Chapter 16

Write equilibrium constant expressions for the following reactions. For gases, use either pressures or concentrations. (a) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) (b) \(\mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows \mathrm{CO}_{2}(\mathrm{g})\) (c) \(\mathbf{C}(\mathrm{s})+\mathbf{C O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathbf{C O}(\mathrm{g})\) (d) \(\mathrm{NiO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Ni}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\)

Write equilibrium constant expressions for the following reactions. For gases, use either pressures orl concentrations. (a) \(3 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{O}_{3}(\mathrm{g})\) (b) \(\mathrm{Fe}(\mathrm{s})+5 \mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{g})\) (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(\mathrm{s}) \rightleftarrows 2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{s}) \rightleftarrows 2 \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\)

\(K_{c}=5.6 \times 10^{-12}\) at \(500 \mathrm{K}\) for the dissociation of iodine molecules to iodine atoms. $$ \mathrm{I}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{I}(\mathrm{g}) $$ A mixture has \(\left[\mathrm{I}_{2}\right]=0.020 \mathrm{mol} / \mathrm{L}\) and \([\mathrm{I}]=2.0 \times\) \(\left.10^{-8} \mathrm{mol} / \mathrm{L} . \text { Is the reaction at equilibrium (at } 500 \mathrm{K}\right) ?\) If not, which way must the reaction proceed to reach equilibrium?

The reaction $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) $$ has an equilibrium constant, \(K_{c},\) of 170 at \(25^{\circ} \mathrm{C} .\) If \(2.0 \times 10^{-3} \mathrm{mol}\) of \(\mathrm{NO}_{2}\) is present in a \(10 .-\mathrm{L}\). flask along with \(1.5 \times 10^{-3}\) mol of \(\mathrm{N}_{2} \mathrm{O}_{4},\) is the system at equilibrium? If it is not at equilibrium, does the concentration of \(\mathrm{NO}_{2}\) increase or decrease as the system proceeds to equilibrium?

A mixture of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at \(1000 \mathrm{K}\) contains the gases at the following concentrations: \(\left[\mathrm{SO}_{2}\right]=\) $$ 5.0 \times 10^{-3} \mathrm{mol} / \mathrm{L},\left[\mathrm{O}_{2}\right]=1.9 \times 10^{-3} \mathrm{mol} / \mathrm{L}, \text { and } $$ \(\left[\mathrm{SO}_{3}\right]=6.9 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilib- rium? If not, which way will the reaction proceed to reach equilibrium? $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{SO}_{3}(\mathrm{g}) K_{\mathrm{c}}=279 $$

The equilibrium constant, \(K_{c}\), for the reaction $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ is \(3.9 \times 10^{-3}\) at \(300^{\circ} \mathrm{C} .\) A mixture contains the gases at the following concentrations: \([\mathrm{NOCl}]=\) \(5.0 \times 10^{-3} \mathrm{mol} / \mathrm{L},[\mathrm{NO}]=2.5 \times 10^{-3} \mathrm{mol} / \mathrm{L},\) and \(\left[\mathrm{Cl}_{2}\right]=2.0 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilib- rium at \(300^{\circ} \mathrm{C}\) ? If not, in which direction does the reaction proceed to come to equilibrium?

The reaction $$ \mathrm{PCl}_{5}(\mathrm{g}) \rightleftarrows \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ was examined at \(250^{\circ} \mathrm{C}\). At equilibrium, \(\left[\mathrm{PC} 1_{5}\right]=\) \(4.2 \times 10^{-5} \mathrm{mol} / \mathrm{L},\left[\mathrm{PCl}_{3}\right]=1.3 \times 10^{-2} \mathrm{mol} / \mathrm{I},\) and \(\left[\mathrm{Cl}_{2}\right]=3.9 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\mathrm{c}}\) for the reaction.

