Chapter 14

How are forward and reverse reaction rates related in a system at chemical equilibrium?

Are ice cubes floating in \(0^{\circ} \mathrm{C}\) water in an insulated container an example of a system in dynamic equilibrium? Explain why or why not.

Do rapid reversible reactions always have greater yields of product than slow reversible reactions? Explain why or why not.

At equilibrium, is the sum of the concentrations of all the reactants always equal to the sum of the concentrations of the products? Explain why or why not.

Suppose the rate constant of the forward reaction \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) is greater than the rate constant of the reverse reaction. Do equilibrium mixtures of \(\mathrm{A}\) and \(\mathrm{B}\) have more A or more \(\mathrm{B}\) in them? Explain your answer.

Suppose at \(298 \mathrm{K}\) the reaction \(\mathrm{C}(g) \rightleftharpoons \mathrm{D}(g)\) has a forward rate constant of \(5 / \mathrm{s}\) and a reverse rate constant of 10/s. What is the value of the equilibrium constant of the reaction at \(298 \mathrm{K} ?\)

In a study of the reaction $$ 2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) $$ quantities of all three gases were injected into a reaction vessel. The \(\mathrm{N}_{2} \mathrm{O}\) consisted entirely of isotopically labeled \(^{15} \mathrm{N}_{2} \mathrm{O} .\) Analysis of the reaction mixture after \(1 \mathrm{day}\) revealed the presence of compounds with molar masses 28 \(29,30,32,44,45,\) and \(46 \mathrm{g} / \mathrm{mol} .\) Identify the compounds and account for their appearance.

A mixture of \(^{13} \mathrm{CO},^{12} \mathrm{CO}_{2},\) and \(\mathrm{O}_{2}\) in a sealed reaction vessel was used to follow the reaction $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)$$ Analysis of the reaction mixture after 1 day revealed the presence of compounds with molar masses 28,29,32,44 and \(45 \mathrm{g} / \mathrm{mol} .\) Identify the compounds and account for their appearance.

Under what conditions are the numerical values of \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) equal?

At \(298 \mathrm{K},\) is \(K_{\mathrm{p}}\) greater than or less than \(K_{\mathrm{c}}\) if there is a net increase in the number of moles of gas in the reaction and if \(K_{\mathrm{c}}>1 ?\) Explain your answer.

What is the equilibrium constant \(\left(K_{c}\right)\) expression for the following reversible reaction? $$ 2 \mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons 2 \mathrm{C}(g) $$

What is the equilibrium constant \(\left(K_{\mathrm{p}}\right)\) expression for the following reversible reaction? $$ 2 \mathrm{A}(g)+3 \mathrm{B}(g) \rightleftharpoons 2 \mathrm{C}(g) $$

Write \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) expressions for the following gas- phase reactions. a. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)\) b. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\)

Write \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) expressions for the following reactions at \(500 \mathrm{K}\) a. \(\mathrm{NH}_{2} \mathrm{Cl}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{HCl}(g)\) b. \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)\)

At \(1200 \mathrm{K}\) the partial pressures of an equilibrium mixture of \(\mathrm{H}_{2} \mathrm{S}, \mathrm{H}_{2},\) and \(\mathrm{S}\) are \(0.020,0.045,\) and 0.030 atm, respectively. Calculate the value of the following equilibrium constant at \(1200 \mathrm{K}\) $$ \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{S}(g) \quad K_{\mathrm{p}}=? $$

At \(1045 \mathrm{K}\) the partial pressures of an equilibrium mixture of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2},\) and \(\mathrm{O}_{2}\) are \(0.040,0.0045,\) and \(0.0030 \mathrm{atm}\) respectively. Calculate the value of the equilibrium constant \(K_{\mathrm{p}}\) at \(1045 \mathrm{K}\) $$ 2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) $$

