Chapter 12

The value of \(K_{\mathrm{c}}\) is \(3.7 \times 10^{-23}\) at \(25^{\circ} \mathrm{C}\) for $$ \mathrm{C}(\text { graphite })+\mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g}) $$ Describe what will happen if \(3.5 \mathrm{~mol} \mathrm{CO}\) and \(3.5 \mathrm{~mol}\) \(\mathrm{CO}_{2}\) are mixed in a 1.5-L sealed graphite container with a suitable catalyst so that the reaction rate is rapid at this temperature.

\(K_{\mathrm{p}}\) for this reaction is 0.16 at \(25^{\circ} \mathrm{C}:\) $$ 2 \operatorname{NOBr}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=16.3 \mathrm{~kJ} / \mathrm{mol} $$ Predict the effect of each change on the position of the equilibrium; that is, state which way the equilibrium shifts (left, right, or no change) when each change is made. Assume constant-volume conditions for parts (a), (b), and (c). (a) Add more \(\mathrm{Br}_{2}(\mathrm{~g})\). (b) Remove some \(\mathrm{NOBr}(\mathrm{g})\). (c) Decrease the temperature. (d) Increase the container volume.

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

Assume that the reaction $$ 2 \mathrm{HBr}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) $$ is at equilibrium and the equilibrium conditions are changed as described. Indicate whether the forward or the reverse reaction rate is faster immediately after the change and explain your choice. (a) Some \(\mathrm{HBr}(\mathrm{g})\) is added without changing the total volume. (b) Some \(\mathrm{Br}_{2}(\mathrm{~g})\) is removed without changing the total volume. (c) The total volume of the system is halved.

Hydrogen, bromine, and \(\mathrm{HBr}\) in the gas phase are in equilibrium in a container of fixed volume. \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g}) \quad \Delta_{r} H^{\circ}=-103.7 \mathrm{~kJ} / \mathrm{mol}\) How will each of these changes affect the indicated quantities? Write "increase," "decrease," or "no change." \begin{tabular}{l} \hline Change & {\(\left[\mathrm{Br}_{2}\right]\)} & {\([\mathrm{HBr}]\)} & \(K_{c}\) & \(K_{\mathrm{p}}\) \\ \hline Some \(\mathrm{H}_{2}\) is added to the \\ container. \\ The temperature of the gases \\ in the container is increased. \\ The pressure of \(\mathrm{HBr}\) is \\ increased. \end{tabular}

Nitrogen, oxygen, and nitrogen monoxide are in equilibrium in a container of fixed volume. \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) \quad \Delta_{\mathrm{r}} H^{\circ}=180.5 \mathrm{~kJ} / \mathrm{mol}\) How will each of these changes affect the indicated quantities? Write "increase," "decrease," or "no change." \begin{tabular}{lccc} \hline Change & {\(\left[\mathrm{N}_{2}\right]\)} & {\([\mathrm{NO}]\)} & \(K_{c}\) & \(K_{p}\) \\ \hline Some NO is added to the & & & \\ container. \\ The temperature of the gases & & & \\ in the container is decreased. & & & \\ The pressure of \(\mathrm{N}_{2}\) is & & & \\ decreased. \end{tabular}

The equilibrium constant \(K_{\mathrm{c}}\) for this reaction is 0.16 at \(25^{\circ} \mathrm{C},\) and the standard reaction enthalpy is \(16.1 \mathrm{~kJ}\). $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\ell) $$ Predict the effect of each of these changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of these changes is made for a constant-volume system. (a) Adding more \(\mathrm{Br}_{2}\) (b) Removing some \(\mathrm{NOBr}\) c). Lowering the temnerature

The formation of hydrogen sulfide from the elements is exothermic. $$ \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{8} \mathrm{~S}_{8}(\mathrm{~s}) \rightleftharpoons \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=-20.6 \mathrm{~kJ} / \mathrm{mol} $$ Predict the effect of each of these changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each change is made in a constant-volume system. (a) Adding more sulfur (b) Adding more \(\mathrm{H}_{2}\) (c) Raising the temperature

