \(K_{c} = \frac{{([O_{2}]^{1} \cdot [SO_{2}]^{2})}}{{[SO_{3}]^{2}}}\). Simplifying this expression yields: \(K_{c} = \frac{{[O_{2}] \cdot [SO_{2}]^{2}}}{{[SO_{3}]^{2}}}\)
03

Match the Expression with Options

The derived expression for the equilibrium constant \(K_{c} = \frac{{[O_{2}] \cdot [SO_{2}]^{2}}}{{[SO_{3}]^{2}}}\) matches with option (C). So, option (C) is the correct answer.

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Most popular questions from this chapter

\(2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{AlCl}_{3}(s)\) The reaction above is not thermodynamically favored under standard conditions, but it becomes thermodynamically favored as the temperature decreases toward absolute zero. Which of the following is true at standard conditions? (A) \(\Delta S\) and \(\Delta H\) are both negative. (B) \(\Delta S\) and \(\Delta H\) are both positive. (C) \(\Delta S\) is negative, and \(\Delta H\) is positive. (D) \(\Delta S\) is positive, and \(\Delta H\) is negative.

\(\begin{array}{ll}{\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{4}(g)} & {\Delta H^{\circ}=x} \\\ {\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=y} \\ {\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=\mathrm{z}}\end{array}\) Based on the information given above, what is \(\Delta H^{\circ}\) for the following reaction? \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (A) \(x+y+z\) (B) \(x+y-z\) (C) \(z+y-2 x\) (D) \(2 z+y-x\)

A sealed, rigid container contains three gases: 28.0 \(\mathrm{g}\) of nitrogen, 40.0 \(\mathrm{g}\) of argon, and 36.0 g of water vapor. If the total pressure exerted by the gases is \(2.0 \mathrm{atm},\) what is the partial pressure of the nitrogen? (A) 0.33 atm (B) 0.40 atm (C) 0.50 \(\mathrm{atm}\) (D) 2.0 \(\mathrm{atm}\)

Use the following information to answer questions 25-28. A voltaic cell is created using the following half-cells: \(\begin{array}{ll}{\mathrm{Cr}^{3+}+3 e \rightarrow \mathrm{Cr}(s)} & {E^{\circ}=-0.41 \mathrm{V}} \\ {\mathrm{Pb}^{2+}+2 e \rightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.12 \mathrm{V}}\end{array}\) The concentrations of the solutions in each half-cell are 1.0 M. Which of the following occurs at the cathode? (A) \(\mathrm{Cr}^{3+}\) is reduced to \(\mathrm{Cr}(\mathrm{s})\) (B) \(\mathrm{Pb}^{2+}\) is reduced to \(\mathrm{Pb}(\mathrm{s})\) (C) \(\mathrm{Cr}(s)\) is oxidized to \(\mathrm{Cr}^{3+}\) (D) \(\quad \mathrm{Pb}(s)\) is oxidized to \(\mathrm{Pb}^{2+}\)

1.50 g of \(\mathrm{NaNO}_{3}\) is dissolved into 25.0 \(\mathrm{mL}\) of water, causing the temperature to increase by \(2.2^{\circ} \mathrm{C}\) . The density of the final solution is found to be 1.02 \(\mathrm{g} / \mathrm{mL}\) . Which of the following expressions will correctly calculate the heat gained by the water as the NaNO, dissolves? Assume the volume of the solution remains unchanged. (A) \((25.0)(4.18)(2.2)\) (B) \(\frac{(26.5)(4.18)(2.2)}{1.02}\) (C) \(\frac{(1.02)(4.18)(2.2)}{1.50}\) (D) \((25.0)(1.02)(4.18)(2.2)\)
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