169 Equilibrium Calculations

A reaction is represented by this equation: \(\text{A}\left(aq\right)+2\text{B}\left(aq\right)⇌2\text{C}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\)

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations ≤1 M, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

\({K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[\text{C}\right]}^{2}}{\left[\text{A}\right]{\left[\text{B}\right]}^{2}}.\) [A] = 0.1 M, [B] = 0.1 M, [C] = 1 M; and [A] = 0.01, [B] = 0.250, [C] = 0.791.

A reaction is represented by this equation: \(2\text{W}\left(aq\right)⇌\text{X}\left(aq\right)+2\text{Y}\left(aq\right)\phantom{\rule{5em}{0ex}}{K}_{c}=5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\)

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations of ≤1 M, identify two sets of concentrations that describe a mixture of W, X, and Y at equilibrium.

What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?

\({\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\)

An equilibrium mixture of NH₃(g), H₂(g), and N₂(g) at 500 °C was found to contain 1.35 M H₂, 1.15 M N₂, and 4.12 \(×\) 10⁻¹M NH₃.

K_c = 6.00 \(×\) 10⁻²

Hydrogen is prepared commercially by the reaction of methane and water vapor at elevated temperatures.

\({\text{CH}}_{4}\left(g\right)+{\text{H}}_{2}\text{O}\left(g\right)⇌3{\text{H}}_{2}\left(g\right)+\text{CO}\left(g\right)\)

What is the equilibrium constant for the reaction if a mixture at equilibrium contains gases with the following concentrations: CH₄, 0.126 M; H₂O, 0.242 M; CO, 0.126 M; H₂ 1.15 M, at a temperature of 760 °C?

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

K_c = 0.50

At 1 atm and 25 °C, NO₂ with an initial concentration of 1.00 M is 0.0033% decomposed into NO and O₂. Calculate the value of the equilibrium constant for the reaction.

\(2{\text{NO}}_{2}\left(g\right)⇌2\text{NO}\left(g\right)+{\text{O}}_{2}\left(g\right)\)

Calculate the value of the equilibrium constant K_P for the reaction \(2\text{NO}\left(g\right)+{\text{Cl}}_{2}\left(g\right)⇌2\text{NOCl}\left(g\right)\) from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.

K_P = 1.9 \(×\) 10³

When heated, iodine vapor dissociates according to this equation:

\({\text{I}}_{2}\left(g\right)⇌2\text{I}\left(g\right)\)

At 1274 K, a sample exhibits a partial pressure of I₂ of 0.1122 atm and a partial pressure due to I atoms of 0.1378 atm. Determine the value of the equilibrium constant, K_P, for the decomposition at 1274 K.

A sample of ammonium chloride was heated in a closed container.

\({\text{NH}}_{4}\text{Cl}\left(s\right)⇌{\text{NH}}_{3}\left(g\right)+\text{HCl}\left(g\right)\)

At equilibrium, the pressure of NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K_P for the decomposition at this temperature?

K_P = 3.06

At a temperature of 60 °C, the vapor pressure of water is 0.196 atm. What is the value of the equilibrium constant K_P for the vaporization equilibrium at 60 °C?

\({\text{H}}_{2}\text{O}\left(l\right)⇌{\text{H}}_{2}\text{O}\left(g\right)\)

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

\(\begin{array}{llll}2{\text{SO}}_{3}\left(g\right)\hfill & ⇌\hfill & 2{\text{SO}}_{2}\left(g\right)+\hfill & {\text{O}}_{2}\left(g\right)\hfill \\ \text{___}\hfill & & \text{___}\hfill & +x\hfill \\ \text{___}\hfill & & \text{___}\hfill & 0.125\phantom{\rule{0.2em}{0ex}}M\hfill \end{array}\)

(b)

\(\begin{array}{lllll}4{\text{NH}}_{3}\left(g\right)\hfill & +\phantom{\rule{0.2em}{0ex}}3{\text{O}}_{2}\left(g\right)\hfill & ⇌\hfill & 2{\text{N}}_{2}\left(g\right)+\hfill & 6{\text{H}}_{2}\text{O}\left(g\right)\hfill \\ \text{___}\hfill & 3x\hfill & & \text{___}\hfill & \text{___}\hfill \\ \text{___}\hfill & 0.24\phantom{\rule{0.2em}{0ex}}M\hfill & & \text{___}\hfill & \text{___}\hfill \end{array}\)