Heating a metal carbonate leads to decomposition. $$ \mathrm{BaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) $$ Predict the effect on the equilibrium of each change listed below. Answer by choosing (i) no change, (ii) shifts left, or (iii) shifts right. (Except for part (e), assume that the volume is constant.) (a) Add \(\mathrm{BaCO}_{3}\) (b) Add \(\mathrm{CO}_{2}\) (c) Add \(\mathrm{BaO}\) (d) Raise the temperature (e) Increase the volume of the reaction flask

Consider the system $$ \begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~N}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ} &=-1530.4 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ (a) How will the amount of ammonia at equilibrium be affected by (i) removing \(\mathrm{O}_{2}(\mathrm{~g})\) without changing the total gas volume? (ii) adding \(\mathrm{N}_{2}(\mathrm{~g})\) without changing the total gas volume? (iii) adding water without changing the total gas volume? (iv) expanding the container? (v) increasing the temperature? (b) Which of these changes (i to v) increases the value of \(K ?\) Which decreases it?

Phosphorus pentachloride decomposes at high temperatures. $$ \mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ An equilibrium mixture at some temperature consists of \(3.120 \mathrm{~g} \mathrm{PCl}_{5}, 3.845 \mathrm{~g} \mathrm{PCl}_{3},\) and \(1.787 \mathrm{~g} \mathrm{Cl}_{2}\) in a sealed 1.00-L flask. (a) If you add \(1.418 \mathrm{~g} \mathrm{Cl}_{2}\) without changing the volume, how will the equilibrium be affected? (b) Calculate the concentrations of all three substances when equilibrium is reestablished.

Predict whether the equilibrium for the photosynthesis reaction described by the equation $$ \begin{array}{r} 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \\ \Delta_{1} H^{\circ}=2801.69 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ would (i) shift to the right, (ii) shift to the left, or (iii) remain unchanged for each of these changes: (a) decrease the concentration of \(\mathrm{CO}_{2}\) at constant volume. (b) increase the partial pressure of \(\mathrm{O}_{2}\) at constant volume. (c) remove one half of the \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (d) decrease the total pressure by increasing the volume. (e) increase the temperature. (f) introduce a catalyst into a constant-volume system.

For each of these reactions at \(25^{\circ} \mathrm{C}\), indicate whether the entropy effect, the energy effect, both, or neither favors the reaction. (a) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NF}_{3}(\mathrm{~g}) \quad \Delta_{1} H^{\circ}=-249 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\mathrm{N}_{2} \mathrm{~F}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NF}_{2}(\mathrm{~g})\) \(\Delta_{t} H^{\circ}=93.3 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NCl}_{3}(\mathrm{~g}) \quad \Delta_{1} H^{\circ}=460 \mathrm{~kJ} / \mathrm{mol}\)

For each of these processes at \(25^{\circ} \mathrm{C}\), indicate whether the entropy effect, the energy effect, both, or neither favors the process. $$ \text { (a) } \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ \Delta_{t} H^{\circ}=&-2045 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ (b) \(\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{Br}_{2}(\ell)\) $$ \Delta_{r} H^{\circ}=-31 \mathrm{~kJ} / \mathrm{mol} $$ $$ \text { (c) } 2 \mathrm{Ag}(\mathrm{s})+3 \mathrm{~N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{AgN}_{3}(\mathrm{~s}) \quad \Delta_{\mathrm{r}} H^{\circ}=618 \mathrm{~kJ} / \mathrm{mol} $$

For each of these chemical reactions, predict whether the equilibrium constant at \(25^{\circ} \mathrm{C}\) is greater than 1 or less than \(1,\) or state that insufficient information is available. Also indicate whether each reaction is product-favored or reactant-favored. (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=-115 \mathrm{~kJ} / \mathrm{mol}\) (b) \(2 \mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{O}_{2}(\mathrm{~g})\) \(\Delta_{\mathrm{r}} H^{\circ}=-285 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NCl}_{3}(\mathrm{~g})\) \(\Delta_{1} H^{\circ}=460 \mathrm{~kJ} / \mathrm{mol}\)

For each of these chemical reactions, predict whether the equilibrium constant at \(25^{\circ} \mathrm{C}\) is greater than 1 or less than \(1,\) or state that insufficient information is available. Also indicate whether each reaction is product-favored or reactant-favored. $$ \begin{array}{l} \text { (a) } 2 \mathrm{NaCl}(\mathrm{s}) \rightleftharpoons 2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=823 \mathrm{~kJ} / \mathrm{mol} \\ \text { (b) } 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=-566 \mathrm{~kJ} / \mathrm{mol} \\ \text { (c) } 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \\ \Delta_{\mathrm{r}} H^{\circ}=2045 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Considering both the enthalpy effect and the entropy effect for the Haber- Bosch process, explain why choosing the temperature at which to run this reaction is very important.