An equilibrium mixture of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at a high temperature contains the gases at the following concentrations: \(\left[\mathrm{SO}_{2}\right]=3.77 \times 10^{-3} \mathrm{mol} / \mathrm{L},\left[\mathrm{O}_{2}\right]=\) \(4.30 \times 10^{-3} \mathrm{mol} / \mathrm{L},\) and \(\left[\mathrm{SO}_{3}\right]=4.13 \times 10^{-3} \mathrm{mol} / \mathrm{L}\) Calculate the equilibrium constant, \(K_{c}\), for the reaction. $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{SO}_{3}(\mathrm{g}) $$

The reaction $$ \mathrm{C}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{CO}(\mathrm{g}) $$ occurs at high temperatures. At \(700^{\circ} \mathrm{C},\) a \(2.0-\mathrm{L}\) flask contains 0.10 mol of \(\mathrm{CO}, 0.20 \mathrm{mol}\) of \(\mathrm{CO}_{2}\) and 0.40 mol of \(\mathrm{C}\) at equilibrium. (a) Calculate \(K_{c}\) for the reaction at \(700^{\circ} \mathrm{C}\) (b) Calculate \(K_{c}\) for the reaction, also at \(700^{\circ} \mathrm{C},\) if the amounts at equilibrium in the 2.0 -I. flask are 0.10 mol of \(\mathrm{CO}, 0.20 \mathrm{mol}\) of \(\mathrm{CO}_{2},\) and \(0.80 \mathrm{mol}\) of C. (c) Compare the results of (a) and (b). Does the quantity of carbon affect the value of \(K_{c} ?\) Explain.

Hydrogen and carbon dioxide react at a high temperature to give water and carbon monoxide. $$ \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) $$ (a) Laboratory measurements at \(986^{\circ} \mathrm{C}\) show that there are 0.11 mol each of \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) vapor and 0.087 mol each of \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) at equilibrium in a 1.0-L container. Calculate the equilibrium constant for the reaction at \(986^{\circ} \mathrm{C}\) (b) Suppose 0.050 mol each of \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) are placed in a \(2.0-\mathrm{L}\) container. When equilibrium is achieved at \(986^{\circ} \mathrm{C},\) what amounts of \(\mathrm{CO}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}),\) in moles, would be present? [Use the value of \(K_{\mathrm{c}}\) from part \((a) .]\)

A mixture of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) is placed in a reaction flask: \([\mathrm{CO}]=0.0102 \mathrm{mol} / \mathrm{L}\) and \(\left[\mathrm{Cl}_{2}\right]=0.00609 \mathrm{mol} / \mathrm{L}\) When the reaction $$ \mathbf{C O}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \operatorname{COCl}_{2}(\mathrm{g}) $$ has come to equilibrium at \(600 \mathrm{K},\left[\mathrm{Cl}_{2}\right]=\) \(0.00301 \mathrm{mol} / \mathrm{L}\) (a) Calculate the concentrations of \(\mathrm{CO}\) and \(\mathrm{COCl}_{2}\) at equilibrium. (b) Calculate \(K_{c}\).

You place 3.00 mol of pure \(\mathrm{SO}_{3}\) in an \(8.00-\mathrm{L}\). flask at \(1150 \mathrm{K}\). At equilibrium, 0.58 mol of \(\mathrm{O}_{2}\) has been formed. Calculate \(K_{c}\) for the reaction at \(1150 \mathrm{K}\). $$ 2 \mathrm{sO}_{3}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) $$

The equilibrium constant for the dissociation of iodine molecules to iodine atoms $$ \mathrm{I}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{I}(\mathrm{g}) $$ is \(3.76 \times 10^{-3}\) at \(1000 \mathrm{K}\). Suppose 0.105 mol of \(\mathrm{I}_{2}\) is placed in a \(12.3-\mathrm{L}\). flask at \(1000 \mathrm{K}\). What are the concentrations of \(\mathrm{I}_{2}\) and \(\mathrm{I}\) when the system comes to equilibrium?

The equilibrium constant, \(K_{c}\), for the reaction $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}_{2}(\mathrm{g}) $$ at \(25^{\circ} \mathrm{C}\) is \(170 .\) Suppose \(15.6 \mathrm{g}\) of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is placed in a \(5.000-\mathrm{L}\) flask at \(25^{\circ} \mathrm{C} .\) Calculate the following: (a) the amount of \(\mathrm{NO}_{2}\) (mol) present at equilibrium; (b) the percentage of the original \(\mathrm{N}_{2} \mathrm{O}_{4}\) that is dissociated.

