Problem 40
For the synthesis of ammonia: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g) $$ the equilibrium constant \(K_{\mathrm{c}}\) at \(375^{\circ} \mathrm{C}\) is \(1.2 .\) Starting $$ \text { with }\left[\mathrm{H}_{2}\right]_{0}=0.76 M,\left[\mathrm{~N}_{2}\right]_{0}=0.60 M, \text { and }\left[\mathrm{NH}_{3}\right]_{0}=0.48 $$ \(M\), which gases will have increased in concentration and which will have decreased in concentration when the mixture comes to equilibrium?
Problem 41
For the reaction: $$ \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) $$ at \(700^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.534 .\) Calculate the number of moles of \(\mathrm{H}_{2}\) that are present at equilibrium if a mixture of 0.300 mole of \(\mathrm{CO}\) and 0.300 mole of \(\mathrm{H}_{2} \mathrm{O}\) is heated to \(700^{\circ} \mathrm{C}\) in a 10.0 - \(\mathrm{L}\) container.
Problem 42
At \(1000 \mathrm{~K},\) a sample of pure \(\mathrm{NO}_{2}\) gas decomposes: $$ 2 \mathrm{NO}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ The equilibrium constant \(K_{P}\) is 158 . Analysis shows that the partial pressure of \(\mathrm{O}_{2}\) is 0.25 atm at equilibrium. Calculate the pressure of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) in the mixture.
Problem 43
The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftarrows 2 \mathrm{HBr}(g) $$ is \(2.18 \times 10^{6}\) at \(730^{\circ} \mathrm{C}\). Starting with \(3.20 \mathrm{~mol}\) of \(\mathrm{HBr}\) in a 12.0 - \(\mathrm{L}\) reaction vessel, calculate the concentrations of \(\mathrm{H}_{2}, \mathrm{Br}_{2},\) and \(\mathrm{HBr}\) at equilibrium.
Problem 44
The dissociation of molecular iodine into iodine atoms is represented as: $$ \mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g) $$ At \(1000 \mathrm{~K},\) the equilibrium constant \(K_{\mathrm{c}}\) for the reaction is \(3.80 \times 10^{-5}\). Suppose you start with 0.0456 mole of \(I_{2}\) in a 2.30-L flask at \(1000 \mathrm{~K}\). What are the concentrations of the gases at equilibrium?
Problem 45
The dissociation of molecular iodine into iodine atoms is represented as: $$ \mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g) $$ At \(1000 \mathrm{~K},\) the equilibrium constant \(K_{\mathrm{c}}\) for the reaction is \(3.80 \times 10^{-5}\). Suppose you start with 0.0456 mole of \(\mathrm{I}_{2}\) in a 2.30-L flask at \(1000 \mathrm{~K}\). What are the concentrations of the gases at equilibrium?
Problem 46
Consider the following equilibrium process at \(686^{\circ} \mathrm{C}:\) $$ \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftarrows \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ The equilibrium concentrations of the reacting species $$ \text { are }[\mathrm{CO}]=0.050 \mathrm{M},\left[\mathrm{H}_{2}\right]=0.045 \mathrm{M},\left[\mathrm{CO}_{2}\right]=0.086 \mathrm{M} $$ $$ \text { and }\left[\mathrm{H}_{2} \mathrm{O}\right]=0.040 \mathrm{M} $$ (a) Calculate \(K_{\mathrm{c}}\) for the reaction at \(686^{\circ} \mathrm{C} .\) (b) If we add \(\mathrm{CO}_{2}\) to increase its concentration to \(0.50 \mathrm{~mol} / \mathrm{L},\) what will the concentrations of all the gases be when equilibrium is reestablished?
Problem 47
Consider the heterogeneous equilibrium process: $$ \mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftarrows 2 \mathrm{CO}(g) $$ At \(700^{\circ} \mathrm{C},\) the total pressure of the system is found to be \(4.50 \mathrm{~atm}\). If the equilibrium constant \(K_{P}\) is 1.52 , calculate the equilibrium partial pressures of \(\mathrm{CO}_{2}\) and CO.
Problem 48
The equilibrium constant \(K_{\mathrm{c}}\) for the reaction: $$ \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) $$ is 4.2 at \(1650^{\circ} \mathrm{C}\). Initially \(0.80 \mathrm{~mol} \mathrm{H}_{2}\) and \(0.80 \mathrm{~mol}\) \(\mathrm{CO}_{2}\) are injected into a 5.0-L flask. Calculate the concentration of each species at equilibrium.
Problem 49
The aqueous reaction: L-glutamate \(+\) pyruvate \(\rightleftarrows \alpha\) -ketoglutarate \(+\mathrm{L}\) -alanine is catalyzed by the enzyme \(\mathrm{L}\) -glutamate-pyruvate aminotransferase. At \(300 \mathrm{~K},\) the equilibrium constant for the reaction is 1.11 . Predict whether the forward reaction will occur if the concentrations of the reactants and products are [L-glutamate] \(=3.0 \times 10^{-5} \mathrm{M}\), [pyruvate] \(=3.3 \times 10^{-4} M,[\alpha\) -ketoglutarate \(]=1.6 \times 10^{-2} M\), and \([\mathrm{L}\) -alanine \(]=6.25 \times 10^{-3} \mathrm{M}\)
