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Chapter 12: Problem 9

Given the following descriptions of reversible reactions, write a balanced equation (simplest whole-number coefficients) and the equilibrium constant expression \((K)\) for each. (a) Nitrogen gas reacts with solid sodium carbonate and solid carbon to produce carbon monoxide gas and solid sodium cyanide. (b) Solid magnesium nitride reacts with water vapor to form magnesium hydroxide solid and ammonia gas. (c) Ammonium ion in aqueous solution reacts with a strong base at \(25^{\circ} \mathrm{C}\), giving aqueous ammonia and water. (c) Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) bubbled into an aqueous solution of lead(II) ions produces lead sulfide precipitate and hydrogen ions.

Short Answer

Expert verified
#Answer# a) \(K = \frac{[\mathrm{CO}]^3}{[\mathrm{N}_2]}\) b) \(K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2\mathrm{O}]^6}\) c) \(K = \frac{[\mathrm{NH}_3]}{[\mathrm{NH}_4^+][\mathrm{OH}^-]}\) d) \(K = \frac{[\mathrm{H}^+]^2}{[\mathrm{H}_2\mathrm{S}][\mathrm{Pb}^{2+}]}\)

Step by step solution

01

a) Nitrogen gas reacts with solid sodium carbonate and solid carbon

Write the balanced chemical equation for this reaction: $$ \mathrm{N}_2(g) + 2\mathrm{Na}_2\mathrm{CO}_3(s) + 3\mathrm{C}(s) \rightleftharpoons 2\mathrm{NaCN}(s) + 3\mathrm{CO}(g) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{CO}]^3}{[\mathrm{N}_2]} $$ Keep in mind that the concentrations of pure solids (like \(\mathrm{Na}_2\mathrm{CO}_3\), \(\mathrm{C}\), and \(\mathrm{NaCN}\)) are not included in the equilibrium expression.
02

b) Solid magnesium nitride reacts with water vapor

Write the balanced chemical equation for this reaction: $$ \mathrm{Mg}_3\mathrm{N}_2(s) + 6\mathrm{H}_2\mathrm{O}(g) \rightleftharpoons 3\mathrm{Mg(OH)}_2(s) + 2\mathrm{NH}_3(g) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2\mathrm{O}]^6} $$ Again, the concentrations of pure solids (like \(\mathrm{Mg}_3\mathrm{N}_2\) and \(\mathrm{Mg(OH)}_2\)) are not included in the equilibrium expression.
03

c) Ammonium ion in aqueous solution reacts with a strong base

Write the balanced chemical equation for this reaction: $$ \mathrm{NH}_4^+(aq) + \mathrm{OH}^-(aq) \rightleftharpoons \mathrm{NH}_3(aq) + \mathrm{H}_2\mathrm{O}(l) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{NH}_3]}{[\mathrm{NH}_4^+][\mathrm{OH}^-]} $$ In this case, water is not included in the equilibrium expression because it is a pure liquid.
04

d) Hydrogen sulfide gas reacts with lead(II) ions in an aqueous solution

Write the balanced chemical equation for this reaction: $$ \mathrm{H}_2\mathrm{S}(g) + \mathrm{Pb}^{2+}(aq) \rightleftharpoons \mathrm{PbS}(s) + 2\mathrm{H}^+(aq) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{H}^+]^2}{[\mathrm{H}_2\mathrm{S}][\mathrm{Pb}^{2+}]} $$ In this case, the concentration of pure solid lead sulfide (PbS) is not included in the equilibrium expression.

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Most popular questions from this chapter

At a certain temperature, \(K\) is \(1.3 \times 10^{5}\) for the reaction $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)$$ What is the equilibrium pressure of hydrogen sulfide if those of hydrogen and sulfur gases are \(0.103\) atm and \(0.417\) atm, respectively?

The reaction $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ has an equilibrium constant of \(1.30\) at \(650^{\circ} \mathrm{C}\). Carbon monoxide and steam both have initial partial pressures of \(0.485 \mathrm{~atm}\), while hydrogen and carbon dioxide start with partial pressures of \(0.159\) atm. (a) Calculate the partial pressure of each gas at equilibrium. (b) Compare the total pressure initially with the total pressure at equilibrium. Would that relation be true of all gaseous systems?

At \(1800 \mathrm{~K}\), oxygen dissociates into gaseous atoms: $$\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)$$ \(K\) for the system is \(1.7 \times 10^{-8} .\) If one mole of oxygen molecules is placed in a \(5.0\) -L flask and heated to \(1800 \mathrm{~K}\), what percentage by mass of the oxygen dissociates? How many \(\mathrm{O}\) atoms are in the flask?

For the reaction $$\mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g)$$ \(K\) is \(1.54 \times 10^{-3}\). When equilibrium is established, the partial pressure of nitrogen is \(0.168 \mathrm{~atm}\), and that of \(\mathrm{NO}\) is \(0.225 \mathrm{~atm}\). The total pressure of the system at equilibrium is \(1.87 \mathrm{~atm}\). What are the equilibrium partial pressures of hydrogen and steam?

WEB Consider the following reaction at \(122^{\circ} \mathrm{C}\) : $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ (a) Write an equilibrium constant expression for the reaction and call the constant \(K_{1}\). (b) Write an equilibrium constant expression for the decomposition of one mole of \(\mathrm{SO}_{3}\) to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) and call the constant \(K_{2}\). (c) Relate \(K_{1}\) and \(K_{2}\).
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