Explain in your own words why it was so important to find a highly effective catalyst for the ammonia synthesis reaction before the Haber-Bosch process could become successful.

Write equilibrium constant expressions, in terms of reactant and product concentrations, for each of these reactions. $$ \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \quad K_{\mathrm{c}}=1.0 \times 10^{-14} $$ \(\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})\) $$ \begin{array}{c} K_{\mathrm{c}}=1.8 \times 10^{-5} \\ \mathrm{~N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) \end{array} $$ Assume that all gases and solutes have initial concentrations of \(1.0 \mathrm{~mol} / \mathrm{L}\). Then let the first reactant in each reaction change its concentration by \(-x\). (a) Using the reaction table (ICE table) approach, write equilibrium constant expressions in terms of the unknown variable \(x\) for each reaction. (b) Which of these expressions yield quadratic equations? (c) How would you go about solving the others for \(x ?\)

Write equilibrium constant expressions, in terms of reactant and product concentrations, for each of these reactions. \(2 \mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{O}_{2}(\mathrm{~g})\) $$ K_{c}=7 \times 10^{56} $$ \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) $$ K_{\mathrm{c}}=1.7 \times 10^{2} $$ $$ \begin{array}{ll} \mathrm{HCOO}^{-}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{HCOOH}(\text { aq }) & K_{\mathrm{c}}=5.6 \times 10^{3} \\ \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{AgI}(\mathrm{s}) & K_{\mathrm{c}}=6.7 \times 10^{15} \end{array} $$ Assume that all gases and solutes have initial concentrations of \(1.0 \mathrm{~mol} / \mathrm{L}\). Then, let the first reactant in each reaction change its concentration by \(-x\). (a) Using the reaction table (ICE table) approach, write equilibrium constant expressions in terms of the unknown variable \(x\) for each reaction. (b) Which of these expressions yield quadratic equations? (c) How would you go about solving the others for \(x\) ?

Consider the decomposition of ammonium hydrogen sulfide: $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) $$ In a sealed flask at \(25^{\circ} \mathrm{C}\) are \(10.0 \mathrm{~g} \mathrm{NH}_{4} \mathrm{HS},\) ammonia with a partial pressure of \(0.692 \mathrm{~atm}\), and \(\mathrm{H}_{2} \mathrm{~S}\) with a partial pressure of \(0.0532 \mathrm{~atm}\). When equilibrium is established, it is found that the partial pressure of ammonia has increased by \(12.4 \% .\) Calculate \(K_{\mathrm{P}}\) for the decomposition of \(\mathrm{NH}_{4} \mathrm{HS}\) at \(25^{\circ} \mathrm{C}\).

The equilibrium constant \(K_{\mathrm{c}}\) is \(1.6 \times 10^{5}\) at \(1297 \mathrm{~K}\) and \(3.5 \times 10^{4}\) at \(1495 \mathrm{~K}\) for the reaction $$ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g}) $$ (a) Is \(\Delta_{r} H^{\circ}\) for this reaction positive or negative? (b) Calculate \(K_{\mathrm{c}}\) at \(1297 \mathrm{~K}\) for the reaction $$ \frac{1}{2} \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{HBr}(\mathrm{g}) $$ (c) Pure HBr is placed into an evacuated container of constant volume. The container is sealed and heated to \(1297 \mathrm{~K} .\) Calculate the percentage of HBr that is decomposed to \(\mathrm{H}_{2}\) and \(\mathrm{Br}_{2}\) at equilibrium.