(c) Change in pressure:

\(\begin{array}{llll}2{\text{CH}}_{4}\left(g\right)\hfill & ⇌\hfill & {\text{C}}_{2}{\text{H}}_{2}\left(g\right)+\hfill & 3{\text{H}}_{2}\left(g\right)\hfill \\ \text{___}\hfill & & x\hfill & \text{___}\hfill \\ \text{___}\hfill & & 25\phantom{\rule{0.2em}{0ex}}\text{torr}\hfill & \text{___}\hfill \end{array}\)

(d) Change in pressure:

\(\begin{array}{lllll}{\text{CH}}_{4}\left(g\right)+\hfill & {\text{H}}_{2}\text{O}\left(g\right)\hfill & ⇌\hfill & \text{CO}\left(g\right)+\hfill & 3{\text{H}}_{2}\left(g\right)\hfill \\ \text{___}\hfill & x\hfill & & \text{___}\hfill & \text{___}\hfill \\ \text{___}\hfill & 5\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & & \text{___}\hfill & \text{___}\hfill \end{array}\)

(e)

\(\begin{array}{llll}{\text{NH}}_{4}\text{Cl}\left(s\right)\hfill & ⇌\hfill & {\text{NH}}_{3}\left(g\right)+\hfill & \text{HCl}\left(g\right)\hfill \\ & & x\hfill & \text{___}\hfill \\ & & \hfill 1.03\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\phantom{\rule{0.2em}{0ex}}M\hfill & \text{___}\hfill \end{array}\)

(f) change in pressure:

\(\begin{array}{cccc}\text{Ni}\left(s\right)+\hfill & 4\text{CO}\left(g\right)\hfill & ⇌\hfill & \text{Ni}{\left(\text{CO}\right)}_{4}\left(g\right)\hfill \\ & 4x\hfill & & \text{___}\hfill \\ & \hfill 0.40\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & & \text{___}\hfill \end{array}\)

(a) −2x, 2x, −0.250 M, 0.250 M; (b) 4x, −2x, −6x, 0.32 M, −0.16 M, −0.48 M; (c) −2x, 3x, −50 torr, 75 torr; (d) x, − x, −3x, 5 atm, −5 atm, −15 atm; (e) x, 1.03 \(×\) 10⁻⁴M; (f) x, 0.1 atm.

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

\(\begin{array}{cccc}2{\text{H}}_{2}\left(g\right)+\hfill & {\text{O}}_{2}\left(g\right)\hfill & ⇌\hfill & 2{\text{H}}_{2}\text{O}\left(g\right)\hfill \\ \text{___}\hfill & \text{___}\hfill & & +2x\hfill \\ \text{___}\hfill & \text{___}\hfill & & 1.50\phantom{\rule{0.2em}{0ex}}M\hfill \end{array}\)

(b)

\(\begin{array}{ccccc}{\text{CS}}_{2}\left(g\right)+\hfill & 4{\text{H}}_{2}\left(g\right)\hfill & ⇌\hfill & {\text{CH}}_{4}\left(g\right)+\hfill & 2{\text{H}}_{2}\text{S}\left(g\right)\hfill \\ x\hfill & \text{___}\hfill & & \text{___}\hfill & \text{___}\hfill \\ 0.020\phantom{\rule{0.2em}{0ex}}M\hfill & \text{___}\hfill & & \text{___}\hfill & \text{___}\hfill \end{array}\)

(c) Change in pressure:

\(\begin{array}{cccc}{\text{H}}_{2}\left(g\right)+\hfill & {\text{Cl}}_{2}\left(g\right)\hfill & ⇌\hfill & 2\text{HCl}\left(g\right)\hfill \\ x\hfill & \text{___}\hfill & & \text{___}\hfill \\ 1.50\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & \text{___}\hfill & & \text{___}\hfill \end{array}\)

(d) Change in pressure:

\(\begin{array}{ccccc}2{\text{NH}}_{3}\left(g\right)\hfill & +\phantom{\rule{0.2em}{0ex}}2{\text{O}}_{2}\left(g\right)\hfill & ⇌\hfill & {\text{N}}_{2}\text{O}\left(g\right)+\hfill & 3{\text{H}}_{2}\text{O}\left(g\right)\hfill \\ \text{___}\hfill & \text{___}\hfill & & \text{___}\hfill & x\hfill \\ \text{___}\hfill & \text{___}\hfill & & \text{___}\hfill & 60.6\phantom{\rule{0.2em}{0ex}}\text{torr}\hfill \end{array}\)

(e)

\(\begin{array}{cccc}{\text{NH}}_{4}\text{HS}\left(s\right)\hfill & ⇌\hfill & {\text{NH}}_{3}\left(g\right)+\hfill & {\text{H}}_{2}\text{S}\left(g\right)\hfill \\ & & x\hfill & \text{___}\hfill \\ & & 9.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}M\hfill & \text{___}\hfill \end{array}\)

(f) Change in pressure:

\(\begin{array}{cccc}\text{Fe}\left(s\right)+\hfill & 5\text{CO}\left(g\right)\hfill & ⇌\hfill & \text{Fe}{\left(\text{CO}\right)}_{5}\left(g\right)\hfill \\ & \text{___}\hfill & & x\hfill \\ & \text{___}\hfill & & 0.012\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill \end{array}\)

Why are there no changes specified for Ni in (Figure), part (f)? What property of Ni does change?

Activities of pure crystalline solids equal 1 and are constant; however, the mass of Ni does change.

Why are there no changes specified for NH₄HS in (Figure), part (e)? What property of NH₄HS does change?

Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.

\({\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=0.50\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}400\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\)

Calculate the equilibrium molar concentration of NH₃.

[NH₃] = 9.1 \(×\) 10⁻²M

Calculate the number of moles of HI that are at equilibrium with 1.25 mol of H₂ and 1.25 mol of I₂ in a 5.00−L flask at 448 °C.

\({\text{H}}_{2}+{\text{I}}_{2}⇌2\text{HI}\phantom{\rule{5em}{0ex}}{K}_{c}=50.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}448\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\)

What is the pressure of BrCl in an equilibrium mixture of Cl₂, Br₂, and BrCl if the pressure of Cl₂ in the mixture is 0.115 atm and the pressure of Br₂ in the mixture is 0.450 atm?

\({\text{Cl}}_{2}\left(g\right)+{\text{Br}}_{2}\left(g\right)⇌2\text{BrCl}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=4.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\)

P_BrCl = 4.9 \(×\) 10⁻² atm

What is the pressure of CO₂ in a mixture at equilibrium that contains 0.50 atm H₂, 2.0 atm of H₂O, and 1.0 atm of CO at 990 °C?

\({\text{H}}_{2}\left(g\right)+{\text{CO}}_{2}\left(g\right)⇌{\text{H}}_{2}\text{O}\left(g\right)+\text{CO}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=1.6\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}990\phantom{\rule{0.2em}{0ex}}\text{°C}\)

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.

\(\text{CoO}\left(s\right)+\text{CO}\left(g\right)⇌\text{Co}\left(s\right)+{\text{CO}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=4.90\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\text{at}\phantom{\rule{0.2em}{0ex}}550\phantom{\rule{0.2em}{0ex}}\text{°C}\)

What concentration of CO remains in an equilibrium mixture with [CO₂] = 0.100 M?

[CO] = 2.04 \(×\) 10⁻⁴M

Carbon reacts with water vapor at elevated temperatures.

\(\text{C}\left(s\right)+{\text{H}}_{2}\text{O}\left(g\right)⇌\text{CO}\left(g\right)+{\text{H}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=0.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}1000\phantom{\rule{0.2em}{0ex}}\text{°C}\)

Assuming a reaction mixture initially contains only reactants, what is the concentration of CO in an equilibrium mixture with [H₂O] = 0.500 M at 1000 °C?

Sodium sulfate 10−hydrate, Na₂SO₄·10H₂O, dehydrates according to the equation

\({\text{Na}}_{2}{\text{SO}}_{4}\text{·}10{\text{H}}_{2}\text{O}\left(s\right)⇌{\text{Na}}_{2}{\text{SO}}_{4}\left(s\right)+10{\text{H}}_{2}\text{O}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=4.08\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-25}\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{°C}\)

What is the pressure of water vapor at equilibrium with a mixture of Na₂SO₄·10H₂O and NaSO₄?