At equilibrium, the concentrations of gaseous \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and NO in a sealed reaction vessel are \(\left[\mathrm{N}_{2}\right]=3.3 \times 10^{-3} \mathrm{M}\) $$ \left[\mathrm{O}_{2}\right]=5.8 \times 10^{-3} \mathrm{M}, \text { and }[\mathrm{NO}]=3.1 \times 10^{-3} \mathrm{M} . \text { What is } $$ the value of \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$

Exactly 2 moles of ammonia are heated in a sealed 1.00-L container to \(650^{\circ} \mathrm{C}\). At this temperature, ammonia decomposes to nitrogen and hydrogen gas: $$ 2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) $$ At equilibrium, the concentration of ammonia in the container is \(1.00 M .\) What is the value of \(K_{\mathrm{c}}\) for the decomposition reaction at \(650^{\circ} \mathrm{C} ?\)

Hydrogen gas production often begins with the steam-methane reforming reaction $$ \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) $$ At \(1000 \mathrm{K}\) the partial pressures of the gases in an equilibrium mixture are 0.71 atm \(\mathrm{CH}_{4}, 1.41\) atm \(\mathrm{H}_{2} \mathrm{O}\) 1.00 atm \(\mathrm{CO},\) and 3.00 atm \(\mathrm{H}_{2} .\) What is the value of \(K_{\mathrm{p}}\) for the reaction at \(1000 \mathrm{K} ?\)

When the CO produced in the steam-methane reforming reaction is reacted with more steam at \(450 \mathrm{K},\) the water-gas shift reaction: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$ produces more hydrogen. If the equilibrium partial pressures of the gases in the reactor are 0.35 atm \(\mathrm{H}_{2} \mathrm{O}\) 0.24 atm \(\mathrm{CO}, 4.47 \mathrm{atm} \mathrm{H}_{2},\) and \(4.36 \mathrm{atm} \mathrm{CO}_{2},\) what is the value of \(K_{\mathrm{p}} ?\)

At \(500^{\circ} \mathrm{C},\) the equilibrium constant \(K_{\mathrm{p}}\) for the synthesis of ammonia $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(1.45 \times 10^{-5} .\) What is the value of \(K_{\mathrm{c}} ?\)

If the value of the equilibrium constant \(K_{c}\) for the following reaction is \(5 \times 10^{5}\) at \(298 \mathrm{K},\) what is the value of \(K_{\mathrm{p}}\) at \(298 \mathrm{K} ?\) $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$

For which of the following reactions are the values of \(K_{\mathrm{p}}\) and \(K_{\mathrm{c}}\) the same? a. \(2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)\) b. \(2 \mathrm{N}_{2} \mathrm{H}_{4}(\ell)+2 \mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(\ell)\) c. \(\mathrm{NH}_{2} \mathrm{F}(g)+\mathrm{CaCl}_{2}(s) \rightleftharpoons \mathrm{NH}_{2} \mathrm{Cl}(g)+\mathrm{CaClF}(s)\)

For which of the following reactions are the values of \(K_{\mathrm{p}}\) and \(K_{\mathrm{c}}\) different? a. \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\) b. \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2} \mathrm{O}(g)\) c. \(4 \mathrm{HCl}(a q)+\mathrm{MnO}_{2}(s) \rightleftharpoons\) \(\mathrm{MnCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Cl}_{2}(g)\)

Phosgene \(\left(\mathrm{COCl}_{2}\right)\) is used in the manufacture of foam rubber and bulletproof glass. It is formed from carbon monoxide and chlorine in the following reaction: $$ \mathrm{Cl}_{2}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$ The value of \(K_{\mathrm{c}}\) for the reaction is 5.0 at \(327^{\circ} \mathrm{C} .\) What is the value of \(K_{\mathrm{p}}\) at \(327^{\circ} \mathrm{C} ?\)

If the value of \(K_{\mathrm{p}}\) for the following reaction $$ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{SO}_{3}(g) $$ is 3.45 at \(298 \mathrm{K},\) what is the value of \(K_{\mathrm{c}}\) for the reverse reaction?

