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Chapter 15: Problem 3

Write equilibrium constant expressions, \(K_{\mathrm{c}},\) for the reactions (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\) (b) \(\mathrm{Zn}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Zn}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})\) (c) \(\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{CO}_{3}^{2-}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{MgCO}_{3}(\mathrm{s})+2 \mathrm{OH}^{-}(\mathrm{aq})\)

Short Answer

Expert verified
The equilibrium constant expressions for the provided reactions are (a) \( K_c = \frac{{[\mathrm{NO_{2}}]^2}}{{[\mathrm{NO}]^2 [\mathrm{O_2}]}} \), (b) \( K_c = \frac{{[\mathrm{Zn}^{2+}]}}{{[\mathrm{Ag^{+}}]^2}} \), and (c) \( K_c = \frac{{[\mathrm{OH^{-}}]^2}}{{[\mathrm{CO_{3}^{2-}]}} \).

Step by step solution

01

Writing the Equilibrium Constant Expression for Reaction (a)

For the reaction \(2 \mathrm{NO(g)} + \mathrm{O_{2}(g)} \rightleftharpoons 2 \mathrm{NO_{2}(g)}\), the equilibrium constant expression would be \[ K_c = \frac{{[\mathrm{NO_{2}}]^2}}{{[\mathrm{NO}]^2 [\mathrm{O_2}]}} \] The concentrations of \(NO_{2}\), \(NO\) and \(O_{2}\) are raised to their stoichiometric coefficients.
02

Writing the Equilibrium Constant Expression for Reaction (b)

For the reaction \(\mathrm{Zn(s)} + 2 \mathrm{Ag^{+}(aq)} \rightleftharpoons \mathrm{Zn^{2+}(aq)} + 2 \mathrm{Ag(s)}\), write the equilibrium constant expression as \[ K_c = \frac{{[\mathrm{Zn}^{2+}]}}{{[\mathrm{Ag^{+}}]^2}} \] In this reaction, \(Zn\) is a pure solid and \(Ag\) is a pure metal; therefore, they are not included in the equilibrium expression.
03

Writing the Equilibrium Constant Expression for Reaction (c)

For the reaction \(\mathrm{Mg(OH)_{2}(s)} + \mathrm{CO_{3}^{2-}(aq)} \rightleftharpoons \mathrm{MgCO_{3}(s)} + 2 \mathrm{OH^{-}(aq)}\), the equilibrium constant expression would be \[ K_c = \frac{{[\mathrm{OH^{-}}]^2}}{{[\mathrm{CO_{3}^{2-}]}} \] Here, \(\mathrm{Mg(OH)_{2}}\) and \(\mathrm{MgCO_{3}}\) are both solids so they aren't included in the equilibrium expression.

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Most popular questions from this chapter

In your own words, define or explain the following terms or symbols: (a) \(K_{\mathrm{p}} ;\) (b) \(Q_{\mathrm{c}} ;\) (c) \(\Delta n_{\text {gas }}\)

A classic experiment in equilibrium studies dating from 1862 involved the reaction in solution of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) to produce ethyl acetate and water. $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O}$$ The reaction can be followed by analyzing the equilibrium mixture for its acetic acid content. $$\begin{array}{r} 2 \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq}) \rightleftharpoons \\ \mathrm{Ba}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{array}$$ In one experiment, a mixture of 1.000 mol acetic acid and 0.5000 mol ethanol is brought to equilibrium. A sample containing exactly one-hundredth of the equilibrium mixture requires \(28.85 \mathrm{mL} 0.1000 \mathrm{M}\) \(\mathrm{Ba}(\mathrm{OH})_{2}\) for its titration. Calculate the equilibrium constant, \(K_{c}\), for the ethanol-acetic acid reaction based on this experiment.

Can a mixture of \(2.2 \mathrm{mol} \mathrm{O}_{2}, 3.6 \mathrm{mol} \mathrm{SO}_{2},\) and \(1.8 \mathrm{mol}\) \(\mathrm{SO}_{3}\) be maintained indefinitely in a \(7.2 \mathrm{L}\) flask at a temperature at which \(K_{\mathrm{c}}=100\) in this reaction? Explain. $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) $$

\(1.00 \times 10^{-3} \mathrm{mol} \mathrm{PCl}_{5}\) is introduced into a \(250.0 \mathrm{mL}\) flask, and equilibrium is established at \(284^{\circ} \mathrm{C}\) : \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) .\) The quantity of \(\mathrm{Cl}_{2}(\mathrm{g})\) present at equilibrium is found to be \(9.65 \times 10^{-4} \mathrm{mol}\) What is the value of \(K_{c}\) for the dissociation reaction at \(284^{\circ} \mathrm{C} ?\)

Based on these descriptions, write a balanced equation and the corresponding \(K_{\mathrm{p}}\) expression for each reversible reaction. (a) Oxygen gas oxidizes gaseous ammonia to gaseous nitrogen and water vapor. (b) Hydrogen gas reduces gaseous nitrogen dioxide to gaseous ammonia and water vapor. (c) Nitrogen gas reacts with the solid sodium carbonate and carbon to produce solid sodium cyanide and carbon monoxide gas.
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