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Chapter 15: Problem 13

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) \(\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\) (e) \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\)

Short Answer

Expert verified
(a) Homogeneous. \(K_c = \frac{[\mathrm{N}_{2}\mathrm{O}][\mathrm{NO}_{2}]}{[\mathrm{NO}]^3}\) (b) Homogeneous. \(K_c = \frac{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^4}{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^2}\) (c) Heterogeneous. \(K_c = [\mathrm{CO}]^4\) (d) Homogeneous. \(K_c = \frac{[\mathrm{H}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\) (e) Heterogeneous. \(K_c = \frac{[\mathrm{Ag}^+]^2}{[\mathrm{Zn}^{2+}]}\)

Step by step solution

01

(a) Identify reaction type and write Kc expression

The reaction is given as: \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g)\) All species are in the gas phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{N}_{2}\mathrm{O}][\mathrm{NO}_{2}]}{[\mathrm{NO}]^3}\]
02

(b) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) All species are in the gas phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^4}{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^2}\]
03

(c) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{Ni}(\mathrm{CO})_{4}(g) \rightleftharpoons \mathrm{Ni}(s)+4 \mathrm{CO}(g)\) We have one species in the gas phase and one in the solid phase, so the reaction is heterogeneous. The expression for Kc is: \[K_c = [\mathrm{CO}]^4\] (Since the concentration of solid Ni is constant, it is not included in the Kc expression)
04

(d) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\) All species are in the aqueous phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{H}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\]
05

(e) Identify reaction type and write Kc expression

The reaction is given as: \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\) We have species in the aqueous and solid phases, so the reaction is heterogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{Ag}^+]^2}{[\mathrm{Zn}^{2+}]}\] (The concentrations of solid Ag and Zn are constant and not included in the Kc expression)

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Most popular questions from this chapter

If \(K_{c}=1\) for the equilibrium \(2 \mathrm{~A}(g) \rightleftharpoons \mathrm{B}(g)\), what is the relationship between [A] and [B] at equilibrium?

(a) At \(800 \mathrm{~K}\) the equilibrium constant for \(\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)\) is \(K_{c}=3.1 \times 10^{-5} .\) If an equilibrium mixture in a 10.0-L vessel contains \(2.67 \times 10^{-2} \mathrm{~g}\) of \(\mathrm{I}(\mathrm{g})\), how many grams of \(I_{2}\) are in the mixture? (b) For \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \quad K_{p}=3.0 \times 10^{4}\) \(700 \mathrm{~K}\). In a 2.00-L vessel the equilibrium mixture contains \(1.17 \mathrm{~g}\) of \(\mathrm{SO}_{3}\) and \(0.105 \mathrm{~g}\) of \(\mathrm{O}_{2}\). How many grams of \(\mathrm{SO}_{2}\) are in the vessel?

Consider the hypothetical reaction \(\mathrm{A}(\mathrm{g})+2 \mathrm{~B}(\mathrm{~g})=\) \(2 \mathrm{C}(\mathrm{g})\), for which \(K_{c}=0.25\) at some temperature. A 1.00-L reaction vessel is loaded with \(1.00 \mathrm{~mol}\) of compound \(\mathrm{C}\), which is allowed to reach equilibrium. Let the variable \(x\) represent the number of \(\mathrm{mol} / \mathrm{L}\) of compound A present at equilibrium. (a) In terms of \(x\), what are the equilibrium concentrations of compounds \(\mathrm{B}\) and \(\mathrm{C}\) ? (b) What limits must be placed on the value of \(x\) so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of \(x\) ) into the equilibriumconstant expression, derive an equation that can be solved for \(x\). (d) The equation from part (c) is a cubic equation (one that hasthe form \(a x^{3}+b x^{2}+c x+d=0\) ) In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of \(x\) that you specified in part (b). The point at which the cubic equation crosses the \(x\) -axis is the solution. (e) From the plot in part (d), estimate the equilibrium concentrations of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

When \(1.50 \mathrm{~mol} \mathrm{CO}_{2}\) and \(1.50 \mathrm{~mol} \mathrm{H}_{2}\) are placed in a \(0.750-\mathrm{L}\) container at \(395^{\circ} \mathrm{C}\), the following equilibrium is achieved: \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) .\) If \(K_{c}=0.802\), what are the concentrations of each substance in the equilibrium mixture?

A flask is charged with \(1.500\) atm of \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) and \(1.00 \mathrm{~atm} \mathrm{NO}_{2}(g)\) at \(25^{\circ} \mathrm{C}\), and the following equilibrium is achieved: $$ \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$ After equilibrium is reached, the partial pressure of \(\mathrm{NO}_{2}\) is \(0.512\) atm. (a) What is the equilibrium partial pressure of \(\mathrm{N}_{2} \mathrm{O}_{4} ?\) (b) Calculate the value of \(K_{p}\) for the reaction.
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