# 3.4 Practice Problems 1. Write $Q_c$ expressions for the following reactions: $$ \begin{align*} \ce{ 2 N2O &<=> 2 N2 + O2 \\ 2 NOBr &<=> 2 NO + Br2 \\ HF &<=> H+ + F- \\ CO + H2O &<=> CO2 + H2 \\ CH4 + 2 H2S &<=> CS2 + 4 H2 \\ H2C2O4 &<=> 2 H+ + C2O4^2- } \end{align*} $$ 2. A reaction vessel contains $\ce{NH3 (g)}$, $\ce{N2 (g)}$, and $\ce{H2 (g)}$ at equilibrium at a certain temperature. The equilibrium concentrations are $[\ce{NH3}] = \pu{0.25 M}$, $[\ce{N2}] = \pu{0.11 M}$, and $[\ce{H2}] = \pu{1.91 M}$. Calculate the equilibrium constant $K_c$ for each of the two reactions representing synthesis of ammonia as $$ \begin{align*} \ce{N2 + 3 H2 & <=> 2 NH3\\ 1/2 N2 + 3/2 H2 & <=> NH3 } \end{align*} $$ 3. Create a table of all gases present in Earth's atmosphere from the most abundant at top to less abundant (minimum of 6 gases). In adjacent columns, list concentrations in fraction ($\%$), partial pressure ($P,\, \pu{atm}$), and concentration ($C,\, \pu{mol L-1}$). See template below: | Gas | Fraction | $P$ | $C$ | |------ |-----: | ------: | --------: | | | $\%$ | $\pu{atm}$ | $\pu{mol L-1}$ | | $\ce{N2}$ | | | | | $\ce{O2}$ | $21$ | $0.21$ | $\pu{8.58e-3}$ | | $\vdots$ | | | | 4. Carbonyl chloride ($\ce{COCl2}$), also called phosgene, is a highly poisonous gas that was used on the battlefield in World War I. It is produced by the reaction of carbon monoxide with chlorine gas as follows $$\ce{CO(g) + Cl2(g) <=> COCl2(g)}$$ >In an experiment conducted at $\pu{74 ^\circ C}$, the equilibrium concentrations of the species involved in the reaction were as follows: $[\ce{CO}] = \pu{1.2e-2 M}$, $[\ce{Cl2}]= \pu{0.054 M}$, and $[\ce{COCl2}] = \pu{0.14 M}$. > >(a) Write the equilibrium expression. > >(b) Determine $K_c$ and $K_p$ for this reaction at 74 °C. 5. At equilibrium, the pressure of the reacting mixture (represented below) is $\pu{0.105 atm}$ at $\pu{350 ^\circ C}$. $$\ce{CaCO3(s) <=> CaO(s) + CO2(g) }$$ >Determine $K_c$ and $K_p$ for this reaction. 6. Below is a reaction depicting the composition of water molecules and the production of $\ce{H2(g)}$ at $\pu{25 ^\circ C}$. (In reality, this reaction occurs at a very high temperature.) $$\ce{2 H2O(g) <=> 2 H2(g) + O2(g) }$$ > Using thermodynamic data, calculate the equilibrium constant, $K_p$ for this reaction. 7. The dissolution of silver chloride in water at $\pu{25 ^\circ C}$. $$\ce{AgCl(s) <=>[H2O] Ag+(aq) + Cl-(aq) \qquad $K_{sp} = \pu{1.6e-10}$ }$$ > Calculate $\Delta_{rxn}G^\circ$ for the process using only the data provided here. 8. Consider the decomposition of calcium carbonate as shown in the reaction below. $$\ce{CaCO3 <=> CaO + CO2 }$$ >Assume that $\Delta_{rxn}H^\circ = \pu{177.8 kJ mol-1}$ and $\Delta_{rxn}S^\circ = \pu{160.5 J mol-1 K-1}$ for the temperature range. Calculate the pressure in atm of in an equilibrium process at the following temperatures: > >a. $\pu{25 ^\circ C}$ > >b. $\pu{800 ^\circ C}$ 9. At $\pu{25 ^\circ C}$, $\Delta_{rxn}G^\circ = \pu{8.6 kJ mol-1}$ for the process shown below. $$\ce{H2O(l) <=> H2O(g) }$$ > Calculate the vapor pressure of water at this temperature. 