Explain why representing the same reaction with different chemical equations, like this: (1) \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) \(K_{(1)}\) \((2) \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g)\) \(K_{(2)}\) results in different equilibrium constant values \(\left(K_{(1)} \neq K_{(2)}\right)\).

If the value of \(K_{c}\) for the reaction \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) is \(10,\) what is the value of \(K_{\mathrm{c}}\) for the reaction \(\mathrm{B}(g) \rightleftharpoons \mathrm{A}(g) ?\)

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{IBr}(g) $$ is 120 at \(425 \mathrm{K}\). What is the value of \(K_{\mathrm{c}}\) at \(425 \mathrm{K}\) for the following equilibrium? $$ \frac{1}{2} \mathrm{I}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g) \rightleftharpoons \operatorname{IBr}(g) $$

The equilibrium constant \(K_{\mathrm{p}}\) for the synthesis of ammonia $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.3 \times 10^{-3}\) at \(300^{\circ} \mathrm{C} .\) What is the value of \(K_{\mathrm{p}}\) at \(300^{\circ} \mathrm{C}\) for the following equilibrium? $$ \frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g) $$

The following reaction is one of the elementary steps in the oxidation of NO: $$ \mathrm{NO}(g)+\mathrm{NO}_{3}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$ Write an expression for the equilibrium constant \(K_{\mathrm{c}}\) for this reaction and for the reverse reaction: $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{NO}_{3}(g) $$ How are the two \(K_{\mathrm{c}}\) expressions related?

The value of the equilibrium constant \(K_{\mathrm{p}}\) for the formation of ammonia $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.5 \times 10^{-5}\) at \(450^{\circ} \mathrm{C} .\) What is the value of \(K_{\mathrm{p}}\) at \(450^{\circ} \mathrm{C}\) for the following reaction? $$ 2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) $$

The \(K_{\mathrm{c}}\) value for the reaction $$ 2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) $$ is \(3.0 \times 10^{-4}\) at \(298 \mathrm{K} .\) What is the value of \(K_{\mathrm{c}}\) at \(298 \mathrm{K}\) for the following reaction? $$ \mathrm{NOBr}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g) $$

How is the value of the equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$ 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) $$ related to the value of \(K_{\mathrm{p}}\) for this reaction at the same temperature? $$ \mathrm{H}_{2} \mathrm{O}(g)+\frac{1}{2} \mathrm{N}_{2}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{NO}(g) $$

If the equilibrium constant \(K_{\mathrm{c}}\) for the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) is \(5 \times 10^{12}\) at a given temperature, what is the value of the equilibrium constant \(K_{\mathrm{c}}\) for each of the following reactions at the same temperature? a. \(\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g)\) b. \(2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\)

Calculate the value of the equilibrium constant \(K_{\mathrm{p}}\) at \(298 \mathrm{K}\) for the reaction $$ \mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$ from the following \(K_{\mathrm{p}}\) values at \(298 \mathrm{K}\) $$\begin{aligned} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}(g) & & K_{\mathrm{p}}=4.4 \times 10^{-31} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}_{2}(g) & & K_{\mathrm{p}}=2.4 \times 10^{12} \end{aligned}$$

Calculate the value of the equilibrium constant \(K_{\mathrm{p}}\) at \(298 \mathrm{K}\) for the reaction $$ \frac{1}{4} \mathrm{S}_{8}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ from the following \(K_{\mathrm{p}}\) values at \(298 \mathrm{K}\) $$\frac{1}{4} \mathrm{S}_{8}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$ from the following \(K_{\mathrm{p}}\) values at \(298 \mathrm{K}\) $$\frac{1}{8} \mathrm{S}_{8}(s)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g) \quad K_{\mathrm{p}}=4.0 \times 10^{52}$$ $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) \quad K_{\mathrm{p}}=7.8 \times 10^{24}$$

How is an equilibrium constant different from a reaction quotient?

Explain how comparing the values of reaction quotient \(Q\) and equilibrium constant \(K\) for a given reaction and temperature enables chemists to predict whether a reversible reaction will proceed in the forward direction, in the reverse direction, or in neither direction.