Many common nonmetallic elements exist as diatomic molecules at room temperature. When these elements are heated to \(1500 . \mathrm{K},\) the molecules break apart into atoms. A general equation for this type of reaction is \(\mathrm{E}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{E}(\mathrm{g})\) where E stands for an atom of each element. Equilibrium constants for dissociation of these molecules at \(1500 . \mathrm{K}\) are \begin{tabular}{lcll} \hline Species & \(\kappa_{c}\) & Species & \multicolumn{1}{c} {\(K_{c}\)} \\ \hline \(\mathrm{Br}_{2}\) & \(8.9 \times 10^{-2}\) & \(\mathrm{H}_{2}\) & \(3.1 \times 10^{-10}\) \\ \(\mathrm{Cl}_{2}\) & \(3.4 \times 10^{-3}\) & \(\mathrm{~N}_{2}\) & \(1 \times 10^{-27}\) \\ \(\mathrm{~F}_{2}\) & 7.4 & \(\mathrm{O}_{2}\) & \(1.6 \times 10^{-11}\) \\ \hline \end{tabular} (a) Assume that \(1.00 \mathrm{~mol}\) of each diatomic molecule is placed in a separate \(1.0-\mathrm{L}\) container, sealed, and heated to \(1500 . \mathrm{K}\). Calculate the equilibrium concentration of the atomic form of each element at \(1500 . \mathrm{K}\). (b) From these results, predict which of the diatomic elements has the lowest bond dissociation energy, and compare your results with thermochemical calculations and with Lewis structures.

The total pressure for a mixture of \(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\) is 1.5 atm. If \(K_{\mathrm{p}}=7.0\) (at \(25^{\circ} \mathrm{C}\) ), calculate the partial pressure of each gas in the mixture. $$ 2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) $$

The chemistry of compounds composed of a transition metal and carbon monoxide has been an interesting area of research for more than 70 years. \(\mathrm{Ni}(\mathrm{CO})_{4}\) is formed by the reaction of nickel metal with carbon monoxide. (a) Calculate the mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) that can be formed if you combine \(2.05 \mathrm{~g} \mathrm{CO}\) with \(0.125 \mathrm{~g}\) nickel metal.(b) An excellent way to make pure nickel metal is to decompose \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a vacuum at a temperature slightly higher than room temperature. If the standard formation enthalpy of \(\mathrm{Ni}(\mathrm{CO})_{4}\) gas is \(-602.9 \mathrm{~kJ} / \mathrm{mol}\), calculate the enthalpy change for this decomposition reaction. $$ \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g}) \longrightarrow \mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) $$ (c) Predict whether there is an increase or a decrease in entropy when this reaction occurs. (d) In an experiment at \(100 .{ }^{\circ} \mathrm{C}\) it is determined that with \(0.010 \mathrm{~mol} \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g})\) initially present in a sealed \(1.0-\mathrm{L}\) flask, only 0.000010 mol remains after decomposition. (i) Calculate the equilibrium concentration of \(\mathrm{CO}\) in the flask. (ii) Calculate the value of the equilibrium constant \(K_{\mathrm{c}}\) for this reaction at \(100 .{ }^{\circ} \mathrm{C}\). (iii) Calculate the equilibrium constant \(K_{\mathrm{P}}\) for this reaction at \(100 .{ }^{\circ} \mathrm{C}\).

A small sample of \(c i s\) -dichloroethene in which one carbon atom is the radioactive isotope \({ }^{14} \mathrm{C}\) is added to an equilibrium mixture of the cis and trans isomers at a certain temperature. Eventually, \(40 \%\) of the radioactive molecules are found to be in the trans configuration at any given time. (a) Determine the value of \(K_{\mathrm{c}}\) for the cis \(\rightleftharpoons\) trans equilibrium. (b) What would have happened if a small sample of radioactive trans isomer had been added instead of the cis isomer?

Solid ammonium iodide decomposes to ammonia and hydrogen iodide gases at sufficiently high temperatures. $$ \mathrm{NH}_{4} \mathrm{I}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{HI}(\mathrm{g}) $$ The equilibrium constant, \(K_{\mathrm{P}}\), for the decomposition at \(673 \mathrm{~K}\) is 0.215 . A \(15.0-\mathrm{g}\) sample of ammonium iodide is sealed in a \(5.00-\mathrm{L}\) flask and heated to \(673 \mathrm{~K}\). (a) Calculate the total pressure in the flask at equilibrium. (b) Calculate the amount (in moles) of ammonium iodide that decomposes.