Carbonyl bromide decomposes to carbon monoxide and bromine. $$ \operatorname{COBr}_{2}(\mathrm{g}) \rightleftarrows \mathrm{CO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ \(K_{c}\) is 0.190 at \(73^{\circ} \mathrm{C} .\) If you place 0.500 mol of \(\mathrm{COBr}_{2}\) in a \(2.00-\mathrm{L}\). flask and heat it to \(73^{\circ} \mathrm{C},\) what are the equilibrium concentrations of \(\mathrm{COBr}_{2}, \mathrm{CO},\) and \(\mathrm{Br}_{2} ?\) What percentage of the original \(\mathrm{COBr}_{2}\) decomposed at this temperature?

Which of the following correctly relates the equilibrium constants for the two reactions shown? \(A+B \rightleftarrows 2 C \quad K_{1}\) \(2 \mathrm{A}+2 \mathrm{B} \rightleftharpoons 4 \mathrm{C} \quad K_{2}\) (a) \(K_{2}=2 K_{1} \quad\) (c) \(K_{2}=1 / K_{1}\) (b) \(K_{2}=K_{1}^{2}\) (d) \(K_{2}=1 / K_{1}^{2}\)

Which of the following correctly relates the equilibrium constants for the two reactions shown? \(A+B \rightleftarrows 2 C \quad K_{1}\) \(\mathrm{C} \rightleftarrows 1 / 2 \mathrm{A}+1 / 2 \mathrm{B} \quad K_{2}\) (a) \(K_{2}=1 /\left(K_{1}\right)^{1 / 2}\) (c) \(K_{2}=K_{1}^{2}\) (b) \(K_{2}=1 / K_{1}\) (d) \(K_{2}=-K_{1}^{1 / 2}\)

Consider the following equilibria involving \(\mathrm{SO}_{2}(\mathrm{g})\) and their corresponding equilibrium constants. \(\mathrm{SO}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows \mathrm{SO}_{3}(\mathrm{g}) \quad K_{1}\) \(2 \mathrm{sO}_{3}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \quad K_{2}\) Which of the following expressions relates \(K_{1}\) to \(K_{2} ?\) (a) \(K_{2}=K_{1}^{2}\) (d) \(K_{2}=1 / K_{1}\) (b) \(K_{2}^{2}=K_{1}\) (e) \(K_{2}=1 / K_{1}^{2}\) (c) \(K_{2}=K_{1}\)

The equilibrium constant \(K\) for the reaction $$ \mathrm{CO}_{2}(\mathrm{g}) \rightleftarrows \mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) $$ is \(6.66 \times 10^{-12}\) at \(1000 \mathrm{K}\). Calculate \(K\) for the reaction $$ 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{CO}_{2}(\mathrm{g}) $$

Calculate \(K\) for the reaction $$ \operatorname{SnO}_{2}(\mathrm{s})+2 \mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Sn}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) $$ given the following information: $$ \begin{array}{ll} \mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g}) \rightleftarrows \mathrm{Sn}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & K=8.12 \\ \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) & K=0.771 \end{array} $$

Calculate \(K\) for the reaction $$ \mathrm{Fe}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftarrows \mathrm{FeO}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g}) $$ given the following information: $$ \begin{array}{ll} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) & K=1.6 \\ \mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) & K=0.67 \end{array} $$

Dinitrogen trioxide decomposes to \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) in an endothermic process \(\left(\Delta_{\mathrm{r}} H^{\circ}=40.5 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\right)\) $$ \mathrm{N}_{2} \mathrm{O}_{3}(\mathrm{g}) \rightleftarrows \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) $$ Predict the effect of the following changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of the following changes is made. (a) adding more \(\mathrm{N}_{2} \mathrm{O}_{3}(\mathrm{g})\) (b) adding more \(\mathrm{NO}_{2}(\mathrm{g})\) (c) increasing the volume of the reaction flask (d) lowering the temperature

\(K_{\mathrm{p}}\) for the following reaction is 0.16 at \(25^{\circ} \mathrm{C}\) $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ The enthalpy change for the reaction at standard conditions is \(+16.3 \mathrm{kJ} / \mathrm{mol}\) -rxn. Predict the effect of the following changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of the following changes is made. (a) adding more \(\mathrm{Br}_{2}(\mathrm{g})\) (b) removing some \(\mathrm{NOBr}(\mathrm{g})\) (c) decreasing the temperature (d) increasing the container volume

Consider the isomerization of butane with an equilibrium constant of \(K=2.5 .\) (See Study Question 13.) The system is originally at equilibrium with [butane] \(=\) \(1.0 \mathrm{M}\) and \([\text { isobutane }]=2.5 \mathrm{M}\) (a) If \(0.50 \mathrm{mol} / \mathrm{L}\) of isobutane is suddenly added and the system shifts to a new equilibrium position, what is the equilibrium concentration of each gas? (b) If \(0.50 \mathrm{mol} / \mathrm{L}\) of butane is added to the original equilibrium mixture and the system shifts to a new equilibrium position, what is the equilibrium concentration of each gas?