The equilibrium constant \(K_{\mathrm{c}}\) for the hypothetical reaction $$ 2 \mathrm{C}(g) \rightleftharpoons \mathrm{D}(g)+\mathrm{E}(g) $$ is \(3 \times 10^{-3} .\) At a particular time, the composition of the reaction mixture is \([\mathrm{C}]=[\mathrm{D}]=[\mathrm{E}]=5 \times 10^{-4} M\) In which direction will the reaction proceed to reach equilibrium?

If the equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ is \(1.5 \times 10^{-3},\) in which direction will the reaction proceed if the partial pressures of the three gases are all \(1.00 \times 10^{-3}\) atm?

At \(650 \mathrm{K},\) the value of the equilibrium constant \(K_{\mathrm{p}}\) for the ammonia synthesis reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.3 \times 10^{-4} .\) If a vessel at \(650 \mathrm{K}\) contains a reaction mixture in which \(\left[\mathrm{N}_{2}\right]=0.010 M,\left[\mathrm{H}_{2}\right]=0.030 M,\) and \(\left[\mathrm{NH}_{3}\right]=0.00020 \mathrm{M},\) will more ammonia form?

Use the information below to determine whether a reaction mixture in which the partial pressures of \(\mathrm{PCl}_{3}, \mathrm{Cl}_{2},\) and \(\mathrm{PCl}_{5}\) are \(0.20,0.40,\) and 0.60 atm, respectively, is at equilibrium at \(450 \mathrm{K}\) $$ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) \quad K_{\mathrm{p}}=3.8 \text { at } 450 \mathrm{K} $$ If the reaction mixture is not at equilibrium, in which direction does the reaction proceed to achieve equilibrium?

\(\mathbf{S O}_{2}\) in the Air Combustion of fossil fuels that contain sulfur is an important source of sulfur dioxide in the atmosphere. Write the \(K_{\mathrm{p}}\) expression for the combustion of elemental sulfur: $$ \frac{1}{8} \mathrm{S}_{8}(s)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g) $$

Write the \(K_{\mathrm{c}}\) expression for the oxidation of calcium sulfite to gypsum (calcium sulfate): $$ 2 \mathrm{CaSO}_{3}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CaSO}_{4}(s) $$

Mixing aqueous solutions of sodium bicarbonate and calcium chloride results in this reaction: \(2 \mathrm{NaHCO}_{3}(a q)+\mathrm{CaCl}_{2}(a q) \rightleftharpoons\) $$ 2 \mathrm{NaCl}(a q)+\mathrm{CO}_{2}(g)+\mathrm{CaCO}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) $$ Write the \(K_{\mathrm{c}}\) expression for the reaction.

Write \(K_{\mathrm{p}}\) expressions for the reactions below that take place during the thermal decomposition of the mineral dolomite (a mixture of calcium and magnesium carbonates): $$ \begin{aligned} \mathrm{CaCO}_{3}(s) & \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \\\ \mathrm{MgCO}_{3}(s) & \Longrightarrow \mathrm{MgO}(s)+\mathrm{CO}_{2}(g) \end{aligned} $$

The brown residues that form on the surfaces of plumbing fixtures, such as inside toilet tanks, are the result of the oxidation of more soluble iron(II) compounds with dissolved oxygen, forming less soluble iron(III) compounds. Write the \(K_{\mathrm{c}}\) expression for one such reaction: \(4 \mathrm{Fe}(\mathrm{OH})_{2}(a q)+\mathrm{O}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons 4 \mathrm{Fe}(\mathrm{OH})_{3}(s)\)

Write the \(K_{\mathrm{c}}\) expression for this reaction, which is used to test whether a white, shiny mineral is marble (calcium carbonate): \(2 \mathrm{HCl}(a q)+\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaCl}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(g)\)

Does adding reactants to a system at equilibrium increase the value of the equilibrium constant? Why or why not?