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Chapter 14: Problem 118

Which of the following reactions is described by the equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}\) (a) \(\mathrm{A}_{2}+\mathrm{B}_{3} \rightleftarrows \mathrm{C}_{3}+\mathrm{D}_{2}\) (b) \(2 \mathrm{~A}+3 \mathrm{~B} \rightleftarrows 3 \mathrm{C}+2 \mathrm{D}\) (c) \(3 \mathrm{C}+2 \mathrm{D} \rightleftarrows 2 \mathrm{~A}+3 \mathrm{~B}\) (d) \(A^{2}+B^{3} \rightleftarrows C^{3}+D^{2}\) (e) \(2 \mathrm{C}+3 \mathrm{D} \rightleftarrows 3 \mathrm{~A}+2 \mathrm{~B}\)

Short Answer

Expert verified
The correct balanced chemical equation that matches the given equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}\) is option (b): \(2 \mathrm{~A}+3 \mathrm{~B} \rightleftarrows 3 \mathrm{C}+2 \mathrm{D}\).

Step by step solution

01

Analyze Option (a)

We can compare the equilibrium expression for option (a) with the given equilibrium constant expression: $K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}$ Option (a): $\mathrm{A}_{2}+\mathrm{B}_{3} \rightleftarrows \mathrm{C}_{3}+\mathrm{D}_{2}$ The stoichiometric coefficients in option (a) are not matching the powers of the concentrations in the given equilibrium expression. Therefore, option (a) is incorrect.
02

Analyze Option (b)

We can compare the equilibrium expression for option (b) with the given equilibrium constant expression. $K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}$ Option (b): \(2 \mathrm{~A}+3 \mathrm{~B} \rightleftarrows 3 \mathrm{C}+2 \mathrm{D}\) The stoichiometric coefficients in option (b) match the powers of the concentrations in the given equilibrium expression. Therefore, option (b) is correct.
03

Analyze the Other Options (c), (d), and (e) for Confirmation

We can perform a quick analysis of the other options to confirm that option (b) is the correct answer. Option (c): \(3 \mathrm{C}+2 \mathrm{D} \rightleftarrows 2 \mathrm{~A}+3 \mathrm{~B}\) Option (d): \(A^{2}+B^{3} \rightleftarrows C^{3}+D^{2}\) Option (e): \(2 \mathrm{C}+3 \mathrm{D} \rightleftarrows 3 \mathrm{~A}+2 \mathrm{~B}\) None of these options have the stoichiometric coefficients matching the powers of the concentrations in the given equilibrium expression. This confirms that option (b) is the correct answer.
04

Conclusion

Based on our analysis, the equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}\) corresponds to the balanced chemical equation given in option (b): \(2 \mathrm{~A}+3 \mathrm{~B} \rightleftarrows 3 \mathrm{C}+2 \mathrm{D}\).

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Most popular questions from this chapter

Suppose you are making ammonia \(\left(\mathrm{NH}_{3}\right)\) by the Haber reaction, at \(472{ }^{\circ} \mathrm{C}\) : \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g) K_{\mathrm{eq}}=0.105\) (a) Describe qualitatively where the equilibrium lies for this reaction. (b) On the face of it, would this reaction be a good one for isolating pure ammonia? (c) What would happen if you could keep feeding \(\mathrm{H}_{2}\) and \(\mathrm{N}_{2}\) into the reaction vessel while at the same time removing \(\mathrm{NH}_{3}\) ?

What does a catalyst do to the time it takes for a reaction to reach equilibrium? Explain how it does this.

Hydrochloric acid is added to an aqueous solution of silver nitrate. (a) What precipitate forms? (b) The equilibrium concentration of \(\mathrm{Cl}^{-}(a q)\) is \(2.0 \times 10^{-3} \mathrm{M}\). What is the equilibrium concentration of \(\mathrm{Ag}^{+}(a q) ?\)

Write the expression for \(K_{\text {eq }}\) for the reaction \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftarrows 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

What is "dynamic" about the equilibrium that is established when a sparingly soluble salt is added to water?
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