These amounts of \(\mathrm{HI}, \mathrm{H}_{2},\) and \(\mathrm{I}_{2}\) are introduced into a \(10.00-\mathrm{L}\) flask. The flask is sealed and heated to \(745 \mathrm{~K}\). \begin{tabular}{lccc} \hline & \(n_{\mathrm{HI}}(\mathrm{mol})\) & \(n_{\mathrm{H}_{2}}(\mathrm{~mol})\) & \(\mathrm{n}_{\mathrm{h}_{2}}(\mathrm{~mol})\) \\ \hline Case a & 1.0 & 0.10 & 0.10 \\ Case b & \(10 .\) & 1.0 & 1.0 \\ Case c & \(10 .\) & \(10 .\) & 1.0 \\ Case d & 5.62 & 0.381 & 1.75 \\ \hline \end{tabular} The equilibrium constant for the reaction \(2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g})\) has the value 0.0200 at \(745 \mathrm{~K}\). In which cases does the concentration of HI increase as equilibrium is attained, and in which cases does the concentration of HI decrease?

These amounts of \(\mathrm{CO}(\mathrm{g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{CO}_{2}(\mathrm{~g})\), and \(\mathrm{H}_{2}(\mathrm{~g})\) are introduced into a \(10.00-\mathrm{L}\) flask. The flask is sealed and heated to a very high temperature. \begin{tabular}{lcccc} \hline & \(n_{\mathrm{CO}}(\mathrm{mol})\) & \(n_{\mathrm{H}_{2} \mathrm{O}}(\mathrm{mol})\) & \(n_{\mathrm{CO}_{2}}(\mathrm{~mol})\) & \(n_{\mathrm{H}_{2}}(\mathrm{~mol})\) \\ \hline Case a & 1.0 & 0.10 & 0.10 & 0.10 \\ Case b & \(10 .\) & 1.0 & 1.0 & 1.0 \\ Case c & \(10 .\) & \(10 .\) & 1.0 & 1.0 \\ Case d & 5.62 & 0.381 & 1.75 & 1.75 \\ \hline \end{tabular} The equilibrium constant for the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\) has the value \(K_{\mathrm{c}}=4.00\) at this temperature. For which cases will the concentration of CO increase as equilibrium is attained, and in which cases will the concentration of CO decrease?

Carbonylbromide, \(\mathrm{COBr}_{2}\), can be formed by combining carbon monoxide and bromine gas. $$ \mathrm{CO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{COBr}_{2}(\mathrm{~g}) $$ When equilibrium is established at \(346 \mathrm{~K},\) the partial pressures (in atm) of \(\mathrm{COBr}_{2}, \mathrm{CO},\) and \(\mathrm{Br}_{2}\) are 0.12,1.00 , and \(0.65,\) respectively. (a) Calculate \(K_{\mathrm{p}}\) at \(346 \mathrm{~K}\). (b) Enough bromine condenses to decrease its partial pressure to 0.50 atm. Calculate the equilibrium partial pressures of all gases after equilibrium is re-established.

Mustard gas was used in chemical warfare in World War I. Mustard gas can be produced according to this reaction: $$ \mathrm{SCl}_{2}(\mathrm{~g})+2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g}) \rightleftharpoons \mathrm{S}\left(\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\right)_{2}(\mathrm{~g}) $$ An evacuated 5.00 -L flask at \(20.0^{\circ} \mathrm{C}\) is filled with \(0.258 \mathrm{~mol} \mathrm{SCl}_{2}\) and \(0.592 \mathrm{~mol} \mathrm{C}_{2} \mathrm{H}_{4}\) and sealed. After equilibrium is established, 0.0349 mol mustard gas is present. (a) Calculate the partial pressure of each gas at equilibrium. (b) Calculate \(K_{\mathrm{c}}\) at \(20.0^{\circ} \mathrm{C}\).

Limestone decomposes at high temperatures. $$ \mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) $$ At \(1000 .{ }^{\circ} \mathrm{C}, K_{\mathrm{P}}=3.87\). Pure \(\mathrm{CaCO}_{3}\) is placed into an empty \(5.00-\mathrm{L}\) flask. The flask is sealed and heated to \(1000 .{ }^{\circ} \mathrm{C}\). Calculate the mass of \(\mathrm{CaCO}_{3}\) that must decompose to achieve the equilibrium pressure of \(\mathrm{CO}_{2}\).

