Equilibrium Calculations

(a) 2x, x, −2x; (b) x, −2x; (c) 4x, 7x, −4x, −6x or −4x, −7x, 4x, 6x

${\text{I}}_2(aq)+{\text{I}}^{\text{−}}(aq)\rightleftharpoons {\text{I}}_3{}^{\text{−}}(aq)$

$1.000\times {10}^{\mathrm{-3}}-x=6.61\times {10}^{\mathrm{-4}}$

$x=1.000\times {10}^{\mathrm{-3}}-6.61\times {10}^{\mathrm{-4}}$

$=3.39\times {10}^{\mathrm{-4}}M$

$K_c=Q_c=\frac{[{\text{I}}_3{}^{\text{−}}]}{[{\text{I}}_2]\left[{\text{I}}^{\text{−}}\right]}$

$=\frac{3.39\times {10}^{\mathrm{-4}}M}{(6.61\times {10}^{\mathrm{-4}}M)(6.61\times {10}^{\mathrm{-4}}M)}=776$

${\text{C}}_2{\text{H}}_5\text{OH}+{\text{CH}}_3{\text{CO}}_2\text{H}\rightleftharpoons {\text{CH}}_3{\text{CO}}_2{\text{C}}_2{\text{H}}_5+{\text{H}}_2\text{O}$

K_c = 4

$K_c=Q_c=\frac{{\left[\text{NO}\right]}^2}{\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]}$

${\left[\text{NO}\right]}^2=K_c\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]$

$\left[\text{NO}\right]=\sqrt{K_c\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]}$

$=\sqrt{(4.1\times {10}^{\mathrm{-4}})(0.036)(0.0089)}$

$=\sqrt{1.31\times {10}^{\mathrm{-7}}}$

$=3.6\times {10}^{\mathrm{-4}}$

$Q_c=\frac{{\left[\text{NO}\right]}^2}{\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]}$

$=\frac{{(3.6\times {10}^{\mathrm{-4}})}^2}{(0.036)(0.0089)}$

$Q_c=4.0\times {10}^{\mathrm{-4}}=K_c$

1.53 mol/L

${\text{CH}}_3{\text{CO}}_2\text{H}+{\text{C}}_2{\text{H}}_5\text{OH}\rightleftharpoons {\text{CH}}_3{\text{CO}}_2{\text{C}}_2{\text{H}}_5+{\text{H}}_2\text{O}$

[CH₃CO₂H] = 0.36 M, [C₂H₅OH] = 0.36 M, [CH₃CO₂C₂H₅] = 0.17 M, [H₂O] = 0.17 M

${\text{H}}_2(g)+{\text{I}}_2(g)\rightleftharpoons 2\text{HI}(g)$

[H₂] = 0.06 M, [I₂] = 1.06 M, [HI] = 1.88 M

$\text{HCN}(aq)\rightleftharpoons {\text{H}}^{\text{+}}(aq)+{\text{CN}}^{\text{−}}(aq)K_c=4.9\times {10}^{\text{−10}}$

$K_c=\frac{(x)(x)}{0.15-x}$

$x^2+4.9\times {10}^{\text{−10}}-7.35\times {10}^{\text{−11}}=0$

$x=8.56\times {10}^{\text{−6}}M(\text{3 sig. figs.})=8.6\times {10}^{\text{−6}}M(\text{2 sig. figs.})$

$K_c=\frac{(x)(x)}{0.15-x}\approx \frac{x^2}{0.15}$

$4.9\times {10}^{\text{−10}}=\frac{x^2}{0.15}$

$x^2=(0.15)(4.9\times {10}^{\text{−10}})=7.4\times {10}^{\text{−11}}$

$x=\sqrt{7.4\times {10}^{\text{−11}}}=8.6\times {10}^{\text{−6}}M$

$\frac{x}{0.15}\times 100\%=\frac{8.6\times {10}^{\text{−6}}}{0.15}\times 100\%=0.006\%$

${\text{NH}}_3(aq)+{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{NH}}_4{}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)K_{\text{c}}=1.8\times {10}^{\text{−5}}$

$[{\text{OH}}^{\text{−}}]=[{\text{NH}}_4{}^{\text{+}}]=0.0021M;$

[NH₃] = 0.25 M, error = 0.84%

${\text{Cu}}^{\mathrm{2+}}(aq)+{\text{4NH}}_3(aq)\rightleftharpoons \text{Cu}{({\text{NH}}_3)}_4{}^{\mathrm{2+}}(aq)K_{\text{c}}=5.0\times {10}^{13}=\frac{[\text{Cu}{({\text{NH}}_3)}_4{}^{\mathrm{2+}}]}{[{\text{Cu}}^{\mathrm{2+}}(aq)]{[{\text{NH}}_3]}^4}$

