Chapter 13: Fundamental Equilibrium ConceptsContent check — Chemistry: Atoms First, Chapter 13: Fundamental Equilibrium Concepts

(a) $2{\text{SO}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2{\text{SO}}_3(g)$

(b) ${\text{C}}_4{\text{H}}_8(g)\rightleftharpoons$ $2{\text{C}}_2{\text{H}}_4(g)$

(c) $2{\text{C}}_4{\text{H}}_{10}(g)+$ $13{\text{O}}_2(g)\rightleftharpoons$ $8{\text{CO}}_2(g)+$ $10{\text{H}}_2\text{O}(g)$

(a) A 1.00-L flask containing 0.0500 mol of NO(g), 0.0155 mol of Cl₂(g), and 0.500 mol of NOCl:

(b) A 5.0-L flask containing 17 g of NH₃, 14 g of N₂, and 12 g of H₂:

(c) A 2.00-L flask containing 230 g of SO₃(g):

(a) $2{\text{SO}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2{\text{SO}}_3(g)$

(b) ${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons$ $2{\text{NO}}_2(g)$

(c) ${\text{C}}_3{\text{H}}_8(g)+$ $5{\text{O}}_2(g)\rightleftharpoons$ $3{\text{CO}}_2(g)+$ $4{\text{H}}_2\text{O}(g)$

(d) At 227 °C, the following reaction has K_c = 0.0952:

What would be the value of K_P at this temperature?

(a) $$\begin{array}{llll}2{\text{SO}}_2(g)+\hfill & {\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 2{\text{SO}}_3(g)\hfill \\ \_\_\_\_\_\hfill & x\hfill & & \_\_\_\_\_\hfill \end{array}$$

(b) $$\begin{array}{lll}{\text{C}}_4{\text{H}}_8(g)\hfill & \rightleftharpoons \hfill & 2{\text{C}}_2{\text{H}}_4(g)\hfill \\ \_\_\_\_\_\hfill & & \mathrm{-2}x\hfill \end{array}$$

(c) $$\begin{array}{lllll}4{\text{NH}}_3(g)+\hfill & 7{\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 4{\text{NO}}_2(g)+\hfill & 6{\text{H}}_2\text{O}(g)\hfill \\ \\ \_\_\_\_\_\hfill & \_\_\_\_\_\hfill & & \_\_\_\_\_\hfill & \_\_\_\_\_\hfill \end{array}$$

When 1 mol each of C₂H₅OH and CH₃CO₂H are allowed to react in 1 L of the solvent dioxane, equilibrium is established when $\frac{1}{3}$ mol of each of the reactants remains. Calculate the equilibrium constant for the reaction. (Note: Water is a solute in this reaction.)

The equilibrium constant for this reaction with dioxane as a solvent is 4.0. What are the equilibrium concentrations for a mixture that is initially 0.15 M in CH₃CO₂H, 0.15 M in C₂H₅OH, 0.40 M in CH₃CO₂C₂H₅, and 0.40 M in H₂O?

How does the spontaneity of this process depend upon temperature?

Among the solubility rules previously discussed is the statement: All chlorides are soluble except Hg₂Cl₂, AgCl, PbCl₂, and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation $\text{AgCl}(s)\rightleftharpoons$ ${\text{Ag}}^{\text{+}}(aq)+$ ${\text{Cl}}^{\text{−}}(aq).$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation ${\text{Pb}}^{\mathrm{2+}}(aq)+$ $2{\text{Cl}}^{\text{−}}(aq)\rightleftharpoons$ ${\text{PbCl}}_2(s).$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

Write the mathematical expression for the reaction quotient, Q_c, for each of the following reactions:

(a) ${\text{CH}}_4(g)+$ ${\text{Cl}}_2(g)\rightleftharpoons$ ${\text{CH}}_3\text{Cl}(g)+$ $\text{HCl}(g)$

(b) ${\text{N}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2\text{NO}(g)$

(c) $2{\text{SO}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2{\text{SO}}_3(g)$

(d) ${\text{BaSO}}_3(s)\rightleftharpoons$ $\text{BaO}(s)+$ ${\text{SO}}_2(g)$

(e) ${\text{P}}_4(g)+$ $5{\text{O}}_2(g)\rightleftharpoons$ ${\text{P}}_4{\text{O}}_{10}(s)$