\({P}_{{\text{H}}_{\text{2}}}{}_{\text{O}}=3.64\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−3}}\phantom{\rule{0.2em}{0ex}}\text{atm}\)

Calcium chloride 6−hydrate, CaCl₂·6H₂O, dehydrates according to the equation

\({\text{CaCl}}_{\text{2}}\text{·}6{\text{H}}_{2}\text{O}\left(s\right)⇌{\text{CaCl}}_{2}\left(s\right)+6{\text{H}}_{2}\text{O}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=5.09\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-44}\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{°C}\)

What is the pressure of water vapor at equilibrium with a mixture of CaCl₂·6H₂O and CaCl₂ at 25 °C?

A student solved the following problem and found the equilibrium concentrations to be [SO₂] = 0.590 M, [O₂] = 0.0450 M, and [SO₃] = 0.260 M. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:

\(2{\text{SO}}_{2}\left(g\right)+{\text{O}}_{2}\left(g\right)⇌2{\text{SO}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=4.32\)

What are the equilibrium concentrations of all species in a mixture that was prepared with [SO₃] = 0.500 M, [SO₂] = 0 M, and [O₂] = 0.350 M?

Calculate Q based on the calculated concentrations and see if it is equal to K_c. Because Q does equal 4.32, the system must be at equilibrium.

A student solved the following problem and found [N₂O₄] = 0.16 M at equilibrium. How could this student recognize that the answer was wrong without reworking the problem? The problem was: What is the equilibrium concentration of N₂O₄ in a mixture formed from a sample of NO₂ with a concentration of 0.10 M?

\(2{\text{NO}}_{2}\left(g\right)⇌{\text{N}}_{2}{\text{O}}_{4}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=160\)

Assume that the change in concentration of N₂O₄ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N₂O₄ with chloroform as the solvent.

\({\text{N}}_{2}{\text{O}}_{4}\left(g\right)⇌2{\text{NO}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=1.07\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\) in chloroform

(b) Confirm that the change is small enough to be neglected.

(a) [NO₂] = 1.17 \(×\) 10⁻³M
[N₂O₄] = 0.128 M
(b) The assumption that x is negligibly small compared to 0.129 is confirmed by comparing the initial concentration of the N₂O₄ to its concentration at equilibrium (they differ by just 1 in the least significant digit’s place).

Assume that the change in concentration of COCl₂ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of all species in an equilibrium mixture that results from the decomposition of COCl₂ with an initial concentration of 0.3166 M.

\({\text{COCl}}_{2}\left(g\right)⇌\text{CO}\left(g\right)+{\text{Cl}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=2.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-10}\)

(b) Confirm that the change is small enough to be neglected.

Assume that the change in pressure of H₂S is small enough to be neglected in the following problem.

(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H₂S with an initial pressure of 0.824 atm.

\(2{\text{H}}_{2}\text{S}\left(g\right)⇌2{\text{H}}_{2}\left(g\right)+{\text{S}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=2.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\)

(b) Confirm that the change is small enough to be neglected.

(a) [H₂S] = 0.810 atm
[H₂] = 0.014 atm
[S₂] = 0.0072 atm
(b) The assumption that 2x is negligibly small compared to 0.824 is confirmed by comparing the initial concentration of the H₂S to its concentration at equilibrium (0.824 atm versus 0.810 atm, a difference of less than 2%).

What are all concentrations after a mixture that contains [H₂O] = 1.00 M and [Cl₂O] = 1.00 M comes to equilibrium at 25 °C?

\({\text{H}}_{2}\text{O}\left(g\right)+{\text{Cl}}_{2}\text{O}\left(g\right)⇌2\text{HOCl}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=0.0900\)

Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H₂ and 63.5 g of iodine at 448 °C.

\({\text{H}}_{2}+{\text{I}}_{2}⇌2\text{HI}\phantom{\rule{5em}{0ex}}{K}_{c}=50.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}448\phantom{\rule{0.2em}{0ex}}\text{°C}\)

507 g

Butane exists as two isomers, n−butane and isobutane.