$[{\text{Cu}}^{\mathrm{2+}}]=0.010-0.010=0M$

$[\text{Cu}{({\text{NH}}_3)}_4{}^{\mathrm{2+}}]=0.010M$

$[{\text{NH}}_3]=1.00-4\times 0.010=0.96M$

$0.96+4x\approx 0.96M$

$0.010-x\approx 0.010M$

$K_c=\frac{(0.010-x)}{x{(0.96-4x)}^4}\approx \frac{(0.010)}{x{(0.96)}^4}=5.0\times {10}^{13}$

$x=\frac{(0.010)}{K_c{(0.96)}^4}=2.4\times {10}^{\text{−16}}M$

$\frac{2.4\times {10}^{\text{−16}}}{0.010}\times 100\%=2\times {10}^{\text{−12}}\%$

$[{\text{Cu}}^{\mathrm{2+}}]=x=2.4\times {10}^{\text{−16}}M$

$[{\text{NH}}_3]=0.96-4x=0.96M$

$[\text{Cu}{({\text{NH}}_3)}_4{}^{\mathrm{2+}}]=0.010-x=0.010M$

${\text{Ni}}^{\mathrm{2+}}(aq)+{\text{6NH}}_3(aq)\rightleftharpoons \text{Ni}{({\text{NH}}_3)}_6{}^{\mathrm{2+}}(aq)K_{\text{c}}=5.5\times {10}^8$

$[\text{Ni}{({\text{NH}}_3)}_6{}^{\mathrm{2+}}]=0.25M,$

[NH₃] = 0.50 M, [Ni²⁺] = 2.9 $\times$

10^–8 M, error = 1.2 $\times$

10^–5%

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, make up two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

$K_c=\frac{{[\text{C}]}^2}{\left[\text{A}\right]{\left[\text{B}\right]}^2}.$

[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: $2\text{W}(aq)\rightleftharpoons \text{X}(aq)+2\text{Y}(aq)K_c=5\times {10}^{\mathrm{-4}}$

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

(b) Using concentrations of ≤1 M, make up 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?

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

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.

K_c = 6.00 $\times$

10⁻²

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

${\text{CH}}_4(g)+{\text{H}}_2\text{O}(g)\rightleftharpoons 3{\text{H}}_2(g)+\text{CO}(g)$

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 3.3 $\times$

10⁻³% decomposed into NO and O₂. Calculate the value of the equilibrium constant for the reaction.

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

Calculate the value of the equilibrium constant K_P for the reaction $2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)$

from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.

K_P = 1.9 $\times$

10³

When heated, iodine vapor dissociates according to this equation:

${\text{I}}_2(g)\rightleftharpoons 2\text{I}(g)$

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.

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

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?

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 transformation at 60 °C?

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

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

(a)

$\begin{array}{llll}2{\text{SO}}_3(g)\hfill & \rightleftharpoons \hfill & 2{\text{SO}}_2(g)+\hfill & {\text{O}}_2(g)\hfill \\ \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & +x\hfill \\ \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & 0.125M\hfill \end{array}$

(b)

$\begin{array}{lllll}4{\text{NH}}_3(g)\hfill & +3{\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 2{\text{N}}_2(g)+\hfill & 6{\text{H}}_2\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & 3x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & 0.24M\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(c) Change in pressure:

$\begin{array}{llll}2{\text{CH}}_4(g)\hfill & \rightleftharpoons \hfill & {\text{C}}_2{\text{H}}_2(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{\_\_\_}\hfill & & x\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & & 25\text{torr}\hfill & \text{\_\_\_}\hfill \end{array}$

(d) Change in pressure:

$\begin{array}{lllll}{\text{CH}}_4(g)+\hfill & {\text{H}}_2\text{O}(g)\hfill & \rightleftharpoons \hfill & \text{CO}(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{\_\_\_}\hfill & x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & 5\text{atm}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(e)

$\begin{array}{llll}{\text{NH}}_4\text{Cl}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_3(g)+\hfill & \text{HCl}(g)\hfill \\ & & x\hfill & \text{\_\_\_}\hfill \\ & & \hfill 1.03\times {10}^{\mathrm{-4}}M\hfill & \text{\_\_\_}\hfill \end{array}$

(f) change in pressure:

$\begin{array}{cccc}\text{Ni}(s)+\hfill & 4\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Ni}{(\text{CO})}_4(g)\hfill \\ & 4x\hfill & & \text{\_\_\_}\hfill \\ & \hfill 0.40\text{atm}\hfill & & \text{\_\_\_}\hfill \end{array}$

(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 $\times$

10⁻⁴ M; (f) x, 0.1 atm.

