Problem 47
At \(450^{\circ} \mathrm{C}, 3.60\) mol of ammonia is placed in a \(2.00-\mathrm{L}\) vessel and allowed to decompose to the elements. $$ 2 \mathrm{NH}_{3}(\mathrm{g}) \rightleftarrows \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) $$ If the experimental value of \(K\) is 6.3 for this reaction at this temperature, calculate the equilibrium concentration of each reagent. What is the total pressure in the flask?
Problem 48
The total pressure for a mixture of \(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\) is 1.5 atm. If \(K_{p}=6.75\) (at \(25^{\circ} \mathrm{C}\) ), calculate the partial pressure of each gas in the mixture. $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) $$
Problem 49
\(K_{c}\) for the decomposition of ammonium hydrogen sulfide is \(1.8 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftarrows \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ (a) When the pure salt decomposes in a flask, what are the equilibrium concentrations of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{S} ?\) (b) If \(\mathrm{NH}_{1} \mathrm{HS}\) is placed in a flask already containing \(0.020 \mathrm{mol} / \mathrm{L}\) of \(\mathrm{NH}_{3}\) and then the system is allowed to come to equilibrium, what are the equilibrium concentrations of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{S} ?\)
Problem 54
Sulfuryl chloride, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\), is a compound with very irritating vapors; it is used as a reagent in the synthesis of organic compounds. When heated to a sufficiently high temperature it decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\). \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \quad K=0.045\) at \(375^{\circ} \mathrm{C}\) (a) Suppose \(6.70 \mathrm{g}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a \(1.00-\mathrm{L}\). flask and then heated to \(375^{\circ} \mathrm{C}\). What is the concentration of each of the compounds in the system when equilibrium is achieved? What fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) has dissociated? (b) What are the concentrations of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{SO}_{2},\) and \(\mathrm{Cl}_{2}\) at equilibrium in the \(1.00-\mathrm{L}\) flask at \(375^{\circ} \mathrm{C}\) if you begin with a mixture of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(6.70 \mathrm{g})\) and \(\mathrm{Cl}_{2}(1.00 \mathrm{atm}) ?\) What fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) has dissociated? (c) Compare the fractions of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) in parts (a) and (b). Do they agree with your expectations based on Le Chatelier's principle?
Problem 55
Hemoglobin (Hb) can form a complex with both \(\mathrm{O}_{2}\) and CO. For the reaction $$ \mathrm{HbO}_{2}(\mathrm{aq})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{HbCO}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g}) $$ at body temperature, \(K\) is about \(200 .\) If the ratio \([\mathrm{HbCO}] /\left[\mathrm{HbO}_{2}\right]\) comes close to \(1,\) death is probable. What partial pressure of CO in the air is likely to be fatal? Assume the partial pressure of \(\mathrm{O}_{2}\) is \(0.20 \mathrm{atm}\).
Problem 56
Limestone decomposes at high temperatures. $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftarrows \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ At \(1000^{\circ} \mathrm{C}, K_{\mathrm{p}}=3.87 .\) If pure \(\mathrm{CaCO}_{3}\) is placed in a \(5.00-\mathrm{I}\) flask and heated to \(1000^{\circ} \mathrm{C},\) what quantity of \(\mathrm{CaCO}_{3}\) must decompose to achieve the equilibrium pressure of \(\mathrm{CO}_{2} ?\)
Problem 57
At \(1800 \mathrm{K}\), oxygen dissociates very slightly into its atoms. $$ \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{O}(\mathrm{g}) \quad K_{\mathrm{p}}=1.2 \times 10^{-10} $$ If you place 1.0 mol of \(\mathrm{O}_{2}\) in a \(10 .\).I. vessel and heat it to \(1800 \mathrm{K},\) how many \(\mathrm{O}\) atoms are present in the flask?
Problem 59
A Boric acid and glycerin form a complex \(\mathrm{B}(\mathrm{OH})_{3}(\mathrm{aq})+\) glycerin \((\mathrm{aq}) \rightleftarrows \mathrm{B}(\mathrm{OH})_{3} \cdot\) glycerin \((\mathrm{aq})\) with an equilibrium constant of \(0.90 .\) If the concentration of boric acid is \(0.10 \mathrm{M}\), how much glycerin should be added, per liter, so that \(60 . \%\) of the boric acid is in the form of the complex?
Problem 61
A A sample of \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas with a pressure of \(1.00 \mathrm{atm}\) is placed in a flask. When equilibrium is achieved, \(20.0 \%\) of the \(\mathrm{N}_{2} \mathrm{O}_{4}\) has been converted to \(\mathrm{NO}_{2}\) gas. (a) Calculate \(K_{\mathrm{p}}\) (b) If the original pressure of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is 0.10 atm, what is the percent dissociation of the gas? Is the result in agree. ment with Le Chatelier's principle?
Problem 62
The equilibrium constant, \(K_{\mathrm{p}}\), is 0.15 at \(25^{\circ} \mathrm{C}\) for the following reaction: $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}_{2}(\mathrm{g}) $$ If the total pressure of the gas mixture is 2.5 atm at equilibrium, what is the partial pressure of each gas?