The decomposition of \(\mathrm{NH}_{4} \mathrm{HS}\) $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ is an endothermic process. Using Le Chatelier's principle, explain how increasing the temperature would affect the equilibrium. If more \(\mathrm{NH}_{4} \mathrm{HS}\) is added to a flask in which this equilibrium exists, how is the equilibrium affected? What if some additional \(\mathrm{NH}_{3}\) is placed in the flask? What will happen to the pressure of \(\mathrm{NH}_{3}\) if some \(\mathrm{H}_{2} \mathrm{S}\) is removed from the flask?

Suppose 0.086 mol of \(\mathrm{Br}_{2}\) is placed in a \(1.26-\mathrm{L}\). flask and heated to \(1756 \mathrm{K}\), a temperature at which the halogen dissociates to atoms. $$ \mathrm{Br}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{Br}(\mathrm{g}) $$ If \(\mathrm{Br}_{2}\) is \(3.7 \%\) dissociated at this temperature, calculate \(K_{\mathrm{c}}\).

The equilibrium constant for the reaction $$ \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) $$ is \(1.7 \times 10^{-3}\) at \(2300 K\) (a) What is \(K\) for the reaction when written as follows? $$ 1 / 2 \mathrm{N}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows \mathrm{NO}(\mathrm{g}) $$ (b) What is \(K\) for the following reaction? $$ 2 \mathrm{NO}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) $$

\(K_{\mathrm{p}}\) for the formation of phosgene, \(\mathrm{COCl}_{2},\) is \(6.5 \times 10^{11}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) $$ What is the value of \(K_{p}\) for the dissociation of phosgene? $$ \operatorname{COCl}_{2}(g) \rightleftarrows \operatorname{CO}(g)+\mathrm{Cl}_{2}(g) $$

The equilibrium constant, \(K_{c},\) for the following reaction is 1.05 at \(350 \mathrm{K}\) $$ 2 \mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CCl}_{4}(\mathrm{g}) $$ If an equilibrium mixture of the three gases at \(350 \mathrm{K}\) contains \(0.0206 \mathrm{M} \mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{g})\) and \(0.0163 \mathrm{M} \mathrm{CH}_{4},\) what is the equilibrium concentration of \(\mathrm{CCl}_{4} ?\)

Carbon tetrachloride can be produced by the following reaction: $$ \mathrm{CS}_{2}(\mathrm{g})+3 \mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows \mathrm{S}_{2} \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{CCl}_{4}(\mathrm{g}) $$ Suppose 1.2 mol of \(\mathrm{CS}_{2}\) and 3.6 mol of \(\mathrm{Cl}_{2}\) are placed in a \(1.00-\mathrm{L}\). flask. After equilibrium has been achieved, the mixture contains 0.90 mol \(\mathrm{CCl}_{4}\). Calculate \(K_{c}\).

Equal numbers of moles of \(\mathrm{H}_{2}\) gas and \(\mathrm{I}_{2}\) vapor are mixed in a flask and heated to \(700^{\circ} \mathrm{C}\). The initial concentration of each gas is \(0.0088 \mathrm{mol} / \mathrm{L},\) and \(78.6 \%\) of the \(I_{2}\) is consumed when equilibrium is achieved according to the equation $$ \mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{HI}(\mathrm{g}) $$ Calculate \(K_{\mathrm{c}}\) for this reaction.

At \(2300 \mathrm{K}\) the equilibrium constant for the formation of \(\mathrm{NO}(\mathrm{g})\) is \(1.7 \times 10^{-3}\) $$ \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}(\mathrm{g}) $$ (a) Analysis shows that the concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are both \(0.25 \mathrm{M},\) and that of \(\mathrm{NO}\) is \(0.0042 \mathrm{M}\) under certain conditions. Is the system at equilibrium? (b) If the system is not at equilibrium, in which direction does the reaction proceed? (c) When the system is at equilibrium, what are the equilibrium concentrations?