(f) ${\text{Br}}_2(g)\rightleftharpoons$ $2\text{Br}(g)$

(g) ${\text{CH}}_4(g)+$ $2{\text{O}}_2(g)\rightleftharpoons$ ${\text{CO}}_2(g)+$ $2{\text{H}}_2\text{O}(l)$

(h) ${\text{CuSO}}_4\text{·}5{\text{H}}_2\text{O}(s)\rightleftharpoons$ ${\text{CuSO}}_4(s)+$ $5{\text{H}}_2\text{O}(g)$

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction in which each system will proceed to reach equilibrium.

$$\begin{array}{cccc}\text{(a)}2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)\hfill & & & K_c=17;[{\text{NH}}_3]=0.20M,[{\text{N}}_2]=1.00M,[{\text{H}}_2]=1.00M\hfill \\ \text{(b)}2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)\hfill & & & K_P=6.8\times {10}^4;{\text{NH}}_3=3.0\text{atm},{\text{N}}_2=2.0\text{atm},{\text{H}}_2=1.0\text{atm}\hfill \\ \text{(c)}2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2\left(g\right)\hfill & & & K_c=0.230;[{\text{SO}}_3]=0.00M,[{\text{SO}}_2]=1.00M,[{\text{O}}_2]=1.00M\hfill \\ \text{(d)}2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2(g)\hfill & & & K_P=16.5;{\text{SO}}_3=1.00\text{atm},{\text{SO}}_2=1.00\text{atm},{\text{O}}_2=1.00\text{atm}\hfill \\ \text{(e)}2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)\hfill & & & K_c=4.6\times {10}^4;[\text{NO}]=1.00M,[{\text{Cl}}_2]=1.00M,[\text{NOCl}]=0M\hfill \\ \text{(f)}{\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)\hfill & & & K_P=0.050;\text{NO}=10.0\text{atm},{\text{N}}_2={\text{O}}_2=\text{5 atm}\hfill \end{array}$$

The following reaction has K_P = 4.50 $\times$ 10⁻⁵ at 720 K.
${\text{N}}_2(g)+$ $3{\text{H}}_2(g)\rightleftharpoons$ $2{\text{NH}}_3(g)$

If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? P(NH₃) = 93 atm, P(N₂) = 48 atm, and P(H₂) = 52 atm

Convert the values of K_c to values of K_P or the values of K_P to values of K_c.

$$\begin{array}{cccc}\text{(a)}{\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)\hfill & & & K_c=0.50\text{at}400\text{°C}\hfill \\ \text{(b)}{\text{H}}_2(g)+{\text{I}}_2(g)\rightleftharpoons 2\text{HI}(g)\hfill & & & K_c=50.2\text{at}448\text{°C}\hfill \\ \text{(c)}{\text{Na}}_2{\text{SO}}_4\text{·}10{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{Na}}_2{\text{SO}}_4(s)+10{\text{H}}_2\text{O}(g)\hfill & & & K_P=4.08\times {10}^{\mathrm{-25}}\text{at}25\text{°C}\hfill \\ \text{(d)}{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\hfill & & & K_P=0.122\text{at}50\text{°C}\hfill \end{array}$$

The following equation represents a reversible decomposition:
${\text{CaCO}}_3(s)\rightleftharpoons$ $\text{CaO}(s)+$ ${\text{CO}}_2(g)$

Under what conditions will decomposition in a closed container proceed to completion so that no CaCO₃ remains?

The following reaction occurs when a burner on a gas stove is lit:
${\text{CH}}_4(g)+$ $2{\text{O}}_2(g)\rightleftharpoons$ ${\text{CO}}_2(g)+$ $2{\text{H}}_2\text{O}(g)$

Is an equilibrium among CH₄, O₂, CO₂, and H₂O established under these conditions? Explain your answer.

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?

