Chapter 14

Can a reaction that is not reversible achieve chemical equilibrium?

At equilibrium, is the sum of the concentrations of all the reactants always equal to the sum of the concentrations of the products? Explain.

Suppose the forward rate constant of the reaction \(\mathrm{A} \rightleftharpoons \mathrm{B}\) is greater than the rate constant of the reverse reaction at a given temperature. Is the valuc of the cquilibrium constant less than, greater than, or cqual to \(1 ?\)

Explain how it is possible for a reaction to have a large equilibrium constant but small forward and reverse rate constants.

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 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 presence.

A mixture of \(^{13} \mathrm{CO},^{12} \mathrm{CO}_{2},\) and \(\mathrm{O}_{2}\) in a scaled 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 presence.

Suppose the reaction \(A \rightleftharpoons B\) in the forward direction is first order in \(\mathrm{A}\) with \(k_{\mathrm{f}}=1.50 \times 10^{-2} \mathrm{s}^{-1} .\) The reverse reaction is first order in \(\mathrm{B}\) with \(k_{\mathrm{r}}=4.50 \times 10^{-2} \mathrm{s}^{-1}\) at the same temperature. What is the valuc of the cquilibrium constant for the reaction \(\mathrm{A} \rightleftharpoons \mathrm{B}\) at this temperature?

At \(700 \mathrm{K}, K_{c}=8.7 \times 10^{6}\) for the gas-phase reaction between \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) forming \(\mathrm{NO}_{2}\). The rate constant for the reverse reaction at this temperature is \(0.54 M^{-1} \mathrm{s}^{-1}\) What is the value of the rate constant for the forward reaction at \(700 \mathrm{K} ?\)

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

Nitrogen oxides play important roles in air pollution. Write expressions for \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\) for the following reactions involving nitrogen oxides. a. \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)\) b. \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g)\) c. \(2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\)

Write expressions for \(K_{c}\) and \(K_{p}\) for the following reactions, which contribute to the destruction of stratospheric ozone. a. \(\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) b. \(2 \mathrm{ClO}(g) \rightleftharpoons 2 \mathrm{Cl}(g)+\mathrm{O}_{2}(g)\) c. \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\)

At \(1200 \mathrm{K}\) the partial pressures of an cquilibrium mixture of \(\mathrm{H}_{2} \mathrm{S}, \mathrm{H}_{2},\) and \(\mathrm{S}\) are \(0.020,0.045,\) and \(0.030 \mathrm{atm}\) respectively. Calculate the value of \(K_{\mathrm{p}}\) at \(1200 \mathrm{K}\)

At \(1045 \mathrm{K}\) the partial pressures of an cquilibrium 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 \(K_{\mathrm{p}}\) 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 scaled reaction vessel are \(\left[\mathrm{N}_{2}\right]=3.3 \times 10^{-3} \mathrm{M}\) \(\left[\mathrm{O}_{2}\right]=5.8 \times 10^{-3} \mathrm{M},\) and \([\mathrm{NO}]=3.1 \times 10^{-3} \mathrm{M}\) What is the value of \(K_{e}\) for the following reaction at the temperature of the mixture? $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$

Analyses of an equilibrium mixture of gaseous \(\mathrm{N}_{2} \mathrm{O}_{4}\) and NO, gave the following results: \(\left[\mathrm{NO}_{2}\right]=4.2 \times 10^{-3} \mathrm{M}\) and \(\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=2.9 \times 10^{-3} \mathrm{M} .\) What is the value of \(K_{e}\) for the following reaction at the temperature of the mixture? $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) $$

A 100 mL reaction vessel initially contains \(2.60 \times 10^{-2} \mathrm{mol} \mathrm{NO}\) and \(1.30 \times 10^{-2} \mathrm{mol} \mathrm{H}_{2}, \mathrm{At}\) cquilibrium, the concentration of NO in the vesscl is \(0.161 M .\) What is the value of \(K_{\mathrm{c}}\) for the following reaction? $$ 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g) $$

\(K_{\eta}=32\) for the following equilibrium at \(298 \mathrm{K}\) $$ \mathrm{A}(z)+\mathrm{B}(g) \rightleftharpoons \mathrm{AB}(g) $$ What is the value of \(K_{c}\) for this same equilibrium at \(298 \mathrm{K} ?\)

\(K_{\mathrm{p}}=0.1764\) for the following equilibrium at \(1773 \mathrm{K}\) $$ \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ What is \(K_{c}\) for this reaction at the same temperature?

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

If the value of \(K_{c}\) 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 \(K_{c}\) and \(K_{\mathrm{p}}\) equal? a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) b. \(F e(s)+C O_{2}(g) \rightleftarrows F e O(s)+C O(g)\) c. \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\)

For which of the following reactions are the values of \(K_{c}\) and \(K_{\mathrm{p}}\) different? a. \(\operatorname{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) b. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) c. \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\)

Bulletproof Glass 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: $$ \mathrm{Cl}_{2}(g)+\mathrm{CO}(g) \rightleftharpoons \operatorname{COCl}_{2}(g) $$

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

How is the value of the equilibrium constant affected by scaling up or down the coefficients of the reactants and products in the chemical equation describing the reaction?

