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Chapter 15: Problem 9

Write the equilibrium constant expressions for \(K_{\mathrm{c}}\) and \(K_{P}\), if applicable, for these reactions: (a) \(2 \mathrm{NO}_{2}(g)+7 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g)\) (c) \(\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)\) (d) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(a q) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(a q)+\mathrm{H}^{+}(a q)\)

Short Answer

Expert verified
\n(a) \(K_c = \frac{[NH_{3}]^2 \cdot [H_{2}O]^4}{[NO_{2}]^2 \cdot [H_{2}]^7}\) and \(K_p = \frac{P_{NH_{3}}^2}{P_{NO_2}^2 \cdot P_{H_{2}}^7}\).\n(b) \(K_c = \frac{[SO_{2}]^2}{[O_{2}]^3}\) and \(K_p = \frac{P_{SO_2}^2}{P_{O_2}^3}\).\n(c) \(K_c = [CO]^2/[CO_2]\) and \(K_p = P_{CO}^2/P_{CO_{2}}\). \n(d) \(K_c = [C_{6}H_{5}COO^-] \cdot [H+]/[C_{6}H_{5}COOH]\)

Step by step solution

01

Determine the \(K_c\) and \(K_p\) for reaction (a)

Reaction (a) involves both gases and liquids. \(K_c\) expression involves concentrations of both reactants and products regardless of their states. Therefore, \(K_c = \frac{[NH_{3}]^2 \cdot [H_{2}O]^4}{[NO_{2}]^2 \cdot [H_{2}]^7}\). For \(K_p\) expression, we only consider gas species. Thus, \(K_p = \frac{P_{NH_{3}}^2}{P_{NO_2}^2 \cdot P_{H_{2}}^7}\).
02

Determine the \(K_c\) and \(K_p\) for reaction (b)

Reaction (b) involves both gases and solids. \(K_c\) expression involves concentrations of both reactants and products. Therefore, \(K_c = \frac{[SO_{2}]^2}{[O_{2}]^3}\) as ZnS and ZnO are omitted due to thier solid states. For \(K_p\) expression, we only consider gas species. Thus, \(K_p = \frac{P_{SO_2}^2}{P_{O_2}^3}\).
03

Determine the \(K_c\) and \(K_p\) for reaction (c)

In reaction (c), as Carbon is a solid, it is omitted from both \(K_c\) and \(K_p\) expressions. Hence, \(K_c = [CO]^2/[CO_2]\) and \(K_p = P_{CO}^2/P_{CO_{2}}\).
04

Determine the \(K_c\) for reaction (d)

Reaction (d) only involves aqueous species and no gas species. Thus, a \(K_p\) expression won't be applicable. For \(K_c\), it would be \(K_c = [C_{6}H_{5}COO^-] \cdot [H+]/[C_{6}H_{5}COOH]\)

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Most popular questions from this chapter

Consider this reaction at equilibrium in a closed container: $$ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ What would happen if (a) the volume is increased, (b) some \(\mathrm{CaO}\) is added to the mixture, (c) some \(\mathrm{CaCO}_{3}\) is removed, (d) some \(\mathrm{CO}_{2}\) is added to the mixture, (e) a few drops of an \(\mathrm{NaOH}\) solution are added to the mixture, (f) a few drops of an \(\mathrm{HCl}\) solution are added to the mixture (ignore the reaction between \(\mathrm{CO}_{2}\) and water \(),(\mathrm{g})\) the temperature is increased?

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) $$ is 54.3 at \(430^{\circ} \mathrm{C}\). At the start of the reaction there are 0.714 mole of \(\mathrm{H}_{2}, 0.984\) mole of \(\mathrm{I}_{2}\), and 0.886 mole of HI in a 2.40-L reaction chamber. Calculate the concentrations of the gases at equilibrium.

The equilibrium constant \(K_{P}\) for the reaction $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ is \(5.60 \times 10^{4}\) at \(350^{\circ} \mathrm{C} . \mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) are mixed initially at 0.350 atm and 0.762 atm, respectively, at \(350^{\circ} \mathrm{C}\). When the mixture equilibrates, is the total pressure less than or greater than the sum of the initial pressures, 1.112 atm?

Consider the reaction $$ \begin{aligned} 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) & \\ \Delta H^{\circ}=&-198.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Comment on the changes in the concentrations of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at equilibrium if we were to \((\mathrm{a})\) increase the temperature, (b) increase the pressure, (c) increase \(\mathrm{SO}_{2},\) (d) add a catalyst, (e) add helium at constant volume.

Consider the gas-phase reaction $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$ Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture (a) at constant pressure and (b) at constant volume.
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