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Chapter 15: Problem 29

Mercury(l) oxide decomposes into elemental mercury and elemental oxygen: \(2 \mathrm{Hg}_{2} \mathrm{O}(s) \rightleftharpoons 4 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Suppose you run this reaction in a solvent that dissolves elemental mercury and elemental oxygen. Rewrite the equilibrium- constant expression in terms of molarities for the reaction, using (solv) to indicate solvation.

Short Answer

Expert verified
(a) The equilibrium-constant expression in terms of partial pressures for the given reaction is: \[K_p = \frac{P_{Hg}^4 P_{O_2}}{(P_{Hg_2O})^2}\] (b) The equilibrium constant expression in terms of molarities considering solvation for the given reaction is: \[K_c = \frac{[Hg_{(solv)}]^4 [O_{2(solv)}]}{[Hg_2O]^2}\]

Step by step solution

01

(a) Writing equilibrium-constant expression in terms of partial pressures

To write the equilibrium constant expression (Kp) for the given reaction, we can use the general formula: \[K_p = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] Where A, B, C, and D are the reaction species in the balanced chemical reaction: aA + bB ⇌ cC + dD, and a, b, c, and d are their respective stoichiometric coefficients. For the given reaction: \[2 Hg_2O(s) \rightleftharpoons 4 Hg(l) + O_2(g)\] The equilibrium constant expression in terms of partial pressures will be: \[K_p = \frac{P_{Hg}^4 P_{O_2}}{(P_{Hg_2O})^2}\]
02

(b) Rewriting the equilibrium-constant expression in terms of molarities considering solvation

To rewrite the equilibrium constant expression in terms of molarities, we'll use the equilibrium constant expression using concentrations (Kc) given by: \[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] As the reaction runs in a solvent that dissolves elemental mercury and elemental oxygen, we should represent their solvation with the (solv) index. Thus, for the given reaction: \[2 Hg_2O(s) \rightleftharpoons 4 Hg_{(solv)} + O_{2(solv)}\] The equilibrium constant expression in terms of molarities considering solvation will be: \[K_c = \frac{[Hg_{(solv)}]^4 [O_{2(solv)}]}{[Hg_2O]^2}\]

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Most popular questions from this chapter

At \(900^{\circ} \mathrm{C}, K_{\mathrm{C}}=0.0108\) for the reaction $$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ A mixture of \(\mathrm{CaCO}_{3}, \mathrm{CaO},\) and \(\mathrm{CO}_{2}\) is placed in a 10.0 - \(\mathrm{L}\) vessel at \(900^{\circ} \mathrm{C}\) . For the following mixtures, will the amount of \(\mathrm{CaCO}_{3}\) increase, decrease, or remain the same as the system approaches equilibrium? \begin{equation} \begin{array}{l}{\text { (a) } 15.0 \mathrm{g} \mathrm{CaCO}_{3}, 15.0 \mathrm{g} \mathrm{CaO}, \text { and } 4.25 \mathrm{gCO}_{2}} \\ {\text { (b) } 2.50 \mathrm{g} \mathrm{CaCO}_{3}, 25.0 \mathrm{g} \mathrm{CaO}, \text { and } 5.66 \mathrm{g} \mathrm{CO}_{2}} \\ {\text { (a) } 30.5 \mathrm{g} \mathrm{CaCO}_{3}, 25.5 \mathrm{g} \mathrm{CaO}, \text { and } 6.48 \mathrm{g} \mathrm{CO}_{2}}\end{array} \end{equation}

Consider the following equilibrium, for which\(K_{p}=0.0752\) at \(480^{\circ} \mathrm{C} :\) $$2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g)$$ \begin{equation} \begin{array}{l}{\text { (a) What is the value of } K_{p} \text { for the reaction }} \\ {4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) ?} \\ {\text { (b) } \mathrm{What} \text { is the value of } K_{p} \text { for the reaction }} \\\ {\mathrm{Cl}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\frac{1}{2} \mathrm{O}_{2}(g) ?} \\ {\text { (c) What is the value of } K_{c} \text { for the reaction in part (b)? }}\end{array} \end{equation}

Two different proteins \(X\) and \(Y\) are dissolved in aqueous solution at \(37^{\circ} \mathrm{C}\) . The proteins bind in a \(1 : 1\) ratio to form \(X Y . A\) solution that is initially 1.00 \(\mathrm{mM}\) in each protein is allowed to reach equilibrium. At equilibrium, 0.20 \(\mathrm{mM}\) of free \(\mathrm{X}\) and 0.20 \(\mathrm{mM}\) of free Y remain. What is \(K_{c}\) for the reaction?

Write the expression for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g)\) (b) \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) (c) \(\mathrm{Ni}(\mathrm{CO})_{4}(g) \rightleftharpoons \mathrm{Ni}(s)+4 \mathrm{CO}(g)\) (d) \(\operatorname{HF}(a q) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\) (e) \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\) (f) \(\mathrm{H}_{2} \mathrm{O}(l) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (g) \(2 \mathrm{H}_{2} \mathrm{O}(I) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+2 \mathrm{OH}^{-}(a q)\)

A \(0.831-\) g sample of \(\mathrm{SO}_{3}\) is placed in a 1.00 -L container and heated to 1100 \(\mathrm{K}\) . The SO \(_{3}\) decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) : $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ At equilibrium, the total pressure in the container is 1.300 atm. Find the values of \(K_{p}\) and \(K_{c}\) for this reaction at 1100 \(\mathrm{K}\) .
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