A sample of pure \(\mathrm{SO}_{3}\) weighing \(0.8312 \mathrm{~g}\) was placed into a 1.00 - \(\mathrm{L}\) flask, sealed, and heated to \(1100 . \mathrm{K}\) to decompose it partially. $$ 2 \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ If a total pressure of 1.295 atm was developed, calculate the value of \(K_{\mathrm{c}}\) for this reaction at this temperature.

Two molecules of A react to form one molecule of \(\mathrm{B},\) as in the reaction $$ 2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons \mathrm{B}(\mathrm{g}) $$ Three experiments are done at different temperatures and equilibrium concentrations are measured. For each experiment, calculate the equilibrium constant, \(K_{\mathrm{c}^{*}}\) (a) \([\mathrm{A}]=0.74 \mathrm{~mol} / \mathrm{L},[\mathrm{B}]=0.74 \mathrm{~mol} / \mathrm{L}\) $$ \begin{array}{l} \text { (b) }[\mathrm{A}]=2.0 \mathrm{~mol} / \mathrm{L},[\mathrm{B}]=2.0 \mathrm{~mol} / \mathrm{L} \\ \text { (c) }[\mathrm{A}]=0.01 \mathrm{~mol} / \mathrm{L},[\mathrm{B}]=0.01 \mathrm{~mol} / \mathrm{L} \end{array} $$ What can you conclude about this statement: "If the concentrations of reactants and products are equal, then the equilibrium constant is always \(1.0 . "\)

Suppose that you have heated a mixture of cis-and trans2 -pentene to \(600 . \mathrm{K},\) and after \(1 \mathrm{~h}\) you find that the composition is \(40 \%\) cis. After \(4 \mathrm{~h}\) the composition is found to be \(42 \%\) cis, and after \(8 \mathrm{~h}\) it is \(42 \%\) cis. Next, you heat the mixture to \(800 . \mathrm{K}\) and find that the composition changes to \(45 \%\) cis. When the mixture is cooled to \(600 . \mathrm{K}\) and allowed to stand for \(8 \mathrm{~h}\), the composition is found to be \(42 \%\) cis. Is this system at equilibrium at \(600 . \mathrm{K} ?\) Or, would more experiments be needed before you could conclude that it was at equilibrium? If so, what experiments would you do?

For the reaction cis 2 -butene \(\rightleftharpoons\) trans-2-butene \(K_{\mathrm{c}}\) is 1.65 at \(500 . \mathrm{K}, 1.47\) at \(600 . \mathrm{K},\) and 1.36 at \(700 . \mathrm{K}\) Predict whether the conversion from the cis to the trans isomer of 2 -butene is exothermic or endothermic.

Imagine yourself to be the size of ions and molecules inside a beaker containing this equilibrium mixture with a \(K_{\mathrm{c}}\) greater than \(1 .\) $$ \mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(\mathrm{aq})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CoCl}_{4}^{2-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell)$$ pink blue Write a brief description of what you observe around you before and after additional water is added to the mixture.

Draw a nanoscale (particulate) level diagram for an equilibrium mixture of \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \quad K_{\mathrm{c}}=4.00\)

A solid sample of benzoic acid, a carboxylic acid, is in equilibrium with an aqueous solution of benzoic acid. A tiny quantity of \(\mathrm{D}_{2} \mathrm{O},\) water containing the isotope \({ }^{2} \mathrm{H}\), deuterium, is added to the solution. The solution is allowed to stand at constant temperature for several hours, after which some of the solid benzoic acid is removed and analyzed. The benzoic acid is found to contain a tiny quantity of deuterium, D, and the formula of the deuterium-containing molecules is \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOD}\). Explain how this can happen.