10. The reaction below shows the equilibrium between graphite and diamond. $$\ce{C  (diamond) <=> C  (graphite) }$$ > a. Calculate $\Delta_{rxn}G^\circ$ for the process. > > b. Is the formation of graphite from diamond favored at $\pu{25 ^\circ C}$? If so, why is it that diamonds do not become graphite on standing? 11. $\ce{CaCl2(s)}$ is a strong electrolyte when it is dissolved in water at $\pu{25 ^\circ C}$ to create $\ce{Ca^2+}$ and $\ce{Cl-}$. Calculate activity of $\{\ce{Ca^2+}\}$ and $\{\ce{Cl-}\}$ when the following concentrations of $\ce{CaCl2(s)}$ are dissolved: > (a) $\pu{0.001 mol L-1}$ > > (b) $\pu{0.09 mol L-1}$ > > (c) $\pu{0.4 mol L-1}$ 12. At the start of the following reaction, the concentrations of $\ce{N2}$, $\ce{H2}$, and $\ce{NH3}$ are $\pu{0.071 M}$, $\pu{9.2e-3 M}$, and $\pu{1.83e-4 M}$, respectively. $$\ce{N2 + 3 H2 <=> 2 NH3 \qquad $K_c =1.2$ at $\pu{375 ^\circ C}$ }$$ >Determine whether this system is at equilibrium, and if not, determine in which direction it must proceed to establish equilibrium. 13. Hydrogen sulfide ($\ce{H2S(g)}$) is a commonly found in salt marsh environments. It is removed by reaction with oxygen to produce elemental sulfur. $$\ce{2 H2S(g) + O2(g) <=> 2 S(s) + 2 H2O(g) }$$ >For each of the following scenarios, determine whether the equilibrium will shift to the right, shift to the left, or neither: > >(a) addition of $\ce{O2(g)}$ > >(b) removal of $\ce{H2S(g)}$ > >(c) removal of $\ce{H2O(g)}$ > >(d) addition of $\ce{S(s)}$ 14. Repeat above problem with the following initial data. $$\ce{H2(g) + I2(g) <=> 2 HI(g) }$$ >Calculate concentrations of all components at equilibrium if we start with $\ce{H2(g)}$ = $\pu{0.00623 M}$, $\ce{H2(g)}$ = $\pu{0.00414 M}$, and $\ce{HI(g)}$ = $\pu{0.0424 M}$. $K_c$ for the above reaction is $54.3$ at $\pu{430 ^\circ C}$. > >Hint: Compare $Q_c$ with $K_c$ to determine in which direction the reaction proceeds towards equilibrium. 15. Large quantities of $\ce{H2 (g)}$ are needed to produce $\ce{NH3(g)}$. One preparation for $\ce{H2 (g)}$ is the following reaction, at $\pu{300 ^\circ C}$ in the presence of a Cu-Zn catalyst: $$\ce{CO(g) + H2O(g) <=> CO2(g) + H2(g) \qquad $K_c=1.87$ and $\Delta _{rxn}H^\circ = \pu{-41 kJ mol-1}$ }$$ >(a) Initial concentrations of reactants $\ce{CO(g)}$ and $\ce{H2O(g)}$ were $\pu{3.2 M}$. The final concentration of $\ce{CO(g)}$ was monitored over time and determined to be $\pu{1.35 M}$ at equilibrium. What are the equilibrium concentrations of all gases? (Use ICE method) > >(b) In another reactor, initial concentrations are: $[\ce{CO}] = \pu{0.50 M}$, $[\ce{H2O}] = \pu{0.045 M}$, $[\ce{CO2}] = \pu{0.050 M}$, $[\ce{H2}] = \pu{0.040 M}$. (i) Compare $Q$ to $K$ and determine in which direction the reaction will proceed. (ii) What are the equilibrium concentrations? > >(c) If $\pu{0.80 mole}$ of $\ce{CO(g)}$ and $\ce{H2O(g)}$ are added to a new $\pu{5 L}$ reactor, what are the equilibrium concentrations of all reactants and products? > >(d) If your objective is to increase $\ce{H2(g)}$ production, explain which of the following options work? (i) Remove reactant or product? (ii) Add reactant or product? (iii) Change $P$? (iv) Change $T$?