K_P = 2.5 at 25 °C

What is the pressure of isobutane in a container of the two isomers at equilibrium with a total pressure of 1.22 atm?

What is the minimum mass of CaCO₃ required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (K_c) is 0.50 for the decomposition reaction of CaCO₃ at that temperature?

\({\text{CaCO}}_{3}\left(s\right)⇌\text{CaO}\left(s\right)+{\text{CO}}_{2}\left(g\right)\)

330 g

The equilibrium constant (K_c) for this reaction is 1.60 at 990 °C:

\({\text{H}}_{2}\left(g\right)+{\text{CO}}_{2}\left(g\right)⇌{\text{H}}_{2}\text{O}\left(g\right)+\text{CO}\left(g\right)\)

Calculate the number of moles of each component in the final equilibrium mixture obtained from adding 1.00 mol of H₂, 2.00 mol of CO₂, 0.750 mol of H₂O, and 1.00 mol of CO to a 5.00-L container at 990 °C.

In a 3.0-L vessel, the following equilibrium partial pressures are measured: N₂, 190 torr; H₂, 317 torr; NH₃, 1.00 \(×\) 10³ torr.

\({\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\)

(a) How will the partial pressures of H₂, N₂, and NH₃ change if H₂ is removed from the system? Will they increase, decrease, or remain the same?

(b) Hydrogen is removed from the vessel until the partial pressure of nitrogen, at equilibrium, is 250 torr. Calculate the partial pressures of the other substances under the new conditions.

The equilibrium constant (K_c) for this reaction is 5.0 at a given temperature.

\(\text{CO}\left(g\right)+{\text{H}}_{2}\text{O}\left(g\right)⇌{\text{CO}}_{2}\left(g\right)+{\text{H}}_{2}\left(g\right)\)

(a) On analysis, an equilibrium mixture of the substances present at the given temperature was found to contain 0.20 mol of CO, 0.30 mol of water vapor, and 0.90 mol of H₂ in a liter. How many moles of CO₂ were there in the equilibrium mixture?

(b) Maintaining the same temperature, additional H₂ was added to the system, and some water vapor was removed by drying. A new equilibrium mixture was thereby established containing 0.40 mol of CO, 0.30 mol of water vapor, and 1.2 mol of H₂ in a liter. How many moles of CO₂ were in the new equilibrium mixture? Compare this with the quantity in part (a), and discuss whether the second value is reasonable. Explain how it is possible for the water vapor concentration to be the same in the two equilibrium solutions even though some vapor was removed before the second equilibrium was established.

(a) 0.33 mol.
(b) [CO]₂ = 0.50 M. Added H₂ forms some water as a result of a shift to the left after H₂ is added.

Antimony pentachloride decomposes according to this equation:

\({\text{SbCl}}_{5}\left(g\right)⇌{\text{SbCl}}_{3}\left(g\right)+{\text{Cl}}_{2}\left(g\right)\)

An equilibrium mixture in a 5.00-L flask at 448 °C contains 3.85 g of SbCl₅, 9.14 g of SbCl₃, and 2.84 g of Cl₂. How many grams of each will be found if the mixture is transferred into a 2.00-L flask at the same temperature?

Consider the equilibrium

\(4{\text{NO}}_{2}\left(g\right)+6{\text{H}}_{2}\text{O}\left(g\right)⇌4{\text{NH}}_{3}\left(g\right)+7{\text{O}}_{2}\left(g\right)\)

(a) What is the expression for the equilibrium constant (K_c) of the reaction?

(b) How must the concentration of NH₃ change to reach equilibrium if the reaction quotient is less than the equilibrium constant?

(c) If the reaction were at equilibrium, how would an increase in the volume of the reaction vessel affect the pressure of NO₂?

(d) If the change in the pressure of NO₂ is 28 torr as a mixture of the four gases reaches equilibrium, how much will the pressure of O₂ change?

