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3.4 Practice Problems

3.4 Practice Problems#

  1. Write \(Q_c\) expressions for the following reactions:

\[\begin{split} \begin{align*} \ce{ 2 N2O &<=> 2 N2 + O2 \\ 2 NOBr &<=> 2 NO + Br2 \\ HF &<=> H+ + F- \\ CO + H2O &<=> CO2 + H2 \\ CH4 + 2 H2S &<=> CS2 + 4 H2 \\ H2C2O4 &<=> 2 H+ + C2O4^2- } \end{align*} \end{split}\]

  1. 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

\[\begin{split} \begin{align*} \ce{N2 + 3 H2 & <=> 2 NH3\\ 1/2 N2 + 3/2 H2 & <=> NH3 } \end{align*} \end{split}\]

  1. 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

\(P\)

\(C\)

\(\%\)

\(\pu{atm}\)

\(\pu{mol L-1}\)

\(\ce{N2}\)

\(\ce{O2}\)

\(21\)

\(0.21\)

\(\pu{8.58e-3}\)

\(\vdots\)

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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. \(\pu{800 ^\circ C}\)

  1. 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.

  1. 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?

  1. \(\ce{CaCl2(s)}\) 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) \(\pu{0.4 mol L-1}\)

  1. 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.

  1. 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 \(\ce{S(s)}\)

  1. 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.

  1. 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 \(T\)?