Samples of \(\mathrm{N}_{2} \mathrm{O}_{4}\) can be prepared in which both nitrogen atoms are the heavier isotope \({ }^{15} \mathrm{~N}\). Designating this isotope as \(\mathrm{N}^{*}\), we can write the formula of the molecules in such a sample as \(\mathrm{O}_{2} \mathrm{~N}^{*}-\mathrm{N}^{*} \mathrm{O}_{2}\) and the formula of typical \(\mathrm{N}_{2} \mathrm{O}_{4}\) as \(\mathrm{O}_{2} \mathrm{~N}-\mathrm{NO}_{2}\). When a tiny quantity of \(\mathrm{O}_{2} \mathrm{~N}^{*}-\mathrm{N}^{*} \mathrm{O}_{2}\) is introduced into an equilibrium mixture of \(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\), the \({ }^{15} \mathrm{~N}\) immediately becomes distributed among both \(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\) molecules, and in the \(\mathrm{N}_{2} \mathrm{O}_{4}\) it is invariably in the form \(\mathrm{O}_{2} \mathrm{~N}^{*}-\mathrm{NO}_{2}\). Explain how this observation supports the idea that equilibrium is dynamic.

For the equilibrium $$ \mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(\mathrm{aq})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CoCl}_{4}^{2-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell) $$ pink blue \(K_{\mathrm{c}}\) is somewhat greater than 1 . If water is added to a blue solution of \(\mathrm{CoCl}_{4}^{2-}(\mathrm{aq}),\) the color changes from blue to pink. (a) Does water appear in the equilibrium constant expression for this reaction? (b) How can adding water shift the equilibrium to the left? (c) Is this shift in the equilibrium in accord with Le Chatelier's principle? Why or why not?

A sealed 15.0 -L flask at \(300 . \mathrm{K}\) contains \(64.4 \mathrm{~g}\) of a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) in equilibrium. Calculate the total pressure in the flask. \(\left(\right.\) For \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) K_{\mathrm{P}}=\) 6.67 at \(300 . \mathrm{K} .)\)

The equilibrium constant \(K_{\mathrm{c}}\) has a value of 3.30 at \(760 . \mathrm{K}\) for the decomposition of phosphorus pentachloride, \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (a) Calculate the equilibrium concentrations of all three species arising from the decomposition of \(0.75 \mathrm{~mol} \mathrm{PCl}_{5}\) in a sealed \(5.00-\mathrm{L}\) vessel. (b) Calculate the equilibrium concentrations of all three species resulting from an initial mixture of \(0.75 \mathrm{~mol} \mathrm{PCl}_{5}\) and \(0.75 \mathrm{~mol} \mathrm{PCl}_{3}\) in a sealed 5.00-L vessel.

Use the fact that the equilibrium constant \(K_{\mathrm{c}}\) equals the ratio of the forward rate constant divided by the reverse rate constant, together with the Arrhenius equation \(k=A e^{-E_{\mathrm{a}} / R T}\), to show that a catalyst does not affect the value of an equilibrium constant even though the catalyst increases the rates of forward and reverse reactions. Assume that the frequency factors \(A\) for forward and reverse reactions do not change, and that the catalyst lowers the activation barrier for the catalyzed reaction.

At \(25^{\circ} \mathrm{C}\) the vapor pressure of water is \(0.03126 \mathrm{~atm}\). (a) Calculate \(K_{\mathrm{p}}\) and \(K_{\mathrm{c}}\) for $$ \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ (b) Calculate the value of \(K_{\mathrm{p}}\) for this same system at \(100 .{ }^{\circ} \mathrm{C}\) (c) Suggest a general rule for calculating \(K_{\mathrm{p}}\) for any liquid in equilibrium with its vapor at its normal boiling point.

A student studies the equilibrium $$ \mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g}) $$ at a high temperature. She finds that the total pressure at equilibrium is \(40 . \%\) greater than it was originally, when only \(\mathrm{I}_{2}\) was present at a pressure of \(1.00 \mathrm{~atm}\) in the same sealed container. Calculate \(K_{\mathrm{p}}\).

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) $$ has the value \(5.97 \times 10^{-2}\) at \(500 .{ }^{\circ} \mathrm{C}\). If \(1.00 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{gas}\) and \(1.00 \mathrm{~mol} \mathrm{H}_{2}\) gas are heated to \(500 .{ }^{\circ} \mathrm{C}\) in a \(10.00-\mathrm{L}\) sealed flask together with a catalyst, calculate the percentage of \(\mathrm{N}_{2}\) converted to \(\mathrm{NH}_{3}\). (Hint: Assume that only a very small fraction of the reactants is converted to products. Obtain an approximate answer and use it to obtain a more accurate result.)