Is the numerical value of \(K_{p}\) for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) $$ greater than, equal to, or less than the value of the equilibrium constant for the following reaction? $$ \frac{1}{2} \mathrm{H}_{2}(z)+\frac{1}{2} \mathrm{I}_{2}(g) \rightleftharpoons \mathrm{HI}(g) $$

\(K_{c}=120\) for the following reaction at \(425 \mathrm{K}\) $$ \mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{IBr}(g) $$ What is the value of \(K_{e}\) for the following reaction, also at \(425 \mathrm{K} ?\) $$ \frac{1}{2} \mathrm{I}_{2}(g)+\frac{1}{2} \mathrm{B} \mathrm{r}_{2}(g) \rightleftharpoons \operatorname{IBr}(g) $$

The equilibrium constant \(K_{p}\) 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 valuc of \(K_{\mathrm{p}}\) for the following equilibrium, also at \(300^{\circ} \mathrm{C} ?\) $$ \frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g) $$

At a given temperature, the equilibrium constant \(K_{c}\) for the reaction $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is \(0.11 .\) What is the equilibrium constant \(K_{\mathrm{p}}\) for the following reaction? $$ \mathrm{NO}(g)+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$

Air Pollutants Sulfur oxides are major air pollutants. The reaction between sulfur dioxide and oxygen can be written in two ways: $$ \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) $$ and $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$

At a given temperature, \(K_{e}\) for the reaction $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is \(0.11 .\) What is the equilibrium constant for the following reaction at the same temperature? $$ \mathrm{NO}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$

At a given temperature, \(K_{c}\) for the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) is \(2.4 \times 10^{-3} .\) What is the value of the equilibrium constant for each of the following reactions at the same temperature? a. \(\operatorname{so}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)\) b. \(2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)\) c. \(\operatorname{SO}_{3}(g) \rightleftharpoons \operatorname{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\)

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

Calculate the value of the equilibrium constant \(K_{c}\) for the reaction, $$ 2 \mathrm{D} \rightleftharpoons \mathrm{A}+2 \mathrm{B} $$ given the following information: $$ \begin{array}{rlrl} A+2 B & F C & K_{c} & =3.3 \\ C & \rightleftharpoons 2 D & K_{c} & =0.041 \end{array} $$

What is a reaction quotient?

How is an equilibrium constant different from a reaction quotient?

What does it mean when the reaction quotient \(Q\) is numerically equal to the equilibrium constant \(K ?\)

Explain how knowing \(Q\) and \(K\) for an equilibrium system enables you to say whether it is at equilibrium or whether it will shift in one direction or another.

If \(K_{c}=22\) for the hypothetical reaction \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) at a given temperature, and if \([\mathrm{A}]=0.10 \mathrm{M}\) and \([\mathrm{B}]=2.0 \mathrm{M}\) in a reaction mixture at that temperature, is the reaction at chemical equilibrium? If not, in which direction will the reaction proceed to reach equilibrium?

In which direction will the following hypothetical reaction proceed to reach equilibrium under the conditions given? \(A(g)+B(g) \rightleftharpoons C(g) \quad K_{p}=1.00\) at \(300 K\) a. \(P_{\mathrm{A}}=P_{\mathrm{C}}=1.0 \mathrm{atm}, P_{\mathrm{B}}=0.50 \mathrm{atm}\) b. \([\mathrm{A}]=[\mathrm{B}]=[\mathrm{C}]=1.0 \mathrm{M}\)

If \(K_{c}=1.5 \times 10^{-3}\) for the reaction, $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ 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 valuc of \(K_{\mathrm{p}}\) for the ammonia synthesis reaction $$ \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.3 \times 10^{-4} .\) If a vessel 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?

The hypothetical equilibrium \(\mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z}\) has \(K_{e}=1.00\) at \(350 \mathrm{K}\). If the initial molar concentrations of \(\mathrm{X}, \mathrm{Y},\) and Z in a solution are all \(0.2 M\), in which direction will the reaction shift to reach equilibrium? a. To the left, making more \(X\) and \(Y\) b. To the right, making more \(Z\) c. The system is at cquilibrium and the concentrations will not change.

Reactions between carboxylic acids and alcohols to produce esters typically do not go to completion. Ethyl acetate, a compound used industrially to decaffeinate coffee and tea, is made in the following reaction for which \(K_{c}=3.87\) at \(75^{\circ} \mathrm{C}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\ell)+\mathrm{CH}_{3} \operatorname{cooH}(\ell) \rightleftharpoons\) $$ \mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}(e)+\mathrm{H}_{2} \mathrm{O}(\ell) $$ Is a mixture of \(125 \mathrm{g}\) of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right), 125 \mathrm{g}\) of acctic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right), 125 \mathrm{g}\) of cthyl acctate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}\right),\) and \(125 \mathrm{g}\) of watcr in a \(5 \mathrm{L}\) reactor at equilibrium? b. If not, in which direction will the reaction shift to reach equilibrium?

Write the \(K_{c}\) expression for the following reaction: $$ \mathrm{CuS}(s) \rightleftharpoons \mathrm{Cu}^{2+}(a q)+\mathrm{S}^{2-}(a q) $$

Write the \(K_{c}\) expression for the following reaction: $$ \mathrm{Ml}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons 2 \mathrm{\Lambdal}^{3+}(a q)+6 \mathrm{OH}^{-}(a q) $$

Why docsn't the \(K_{e}\) expression for the reaction $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ contain terms for the concentrations of \(\mathrm{CaCO}_{3}\) and \(\mathrm{CaO}^{2}\)

How many partial pressure terms are there in the \(K_{\mathrm{p}}\) expression for the thermal decomposition of sodium bicarbonate? \(2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Does adding reactants to a system at equilibrium increase the value of the equilibrium constant?

Increasing the concentration of a reactant shifts the position of chemical cquilibrium toward formation of more products. What effect does adding a reactant have on the rates of the forward and reverse reactions?