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Chapter 15: Problem 16

Write the expressions for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\) (b) \(\mathrm{Ti}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{TiCl}_{4}(l)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g)\) (d) \(\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)\) (e) \(4 \mathrm{HCl}(a q)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{Cl}_{2}(g)\) (f) \(2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \rightleftharpoons 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g)\) (g) \(2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \rightleftharpoons 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(l)\)

Short Answer

Expert verified
(a) Homogeneous reaction. Kc expression: \[K_c = \frac{[O_2]^3}{[O_3]^2}\] (b) Heterogeneous reaction. Kc expression: \[K_c = \frac{[TiCl_4]}{[Cl_2]^2}\] (c) Homogeneous reaction. Kc expression: \[K_c = \frac{[C_2H_6]^2 [O_2]}{[C_2H_4]^2 [H_2O]^2}\] (d) Heterogeneous reaction. Kc expression: \[K_c = \frac{[CH_4]}{[H_2]^2}\] (e) Homogeneous reaction. Kc expression: \[K_c = \frac{[H_2O]^2 [Cl_2]^2}{[HCl]^4 [O_2]}\] (f) Heterogeneous reaction. Kc expression: \[K_c = \frac{[CO_2]^{16} [H_2O]^{18}}{[C_8H_{18}]^2 [O_2]^{25}}\] (g) Heterogeneous reaction. Kc expression: \[K_c = \frac{[CO_2]^{16} [H_2O]^{18}}{[C_8H_{18}]^2 [O_2]^{25}}\]

Step by step solution

01

(a) Reaction:

\(2 O_3(g) \rightleftharpoons 3 O_2(g) \) This reaction is homogeneous since all species are in the gas phase.
02

(a) Kc expression:

\[K_c = \frac{[O_2]^3}{[O_3]^2} \]
03

(b) Reaction:

\( Ti(s) + 2 Cl_2(g) \rightleftharpoons TiCl_4(l) \) This reaction is heterogeneous since species are present in different phases (solid, liquid, and gas).
04

(b) Kc expression:

\[K_c = \frac{[TiCl_4]}{[Cl_2]^2} \]
05

(c) Reaction:

\( 2 C_2H_4(g) + 2 H_2O(g) \rightleftharpoons 2 C_2H_6(g) + O_2(g) \) This reaction is homogeneous since all species are in the gas phase.
06

(c) Kc expression:

\[K_c = \frac{[C_2H_6]^2 [O_2]}{[C_2H_4]^2 [H_2O]^2} \]
07

(d) Reaction:

\( C(s) + 2 H_2(g) \rightleftharpoons CH_4(g) \) This reaction is heterogeneous since species are present in different phases (solid and gas).
08

(d) Kc expression:

\[K_c = \frac{[CH_4]}{[H_2]^2} \]
09

(e) Reaction:

\( 4 HCl(aq) + O_2(g) \rightleftharpoons 2 H_2O(l) + 2 Cl_2(g) \) This reaction is homogeneous since all species are either in the gas or aqueous phase.
10

(e) Kc expression:

\[K_c = \frac{[H_2O]^2 [Cl_2]^2}{[HCl]^4 [O_2]} \]
11

(f) Reaction:

\( 2 C_8H_{18}(l) + 25 O_2(g) \rightleftharpoons 16 CO_2(g) + 18 H_2O(g) \) This reaction is heterogeneous since species are present in different phases (liquid and gas).
12

(f) Kc expression:

\[K_c = \frac{[CO_2]^{16} [H_2O]^{18}}{[C_8H_{18}]^2 [O_2]^{25}} \]
13

(g) Reaction:

\( 2 C_8H_{18}(l) + 25 O_2(g) \rightleftharpoons 16 CO_2(g) + 18 H_2O(l) \) This reaction is heterogeneous since species are present in different phases (liquid and gas).
14

(g) Kc expression:

\[K_c = \frac{[CO_2]^{16} [H_2O]^{18}}{[C_8H_{18}]^2 [O_2]^{25}} \]

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Most popular questions from this chapter

A mixture of \(\mathrm{CH}_{4}\) and \(\mathrm{H}_{2} \mathrm{O}\) is passed over a nickel catalyst at \(1000 \mathrm{~K}\). The emerging gas is collected in a \(5.00-\mathrm{L}\) flask and is found to contain \(8.62 \mathrm{~g}\) of \(\mathrm{CO}, 2.60 \mathrm{~g}\) of \(\mathrm{H}_{2}, 43.0 \mathrm{~g}\) of \(\mathrm{CH}_{4},\) and \(48.4 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Assuming that equilibrium has been reached, calculate \(K_{c}\) and \(K_{p}\) for the reaction.

Suppose that you worked at the U.S. Patent Office and a patent application came across your desk claiming that a newly developed catalyst was much superior to the Haber catalyst for ammonia synthesis because the catalyst led to much greater equilibrium conversion of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) into \(\mathrm{NH}_{3}\) than the Haber catalyst under the same conditions. What would be your response?

At \(25^{\circ} \mathrm{C}\) the reaction $$\mathrm{CaCrO}_{4}(s) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{CrO}_{4}^{2-}(a q)$$ has an equilibrium constant \(K_{c}=7.1 \times 10^{-4}\). What are the equilibrium concentrations of \(\mathrm{Ca}^{2+}\) and \(\mathrm{CrO}_{4}^{2-}\) in a saturated solution of \(\mathrm{CaCrO}_{4} ?\)

At \(100^{\circ} \mathrm{C}, K_{c}=0.078\) for the reaction $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ In an equilibrium mixture of the three gases, the concentrations of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) and \(\mathrm{SO}_{2}\) are \(0.108 \mathrm{M}\) and \(0.052 \mathrm{M}\), respectively. What is the partial pressure of \(\mathrm{Cl}_{2}\) in the equilibrium mixture?

Consider the equilibrium $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ Calculate the equilibrium constant \(K_{p}\) for this reaction, given the following information (at \(298 \mathrm{~K}\) ): $$\begin{aligned} 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) & \rightleftharpoons 2 \mathrm{NOBr}(g) & K_{c} &=2.0 \\ 2 \mathrm{NO}(g) & \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & K_{c} &=2.1 \times 10^{30} \end{aligned}$$
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