(a) \({K}_{c}=\phantom{\rule{0.2em}{0ex}}\frac{{\left[{\text{NH}}_{3}\right]}^{4}{\left[{\text{O}}_{2}\right]}^{7}}{{\left[{\text{NO}}_{2}\right]}^{4}{\left[{\text{H}}_{2}\text{O}\right]}^{6}}.\) (b) [NH₃] must increase for Q_c to reach K_c. (c) The increase in system volume would lower the partial pressures of all reactants (including NO₂). (d) \({P}_{{\text{O}}_{\text{2}}}=49\phantom{\rule{0.2em}{0ex}}\text{torr}\)

The binding of oxygen by hemoglobin (Hb), giving oxyhemoglobin (HbO₂), is partially regulated by the concentration of H₃O⁺ and dissolved CO₂ in the blood. Although the equilibrium is complicated, it can be summarized as

\({\text{HbO}}_{2}\left(aq\right)+{\text{H}}_{3}{\text{O}}^{\text{+}}\left(aq\right)+{\text{CO}}_{2}\left(g\right)⇌{\text{CO}}_{2}\text{−}\text{Hb}\text{−}{\text{H}}^{\text{+}}+{\text{O}}_{2}\left(g\right)+{\text{H}}_{2}\text{O}\left(l\right)\)

(a) Write the equilibrium constant expression for this reaction.

(b) Explain why the production of lactic acid and CO₂ in a muscle during exertion stimulates release of O₂ from the oxyhemoglobin in the blood passing through the muscle.

Liquid N₂O₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO₂. At 25 °C, a value of K_P = 1.91 has been established for this decomposition. If 0.236 moles of N₂O₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N₂O₃(g), NO₂(g), and NO(g).

\({P}_{{\text{N}}_{\text{2}}}{}_{{\text{O}}_{\text{3}}}=1.90\phantom{\rule{0.2em}{0ex}}\text{atm and}\phantom{\rule{0.2em}{0ex}}{P}_{\text{NO}}={P}_{{\text{NO}}_{\text{2}}}=1.90\phantom{\rule{0.2em}{0ex}}\text{atm}\)

A 1.00-L vessel at 400 °C contains the following equilibrium concentrations: N₂, 1.00 M; H₂, 0.50 M; and NH₃, 0.25 M. How many moles of hydrogen must be removed from the vessel to increase the concentration of nitrogen to 1.1 M? The equilibrium reaction is

\({\text{N}}_{2}\left(g\right)+3{\text{H}}_{2}\left(g\right)⇌2{\text{NH}}_{3}\left(g\right)\)

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) \({\text{I}}_{2}\left(s\right)+{\text{Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{2ICl}\left(g\right)\phantom{\rule{5em}{0ex}}\text{Δ}G\text{°}=\text{−10.88 kJ}\)

(b) \({\text{H}}_{2}\left(g\right)+{\text{I}}_{2}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{2HI}\left(g\right)\phantom{\rule{5em}{0ex}}\text{Δ}G\text{°}=\text{3.4 kJ}\)

(c) \({\text{CS}}_{2}\left(g\right)+{\text{3Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}\left(g\right)+{\text{S}}_{2}{\text{Cl}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}\text{Δ}G\text{°}=\text{−39 kJ}\)

(d) \({\text{2SO}}_{2}\left(g\right)+{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2SO}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}\text{Δ}G\text{°}=\text{−141.82 kJ}\)

(e) \({\text{CS}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CS}}_{2}\left(l\right)\phantom{\rule{5em}{0ex}}\text{Δ}G\text{°}=\text{−1.88 kJ}\)

Calculate the equilibrium constant at the temperature given.

(a) \({\text{O}}_{2}\left(g\right)+{\text{2F}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2F}}_{2}\text{O}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=100\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(b) \({\text{I}}_{2}\left(s\right)+{\text{Br}}_{2}\left(l\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{2IBr}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=0.0\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(c) \(\text{2LiOH}\left(s\right)+{\text{CO}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{Li}}_{2}{\text{CO}}_{3}\left(s\right)+{\text{H}}_{2}\text{O}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=575\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(d) \({\text{N}}_{2}{\text{O}}_{3}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{NO}\left(g\right)+{\text{NO}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=-10.0\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(e) \({\text{SnCl}}_{4}\left(l\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{SnCl}}_{4}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=200\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

In each of the following, the value of ΔG is not given at the temperature of the reaction. Therefore, we must calculate ΔG from the values ΔH° and ΔS and then calculate ΔG from the relation ΔG = ΔH° − TΔS°.
(a) K = 1.29;
(b) K = 2.51 \(×\) 10⁻³;
(c) K = 4.83 \(×\) 10³;
(d) K = 0.219;
(e) K = 16.1

Calculate the equilibrium constant at the temperature given.