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

(a)

$\begin{array}{cccc}2{\text{H}}_2(g)+\hfill & {\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 2{\text{H}}_2\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & +2x\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & 1.50M\hfill \end{array}$

(b)

$\begin{array}{ccccc}{\text{CS}}_2(g)+\hfill & 4{\text{H}}_2(g)\hfill & \rightleftharpoons \hfill & {\text{CH}}_4(g)+\hfill & 2{\text{H}}_2\text{S}(g)\hfill \\ x\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ 0.020M\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(c) Change in pressure:

$\begin{array}{cccc}{\text{H}}_2(g)+\hfill & {\text{Cl}}_2(g)\hfill & \rightleftharpoons \hfill & 2\text{HCl}(g)\hfill \\ x\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill \\ 1.50\text{atm}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill \end{array}$

(d) Change in pressure:

$\begin{array}{ccccc}2{\text{NH}}_3(g)\hfill & +2{\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & {\text{N}}_2\text{O}(g)+\hfill & 3{\text{H}}_2\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & x\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & 60.6\text{torr}\hfill \end{array}$

(e)

$\begin{array}{cccc}{\text{NH}}_4\text{HS}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_3(g)+\hfill & {\text{H}}_2\text{S}(g)\hfill \\ & & x\hfill & \text{\_\_\_}\hfill \\ & & 9.8\times {10}^{\mathrm{-6}}M\hfill & \text{\_\_\_}\hfill \end{array}$

(f) Change in pressure:

$\begin{array}{cccc}\text{Fe}(s)+\hfill & 5\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Fe}{(\text{CO})}_5(g)\hfill \\ & \text{\_\_\_}\hfill & & x\hfill \\ & \text{\_\_\_}\hfill & & 0.012\text{atm}\hfill \end{array}$

Why are there no changes specified for Ni in [link], 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 [link], 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.

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

Calculate the equilibrium molar concentration of NH₃.

[NH₃] = 9.1 $\times$

10⁻² M

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.

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

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?

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

P_BrCl = 4.9 $\times$

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?

${\text{H}}_2(g)+{\text{CO}}_2(g)\rightleftharpoons {\text{H}}_2\text{O}(g)+\text{CO}(g)K_P=1.6\text{at}990\text{°C}$

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?

[CO] = 2.04 $\times$

10⁻⁴ M

Carbon reacts with water vapor at elevated temperatures.

$\text{C}(s)+{\text{H}}_2\text{O}(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_2(g)K_c=0.2\text{at}1000\text{°C}$

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

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

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

$P_{{\text{H}}_{\text{2}}}{}_{\text{O}}=3.64\times {10}^{\text{−3}}\text{atm}$

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

${\text{CaCl}}_{\text{2}}\text{·}6{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{CaCl}}_2(s)+6{\text{H}}_2\text{O}(g)K_P=5.09\times {10}^{\mathrm{-44}}\text{at}25\text{°C}$

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

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:

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

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?

$2{\text{NO}}_2(g)\rightleftharpoons {\text{N}}_2{\text{O}}_4(g)K_c=160$

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.

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

in chloroform

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

(a) [NO₂] = 1.17 $\times$

10⁻³ *M** * *

[N₂O₄] = 0.128 *M** * *

(b) Percent error $=\frac{5.87\times {10}^{\mathrm{-4}}}{0.129}\times 100\%=0.455\%.$

The change in concentration of N₂O₄ is far less than the 5% maximum allowed.

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.

${\text{COCl}}_2(g)\rightleftharpoons \text{CO}(g)+{\text{Cl}}_2(g)K_c=2.2\times {10}^{\mathrm{-10}}$

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

(a) [H₂S] = 0.810 atm* * *

[H₂] = 0.014 atm* * *

[S₂] = 0.0072 atm* * *

(b) The 2x is dropped from the equilibrium calculation because 0.014 is negligible when subtracted from 0.824. The percent error associated with ignoring 2x is $\frac{0.014}{0.824}\times 100\%=1.7\%,$

which is less than allowed by the “5% test.” The error is, indeed, negligible.

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

${\text{H}}_2\text{O}(g)+{\text{Cl}}_2\text{O}(g)\rightleftharpoons 2\text{HOCl}(g)K_c=0.0900$

What are the concentrations of PCl₅, PCl₃, and Cl₂ in an equilibrium mixture produced by the decomposition of a sample of pure PCl₅ with [PCl₅] = 2.00 M?