Which of the following correctly relates the two equilibrium constants for the two reactions shown? \(\mathrm{NOCl}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+1 / 2 \mathrm{Cl}_{2}(\mathrm{g}) \quad K_{1}\) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{NOCl}(\mathrm{g}) \quad K_{2}\) (a) \(K_{2}=-K_{1}^{2}\) (c) \(K_{2}=1 / K_{1}^{2}\) (b) \(K_{2}=1 /\left(K_{1}\right)^{1 / 2} \quad\) (d) \(K_{2}=2 K_{1}\)

Sulfur dioxide is readily oxidized to sulfur trioxide. $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{SO}_{3}(\mathrm{g}) \quad K_{c}=279 $$ If we add \(3.00 \mathrm{g}\) of \(\mathrm{SO}_{2}\) and \(5.00 \mathrm{g}\) of \(\mathrm{O}_{2}\) to a \(1.0-\mathrm{L}\). flask, approximately what quantity of \(\mathrm{SO}_{3}\) will be in the flask once the reactants and the product reach equilibrium? (a) \(2.21 \mathrm{g}\) (c) \(3.61 \mathrm{g}\) (b) \(4.56 \mathrm{g}\) (d) \(8.00 \mathrm{g}\) (Note: The full solution to this problem results in a cubic equation. Do not try to solve it exactly. Decide only which of the answers is most reasonable.)

Heating a metal carbonate leads to decomposition. $$ \mathrm{BaCO}_{3}(\mathrm{s}) \rightleftarrows \mathrm{BaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ Predict the effect on the equilibrium of each change listed below. Answer by choosing (i) no change, (ii) shifts left, or (iii) shifts right. (a) add BaCO \(_{3}\) (c) add BaO (b) add \(\mathrm{CO}_{2}\) (d) raise the temperature (e) increase the volume of the flask containing the reaction

Carbonyl bromide decomposes to carbon monoxide and bromine. $$ \operatorname{COBr}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ \(K_{\mathrm{c}}\) is 0.190 at \(73^{\circ} \mathrm{C} .\) Suppose you place \(0.500 \mathrm{mol}\) of COBr, in a \(2.00-\) I. flask and heat it to \(73^{\circ} \mathrm{C}\) (see Study Question 17 ). After equilibrium has been achieved, you add an additional 2.00 mol of \(\mathrm{CO}\) (a) How is the equilibrium mixture affected by adding more CO? (b) When equilibrium is reestablished, what are the new equilibrium concentrations of \(\mathrm{COBr}_{2}, \mathrm{CO},\) and \(\mathrm{Br}_{2} ?\) (c) How has the addition of CO affected the percentage of COBr \(_{2}\) that decomposed?

Ammonium hydrogen sulfide decomposes on heating. $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftarrows \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ If \(K_{\mathrm{p}}\) for this reaction is 0.11 at \(25^{\circ} \mathrm{C}\) (when the partial pressures are measured in atmospheres), what is the total pressure in the flask at equilibrium?

When solid ammonium carbamate sublimes, it dissociates completely into ammonia and carbon dioxide according to the following equation: $$ \left(\mathrm{NH}_{4}\right)\left(\mathrm{H}_{2} \mathrm{NCO}_{2}\right)(\mathrm{s}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) $$ At \(25^{\circ} \mathrm{C},\) experiment shows that the total pressure of the gases in equilibrium with the solid is 0.116 atm. What is the equilibrium constant, \(K_{\mathrm{p}} ?\)

The equilibrium reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\) has been thoroughly studied (Figure 16.8 ). (a) If the total pressure in a flask containing \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas at \(25^{\circ} \mathrm{C}\) is 1.50 atm and the value of \(K_{\mathrm{p}}\) at this temperature is \(0.148,\) what fraction of the \(\mathrm{N}_{2} \mathrm{O}_{4}\) has dissociated to \(\mathrm{NO}_{2} ?\) (b) What happens to the fraction dissociated if the volume of the container is increased so that the total equilibrium pressure falls to 1.00 atm?

Assume 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 \(K_{\varepsilon}\) is 6.3 for this reaction at the temperature in the reactor, calculate the equilibrium concentration of each reagent. What is the total pressure in the flask?