(a) \({\text{I}}_{2}\left(s\right)+{\text{Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{2ICl}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=100\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(b) \({\text{H}}_{2}\left(g\right)+{\text{I}}_{2}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{2HI}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=0.0\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(c) \({\text{CS}}_{2}\left(g\right)+{\text{3Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}\left(g\right)+{\text{S}}_{2}{\text{Cl}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=125\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(d) \({\text{2SO}}_{2}\left(g\right)+{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{2SO}}_{3}\left(g\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=675\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

(e) \({\text{CS}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CS}}_{2}\left(l\right)\phantom{\rule{5em}{0ex}}\left(\text{T}=90\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\)

Consider the following reaction at 298 K:
\({\text{N}}_{2}{\text{O}}_{4}\left(g\right)\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}{\text{2NO}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{P}=0.142\)

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.

The standard free energy change is \(\text{Δ}{G}_{298}^{°}=\text{−}RT\phantom{\rule{0.2em}{0ex}}\text{ln}\phantom{\rule{0.2em}{0ex}}K=\text{4.84 kJ/mol}.\) When reactants and products are in their standard states (1 bar or 1 atm), Q = 1. As the reaction proceeds toward equilibrium, the reaction shifts left (the amount of products drops while the amount of reactants increases): Q < 1, and \(\text{Δ}{G}_{298}\) becomes less positive as it approaches zero. At equilibrium, Q = K, and ΔG = 0.

Determine the normal boiling point (in kelvin) of dichloroethane, CH₂Cl₂. Find the actual boiling point using the Internet or some other source, and calculate the percent error in the temperature. Explain the differences, if any, between the two values.

Under what conditions is \({\text{N}}_{2}{\text{O}}_{3}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{NO}\left(g\right)+{\text{NO}}_{2}\left(g\right)\) spontaneous?

The reaction will be spontaneous at temperatures greater than 287 K.

At room temperature, the equilibrium constant (K_w) for the self-ionization of water is 1.00 \(×\) 10⁻¹⁴. Using this information, calculate the standard free energy change for the aqueous reaction of hydrogen ion with hydroxide ion to produce water. (Hint: The reaction is the reverse of the self-ionization reaction.)

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction \({\text{2H}}_{2}\text{S}\left(g\right)+{\text{SO}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}\frac{3}{8}{\text{S}}_{8}\left(s,\phantom{\rule{0.2em}{0ex}}\text{rhombic}\right)+{\text{2H}}_{2}\text{O}\left(l\right).\) What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

K = 5.35 \(×\) 10¹⁵
The process is exothermic.

Consider the decomposition of CaCO₃(s) into CaO(s) and CO₂(g). What is the equilibrium partial pressure of CO₂ at room temperature?

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)

1.0 \(×\) 10⁻⁸ atm. This is the maximum pressure of the gases under the stated conditions.

Benzene can be prepared from acetylene. \({\text{3C}}_{2}{\text{H}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}{\text{C}}_{6}{\text{H}}_{6}\left(g\right).\) Determine the equilibrium constant at 25 °C and at 850 °C. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?

Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?

\(x=1.29\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}\text{atm}={P}_{{\text{O}}_{2}}\)

Carbon tetrachloride, an important industrial solvent, is prepared by the chlorination of methane at 850 K.
\({\text{CH}}_{4}\left(g\right)+{\text{4Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}\left(g\right)+\text{4HCl}\left(g\right)\)

What is the equilibrium constant for the reaction at 850 K? Would the reaction vessel need to be heated or cooled to keep the temperature of the reaction constant?

Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.
\({\text{2CH}}_{3}{\text{CO}}_{2}\text{H}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\left({\text{CH}}_{3}{\text{CO}}_{2}\text{H}\right)}_{2}\left(g\right)\)

The dimer is held together by two hydrogen bonds with a total strength of 66.5 kJ per mole of dimer.

At 25 °C, the equilibrium constant for the dimerization is 1.3 \(×\) 10³ (pressure in atm). What is ΔS° for the reaction?

−0.16 kJ