(a) $2{\text{NH}}_3(g)\rightleftharpoons$ ${\text{N}}_2(g)+$ $3{\text{H}}_2(g)$ $\text{Δ}H=$ $92\text{kJ}$

(b) ${\text{N}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2\text{NO}(g)$ $\text{Δ}H=$ $181\text{kJ}$

(c) $2{\text{O}}_3(g)\rightleftharpoons$ $3{\text{O}}_2(g)$ $\text{Δ}H=$ $\mathrm{-285}\text{kJ}$

(d) $\text{CaO}(s)+$ ${\text{CO}}_2(g)\rightleftharpoons$ ${\text{CaCO}}_3(s)$ $\text{Δ}H=$ $\mathrm{-176}\text{kJ}$

Methanol can be prepared from carbon monoxide and hydrogen at high temperature and pressure in the presence of a suitable catalyst.

(a) Write the expression for the equilibrium constant (K_c) for the reversible reaction
$2{\text{H}}_2(g)+$ $\text{CO}(g)\rightleftharpoons$ ${\text{CH}}_3\text{OH}(g)$ $\text{Δ}H=$ $\mathrm{-90.2}\text{kJ}$

(b) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if more H₂ is added?

(c) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CO is removed?

(d) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CH₃OH is added?

(e) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if the temperature of the system is increased?

Water gas, a mixture of H₂ and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon.

(a) Write the expression for the equilibrium constant for the reversible reaction
$\text{C}(s)+$ ${\text{H}}_2\text{O}(g)\rightleftharpoons$ $\text{CO}(g)+$ ${\text{H}}_2(g)$ $\text{Δ}H=$ $131.30\text{kJ}$

(b) What will happen to the concentration of each reactant and product at equilibrium if more C is added?

(c) What will happen to the concentration of each reactant and product at equilibrium if H₂O is removed?

(d) What will happen to the concentration of each reactant and product at equilibrium if CO is added?

(e) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

Ammonia is a weak base that reacts with water according to this equation:
${\text{NH}}_3(aq)+$ ${\text{H}}_2\text{O}(l)\rightleftharpoons$ ${\text{NH}}_4{}^{\text{+}}(aq)+$ ${\text{OH}}^{\text{−}}(aq)$

Will any of the following increase the percent of ammonia that is converted to the ammonium ion in water?

(a) Addition of NaOH

(b) Addition of HCl

(c) Addition of NH₄Cl

A solution is saturated with silver sulfate and contains excess solid silver sulfate:
${\text{Ag}}_2{\text{SO}}_4(s)\rightleftharpoons$ $2{\text{Ag}}^{\text{+}}(aq)+$ ${\text{SO}}_4{}^{\mathrm{2-}}(aq)$

A small amount of solid silver sulfate containing a radioactive isotope of silver is added to this solution. Within a few minutes, a portion of the solution phase is sampled and tests positive for radioactive Ag⁺ ions. Explain this observation.

A reaction is represented by this equation: $\text{A}(aq)+$ $2\text{B}(aq)\rightleftharpoons$ $2\text{C}(aq)$ $K_c=$ $1\times {10}^3$

(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.

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

${\text{N}}_2(g)+$ $3{\text{H}}_2(g)\rightleftharpoons$ $2{\text{NH}}_3(g)$

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 $\times$ 10⁻¹ M NH₃.

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

${\text{NH}}_4\text{Cl}(s)\rightleftharpoons$ ${\text{NH}}_3(g)+$ $\text{HCl}(g)$

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?

Complete the following partial ICE tables.

(a)

$$\begin{array}{lllll}& 2{\text{SO}}_3(g)\hfill & \rightleftharpoons \hfill & 2{\text{SO}}_2(g)+\hfill & {\text{O}}_2(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & +x\hfill \end{array}$$

(b)

$$\begin{array}{llllll}& 4{\text{NH}}_3(g)\hfill & +3{\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 2{\text{N}}_2(g)+\hfill & 6{\text{H}}_2\text{O}(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & +x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$$

(c)

$$\begin{array}{lllll}& 2{\text{CH}}_4(g)\hfill & \rightleftharpoons \hfill & {\text{C}}_2{\text{H}}_2(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & & +x\hfill & \text{\_\_\_}\hfill \end{array}$$

(d)

$$\begin{array}{llllll}& {\text{CH}}_4(g)+\hfill & {\text{H}}_2\text{O}(g)\hfill & \rightleftharpoons \hfill & \text{CO}(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{change}\hfill & \text{\_\_\_}& +x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$$

(e)

$$\begin{array}{lllll}& {\text{NH}}_4\text{Cl}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_3(g)+\hfill & \text{HCl}(g)\hfill \\ \text{change}& & +x\hfill & \text{\_\_\_}\hfill \end{array}$$

(f)

$$\begin{array}{ccccc}& \text{Ni}(s)+\hfill & 4\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Ni}{(\text{CO})}_4(g)\hfill \\ \text{change}& +x\hfill & & \text{\_\_\_}\hfill \end{array}$$

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.