\(K_{c}\) for the decomposition of ammonium hydrogen sulfide is \(1.8 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ (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 \(\mathrm{NH}_{4} \mathrm{HS}\) 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 \(\mathrm{H}_{2} \mathrm{S} ?\)

The equilibrium constant, \(K_{p},\) is 0.14 at \(25^{\circ} \mathrm{C}\) for the following reaction: $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) $$ If the total pressure of the gas mixture is 2.5 atm at equilibrium, what is the partial pressure of each gas?

Lanthanum oxalate decomposes when heated to lanthanum (III) oxide, \(\mathrm{CO},\) and \(\mathrm{CO}_{2}\) \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}(\mathrm{s}) \rightleftharpoons \mathrm{La}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g})+3 \mathrm{CO}_{2}(\mathrm{g})\) (a) If, at equilibrium, the total pressure in a \(10.0-\mathrm{L}\). flask is 0.200 atm, what is the value of \(K_{p} ?\) (b) Suppose 0.100 mol of \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\) s was originally placed in the \(10.0-\mathrm{L}\). flask. What quantity of \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\) remains unreacted at equilibrium at \(373 \mathrm{K}^{2}\)

Sulfuryl chloride, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\), 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 \(\mathrm{Cl}_{2}\). \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \quad K_{c}=0045 \mathrm{at} 375^{\circ} \mathrm{C}\) (a) A \(1.00-1 .\) flask containing \(6.70 \mathrm{g}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is 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?

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 \(\mathrm{CO}\) in the air is likely to be fatal? Assume the partial pressure of \(\mathrm{O}_{2}\) is \(0.20 \mathrm{atm}\).

limestone decomposes at high temperatures. $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ At \(1000^{\circ} \mathrm{C}, K_{\mathrm{p}}=3.87 .\) If pure \(\mathrm{CaCO}_{3}\) is placed in a \(5.00-\mathrm{L}\). flask and heated to \(1000^{\circ} \mathrm{C},\) what quantity of \(\mathrm{CaCO}_{3}\) must decompose to achieve the equilibrium pressure of \(\mathrm{CO}_{2} ?\)

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 \(10 .\).L. vessel and heat it to \(1800 \mathrm{K}\), how many \(\mathrm{O}\) atoms are present in the flask?

Nitrosy bromide, NOBr, dissociates readily at room temperature. $$ \operatorname{NOBr}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+1 / 2 \mathrm{Br}_{2}(\mathrm{g}) $$ Some NOBr is placed in a flask at \(25^{\circ} \mathrm{C}\) and allowed to dissociate. The total pressure at equilibrium is \(190 \mathrm{mm}\) Hg and the compound is found to be \(34 \%\) dissociated. What is the value of \(K_{\mathrm{p}} ?\)

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?

The ammonia complex of trimethylborane, \(\left(\mathrm{NH}_{3}\right) \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3},\) dissociates at \(100^{\circ} \mathrm{C}\) to its components with \(K_{\mathrm{p}}=4.62\) (when the pressures are in atmospheres). \(\left(\mathrm{NH}_{3}\right) \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3}(\mathrm{g}) \quad \rightleftarrows \quad \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3}(\mathrm{g})+\mathrm{NH}_{3}(\mathrm{g})\) If \(\mathrm{NH}_{3}\) is changed to some other molecule, the equilibrium constant is different. For \(\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{P}\right] \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3} \quad \quad K_{\mathrm{p}}=0.128\) For \(\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N}\right] \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3} \quad \quad K_{\mathrm{p}}=0.472\) (a) If you begin an experiment by placing 0.010 mol of each complex in a flask, which would have the largest partial pressure of \(\mathbf{B}\left(\mathrm{CH}_{3}\right)_{3}\) at \(100^{\circ} \mathrm{C} ?\) (b) If \(0.73 \mathrm{g}(0.010 \mathrm{mol})\) of \(\left(\mathrm{NH}_{3}\right) \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3}\) is placed in a \(100 .\) -mL. flask and heated to \(100^{\circ} \mathrm{C},\) what is the partial pressure of each gas in the equilibrium mixture, and what is the total pressure? What is the percent dissociation of \(\left(\mathrm{NH}_{3}\right) \mathrm{B}\left(\mathrm{CH}_{3}\right)_{3} ?\)