${\text{PCl}}_5(g)\rightleftharpoons {\text{PCl}}_3(g)+{\text{Cl}}_2(g)K_c=0.0211$

[PCl₅] = 1.80 M; [Cl₂] = 0.195 M; [PCl₃] = 0.195 M.

Calculate the pressures of all species at equilibrium in a mixture of NOCl, NO, and Cl₂ produced when a sample of NOCl with a pressure of 10.0 atm comes to equilibrium according to this reaction:* * *

$\text{2NOCl}(g)\rightleftharpoons \text{2NO}(g)+{\text{Cl}}_2(g)K_P=4.0\times {10}^{\text{−4}}$

Calculate the equilibrium concentrations of NO, O₂, and NO₂ in a mixture at 250 °C that results from the reaction of 0.20 M NO and 0.10 M O₂. (Hint: K is large; assume the reaction goes to completion then comes back to equilibrium.)

$2\text{NO}(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{NO}}_2(g)K_c=2.3\times {10}^5\text{at}250\text{°C}$

[NO₂] = 0.19 *M** * *

[NO] = 0.0070 *M** * *

[O₂] = 0.0035 M

Calculate the equilibrium concentrations that result when 0.25 M O₂ and 1.0 M HCl react and come to equilibrium.

$4\text{HCl}(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{Cl}}_2(g)+2{\text{H}}_2\text{O}(g)K_c=3.1\times {10}^{13}$

One of the important reactions in the formation of smog is represented by the equation

${\text{O}}_3(g)+\text{NO}(g)\rightleftharpoons {\text{NO}}_2(g)+{\text{O}}_2(g)K_P=6.0\times {10}^{34}$

What is the pressure of O₃ remaining after a mixture of O₃ with a pressure of 1.2 $\times$

10⁻⁸ atm and NO with a pressure of 1.2 $\times$

10⁻⁸ atm comes to equilibrium? (Hint: K_P is large; assume the reaction goes to completion then comes back to equilibrium.)

$P_{{\text{O}}_3}=4.9\times {10}^{\mathrm{-26}}\text{atm}$

Calculate the pressures of NO, Cl₂, and NOCl in an equilibrium mixture produced by the reaction of a starting mixture with 4.0 atm NO and 2.0 atm Cl₂. (Hint: K_P is small; assume the reverse reaction goes to completion then comes back to equilibrium.)

$2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)K_P=2.5\times {10}^3$

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.

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

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 0.050 for the decomposition reaction of CaCO₃ at that temperature?

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

33 g

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

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

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.

At 25 °C and at 1 atm, the partial pressures in an equilibrium mixture of N₂O₄ and NO₂ are ${\text{P}}_{{\text{N}}_2{\text{O}}_4}=0.70\text{atm}$

and ${\text{P}}_{{\text{NO}}_2}=0.30\text{atm.}$

(a) Predict how the pressures of NO₂ and N₂O₄ will change if the total pressure increases to 9.0 atm. Will they increase, decrease, or remain the same?

(b) Calculate the partial pressures of NO₂ and N₂O₄ when they are at equilibrium at 9.0 atm and 25 °C.

(a) Both gases must increase in pressure.* * *

(b)$P_{{\text{N}}_{\text{2}}}{}_{{\text{O}}_{\text{4}}}=8.0\text{atm and}{P}_{{\text{NO}}_{\text{2}}}=1.0\text{atm}$

In a 3.0-L vessel, the following equilibrium partial pressures are measured: N₂, 190 torr; H₂, 317 torr; NH₃, 1.00 $\times$

10³ torr.

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

(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.

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

(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.

(a) 0.33 mol. * * *

(b) [CO₂] = 0.50 M Added H₂ forms some water to compensate for the removal of water vapor and as a result of a shift to the left after H₂ is added.

Antimony pentachloride decomposes according to this equation:

${\text{SbCl}}_5(g)\rightleftharpoons {\text{SbCl}}_3(g)+{\text{Cl}}_2(g)$

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 reaction between H₂ and O₂ at 1000 K* * *

${\text{2H}}_2(g)+{\text{O}}_2(g)\rightleftharpoons {\text{2H}}_2\text{O}(g)K_P=\frac{{(P_{{\text{H}}_2\text{O}})}^{\text{2}}}{(P_{{\text{O}}_2}){(P_{{\text{H}}_2})}^{\text{2}}}=1.33\times {10}^{20}$

If 0.500 atm of H₂ and 0.500 atm of O₂ are allowed to come to equilibrium at this temperature, what are the partial pressures of the components?