${\text{N}}_2(g)+$ $3{\text{H}}_2(g)\rightleftharpoons$ $2{\text{NH}}_3(g)$ $K_c=$ $0.50\text{at}400\text{°}\text{C}$

Calculate the equilibrium molar concentration of NH₃.

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?

${\text{Cl}}_2(g)+$ ${\text{Br}}_2(g)\rightleftharpoons$ $2\text{BrCl}(g)$ $K_P=$ $4.7\times {10}^{\mathrm{-2}}$

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

$\text{CoO}(s)+$ $\text{CO}(g)\rightleftharpoons$ $\text{Co}(s)+$ ${\text{CO}}_2(g)$ $K_c=$ $4.90\times {10}^2\text{at}550\text{°C}$

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

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

${\text{Na}}_2{\text{SO}}_4\text{·}10{\text{H}}_2\text{O}(s)\rightleftharpoons$ ${\text{Na}}_2{\text{SO}}_4(s)+$ $10{\text{H}}_2\text{O}(g)$ $K_P=$ $4.08\times {10}^{\mathrm{-25}}\text{at}25\text{°C}$

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

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:

$2{\text{SO}}_2(g)+$ ${\text{O}}_2(g)\rightleftharpoons$ $2{\text{SO}}_3(g)$ $K_c=$ $4.32$

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?

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.

${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons$ $2{\text{NO}}_2(g)$ $K_c=$ $1.07\times {10}^{\mathrm{-5}}$ in chloroform

(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.

$2{\text{H}}_2\text{S}(g)\rightleftharpoons$ $2{\text{H}}_2(g)+$ ${\text{S}}_2(g)$ $K_P=$ $2.2\times {10}^{\mathrm{-6}}$

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

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.

${\text{H}}_2+$ ${\text{I}}_2\rightleftharpoons$ $2\text{HI}$ $K_c=$ $50.2\text{at}448\text{°C}$

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?

${\text{CaCO}}_3(s)\rightleftharpoons$ $\text{CaO}(s)+$ ${\text{CO}}_2(g)$

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

$\text{CO}(g)+$ ${\text{H}}_2\text{O}(g)\rightleftharpoons$ ${\text{CO}}_2(g)+$ ${\text{H}}_2(g)$

(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.

Consider the equilibrium

$4{\text{NO}}_2(g)+$ $6{\text{H}}_2\text{O}(g)\rightleftharpoons$ $4{\text{NH}}_3(g)+$ $7{\text{O}}_2(g)$

(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?

Calculate the equilibrium constant at the temperature given.

(a) ${\text{O}}_2(g)+$ ${\text{2F}}_2(g)⟶$ ${\text{2F}}_2\text{O}(g)$ $(\text{T}=100\text{°C})$

(b) ${\text{I}}_2(s)+$ ${\text{Br}}_2(l)⟶$ $\text{2IBr}(g)$ $(\text{T}=0.0\text{°C})$

(c) $\text{2LiOH}(s)+$ ${\text{CO}}_2(g)⟶$ ${\text{Li}}_2{\text{CO}}_3(s)+$ ${\text{H}}_2\text{O}(g)$ $(\text{T}=575\text{°C})$

(d) ${\text{N}}_2{\text{O}}_3(g)⟶$ $\text{NO}(g)+$ ${\text{NO}}_2(g)$ $(\text{T}=\mathrm{-10.0}\text{°C})$

(e) ${\text{SnCl}}_4(l)⟶$ ${\text{SnCl}}_4(g)$ $(\text{T}=200\text{°C})$

Consider the following reaction at 298 K:
${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons$ ${\text{2NO}}_2(g)$ $K_P=$ $0.142$

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.

Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.
${\text{2CH}}_3{\text{CO}}_2\text{H}(g)⟶$ ${({\text{CH}}_3{\text{CO}}_2\text{H})}_2(g)$

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 $\times$ 10³ (pressure in atm). What is ΔS° for the reaction?