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Chapter 13: Problem 34

Write expressions for \(K_{\mathrm{p}}\) for the following reactions. a. \(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{CO}_{2}(g)+\mathrm{MgO}(s) \rightleftharpoons \mathrm{MgCO}_{3}(s)\) c. \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) d. \(4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g)\)

Short Answer

Expert verified
The expressions for \(K_p\) for the given reactions are as follows: a. \(K_{p} = \frac{1}{[\mathrm{O}_{2}]^{\frac{3}{2}}}\) b. \(K_{p} = \frac{1}{[\mathrm{CO}_{2}]}\) c. \(K_{p} = \frac{[\mathrm{CO}][\mathrm{H}_{2}]}{[\mathrm{H}_{2}\mathrm{O}]}\) d. \(K_{p} = \frac{[\mathrm{O}_{2}]^3}{[\mathrm{H}_{2}\mathrm{O}]^2}\)

Step by step solution

01

Reaction a

\(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) For reaction a, we have the following equilibrium: \(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) Since the Kp expression includes only the partial pressures of gases, we will not include Fe(s) and Fe鈧侽鈧�(s) in the expression. Thus, the expression for Kp for reaction a is: \(K_{p} = \frac{1}{[\mathrm{O}_{2}]^{\frac{3}{2}}}\)
02

Reaction b

\(\mathrm{CO}_{2}(g)+\mathrm{MgO}(s) \rightleftharpoons \mathrm{MgCO}_{3}(s)\) For reaction b, we have the following equilibrium: \(\mathrm{CO}_{2}(g)+\mathrm{MgO}(s) \rightleftharpoons \mathrm{MgCO}_{3}(s)\) Since the Kp expression includes only the partial pressures of gases, we will not include MgO(s) and MgCO鈧�(s) in the expression. Thus, the expression for Kp for reaction b is: \(K_{p} = \frac{1}{[\mathrm{CO}_{2}]}\)
03

Reaction c

\(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) For reaction c, we have the following equilibrium: \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) Since the Kp expression includes only the partial pressures of gases, we will not include C(s) in the expression. Thus, the expression for Kp for reaction c is: \(K_{p} = \frac{[\mathrm{CO}][\mathrm{H}_{2}]}{[\mathrm{H}_{2}\mathrm{O}]}\)
04

Reaction d

\(4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g)\) For reaction d, we have the following equilibrium: \(4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g)\) Since the Kp expression includes only the partial pressures of gases, we will not include KO鈧�(s) and KOH(s) in the expression. Thus, the expression for Kp for reaction d is: \(K_{p} = \frac{[\mathrm{O}_{2}]^3}{[\mathrm{H}_{2}\mathrm{O}]^2}\)

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Most popular questions from this chapter

Ethyl acetate is synthesized in a nonreacting solvent (not water) according to the following reaction: \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \quad K=2.2\) \(\begin{array}{ll}\text { Acetic acid } & \text { Ethanol } & \text { Ethyl acetate }\end{array}\) For the following mixtures \((\mathrm{a}-\mathrm{d})\), will the concentration of \(\mathrm{H}_{2} \mathrm{O}\) increase, decrease, or remain the same as equilibrium is established? a. \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=0.22 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}\right]=0.10 \mathrm{M}\), \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.010 \mathrm{M},\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=0.010 \mathrm{M}\) b. \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=0.22 M,\left[\mathrm{H}_{2} \mathrm{O}\right]=0.0020 M\), \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.0020 \mathrm{M},\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=0.10 \mathrm{M}\) c. \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=0.88 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}\right]=0.12 \mathrm{M}\), \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.044 M,\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=6.0 \mathrm{M}\) d. \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=4.4 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}\right]=4.4 \mathrm{M}\), \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.88 \mathrm{M},\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=10.0 \mathrm{M}\) e. What must the concentration of water be for a mixture with \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=2.0 \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.10 \mathrm{M}\), and \(\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]\) \(=5.0 M\) to be at equilibrium? f. Why is water included in the equilibrium expression for this reaction?

At \(327^{\circ} \mathrm{C}\), the equilibrium concentrations are \(\left[\mathrm{CH}_{3} \mathrm{OH}\right]=0.15 \mathrm{M}\), \([\mathrm{CO}]=0.24 M\), and \(\left[\mathrm{H}_{2}\right]=1.1 M\) for the reaction $$ \mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) $$ Calculate \(K_{\mathrm{p}}\) at this temperature.

Nitric oxide and bromine at initial partial pressures of \(98.4\) and \(41.3\) torr, respectively, were allowed to react at \(300 . \mathrm{K}\). At equilibrium the total pressure was \(110.5\) torr. The reaction is $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ a. Calculate the value of \(K_{\mathrm{p}}\). b. What would be the partial pressures of all species if \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\), both at an initial partial pressure of \(0.30 \mathrm{~atm}\), were allowed to come to equilibrium at this temperature?

Novelty devices for predicting rain contain cobalt(II) chloride and are based on the following equilibrium: $$ \underset{\text { Purple }}{\mathrm{CoCl}_{2}(s)}+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \underset{\text { Pink }}{\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s)} $$ What color will such an indicator be if rain is imminent?

At \(900^{\circ} \mathrm{C}, K_{\mathrm{p}}=1.04\) for the reaction $$ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ At a low temperature, dry ice (solid \(\mathrm{CO}_{2}\) ), calcium oxide, and calcium carbonate are introduced into a 50.0-L reaction chamber. The temperature is raised to \(900^{\circ} \mathrm{C}\), resulting in the dry ice converting to gaseous \(\mathrm{CO}_{2} .\) For the following mixtures, will the initial amount of calcium oxide increase, decrease, or remain the same as the system moves toward equilibrium at \(900{ }^{\circ} \mathrm{C}\) ? a. \(655 \mathrm{~g} \mathrm{CaCO}_{3}, 95.0 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=2.55 \mathrm{~atm}\) b. \(780 \mathrm{~g} \mathrm{CaCO}_{3}, 1.00 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=1.04 \mathrm{~atm}\) c. \(0.14 \mathrm{~g} \mathrm{CaCO}_{3}, 5000 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=1.04 \mathrm{~atm}\) d. \(715 \mathrm{~g} \mathrm{CaCO}_{3}, 813 \mathrm{~g} \mathrm{CaO}, P_{\mathrm{CO}_{2}}=0.211 \mathrm{~atm}\)
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