$P_{{\text{H}}_{\text{2}}}=8.64\times {10}^{\text{−11}}\text{atm}$

---

$P_{{\text{O}}_{\text{2}}}=0.250\text{atm}$

---

$P_{{\text{H}}_{\text{2}}}{}_{\text{O}}=0.500\text{atm}$

An equilibrium is established according to the following equation

${\text{Hg}}_2{}^{\mathrm{2+}}(aq)+{\text{NO}}_3{}^{\text{−}}(aq)+3{\text{H}}^{\text{+}}(aq)\rightleftharpoons 2{\text{Hg}}^{\mathrm{2+}}(aq)+{\text{HNO}}_2(aq)+{\text{H}}_2\text{O}(l)K_c=4.6$

What will happen in a solution that is 0.20 M each in ${\text{Hg}}_2{}^{\mathrm{2+}},$

${\text{NO}}_3{}^{\text{−}},$

H⁺, Hg²⁺, and HNO₂?

(a) ${\text{Hg}}_2{}^{\mathrm{2+}}$

will be oxidized and ${\text{NO}}_3{}^{\text{−}}$

reduced.

(b) ${\text{Hg}}_2{}^{\mathrm{2+}}$

will be reduced and ${\text{NO}}_3{}^{\text{−}}$

oxidized.

(c) Hg²⁺ will be oxidized and HNO₂ reduced.

(d) Hg²⁺ will be reduced and HNO₂ oxidized.

(e) There will be no change because all reactants and products have an activity of 1.

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 a decrease in pressure (from 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) $K_c=\frac{{[{\text{NH}}_3]}^4{[{\text{O}}_2]}^7}{{[{\text{NO}}_2]}^4{[{\text{H}}_2\text{O}]}^6}.$

(b) [NH₃] must increase for Q_c to reach K_c. (c) That decrease in pressure would decrease [NO₂]. (d) $P_{{\text{O}}_{\text{2}}}=49\text{torr}$

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

${\text{HbO}}_2(aq)+{\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{CO}}_2(g)\rightleftharpoons {\text{CO}}_2\text{−}\text{Hb}\text{−}{\text{H}}^{\text{+}}+{\text{O}}_2(g)+{\text{H}}_2\text{O}(l)$

(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.

The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose.

${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}(aq)+{\text{H}}_2\text{O}(l)⟶{\text{C}}_6{\text{H}}_{12}{\text{O}}_6(aq)+{\text{C}}_6{\text{H}}_{12}{\text{O}}_6(aq)$

Rate = k[C₁₂H₂₂O₁₁]

In neutral solution, k = 2.1 $\times$

10⁻¹¹/s at 27 °C. (As indicated by the rate constant, this is a very slow reaction. In the human body, the rate of this reaction is sped up by a type of catalyst called an enzyme.) (Note: That is not a mistake in the equation—the products of the reaction, glucose and fructose, have the same molecular formulas, C₆H₁₂O₆, but differ in the arrangement of the atoms in their molecules). The equilibrium constant for the reaction is 1.36 $\times$

10⁵ at 27 °C. What are the concentrations of glucose, fructose, and sucrose after a 0.150 M aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.

[fructose] = 0.15 M

The density of trifluoroacetic acid vapor was determined at 118.1 °C and 468.5 torr, and found to be 2.784 g/L. Calculate K_c for the association of the acid.

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).

$P_{{\text{N}}_{\text{2}}}{}_{{\text{O}}_{\text{3}}}=1.90\text{atm and}{P}_{\text{NO}}=P_{{\text{NO}}_{\text{2}}}=1.90\text{atm}$

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?

A 0.010 M solution of the weak acid HA has an osmotic pressure (see chapter on solutions and colloids) of 0.293 atm at 25 °C. A 0.010 M solution of the weak acid HB has an osmotic pressure of 0.345 atm under the same conditions.

(a) Which acid has the larger equilibrium constant for ionization

HA $[\text{HA}(aq)\rightleftharpoons {\text{A}}^{\text{−}}(aq)+{\text{H}}^{\text{+}}(aq)]$

or HB $[\text{HB}(aq)\rightleftharpoons {\text{H}}^{\text{+}}(aq)+{\text{B}}^{\text{−}}(aq)]$

?

(b) What are the equilibrium constants for the ionization of these acids?

(Hint: Remember that each solution contains three dissolved species: the weak acid (HA or HB), the conjugate base (A⁻ or B⁻), and the hydrogen ion (H⁺). Remember that osmotic pressure (like all colligative properties) is related to the total number of solute particles. Specifically for osmotic pressure, those concentrations are described by molarities.)

(a) HB ionizes to a greater degree and has the larger K_c.* * *

(b) K_c(HA) = 5 $\times$

10⁻⁴* * *

K_c(HB) = 3 $\times$

10⁻³