Topic: 23.4

Hydrogen peroxide is a liquid at 298K. It is moderately stable under room conditions but will decompose quickly if a catalyst is added.
Reaction 1: \(2H_2O_2(l) \to 2H_2O (l) + O_2 (g)\)
(a) (i) Define entropy.
(ii) Predict the sign of the standard entropy change of reaction 1. Explain your answer.
(b) Some bond energy data are shown in Table 3.1.

Use the data in Table 3.1 to show that the enthalpy change of the following reaction is \(–196 \, \text{kJ mol}^{–1}\).
\(2H_2O_2(g) \to 2H_2O(g) + O_2(g)\)

(c) Some standard entropies, \(S^o\), are shown in Table 3.2.

The enthalpy change and Gibbs free energy change for the following reaction are shown.
\(2H_2O_2(l) \to 2H_2O(l) + O_2(g)\)
\(ΔH^o = –196 \, \text{kJ mol}^{-1}\)
\(ΔG^o = –238 \, \text{kJ mol}^{-1}\)
Use the data given to calculate the standard entropy of oxygen, \(S^o\), \(O_2(g)\).

(d) The decomposition of \(H_2O_2(aq)\) is catalysed by aqueous iron(III) chloride and by silver metal. Identify which of these two catalysts is acting as a homogeneous catalyst. Explain your answer.

(e) The \(E^o\) values for two electrode reactions are given.
\(H_2O_2 + 2H^+ + 2e^− \rightleftharpoons 2H_2O\) \(E^o = +1.77 \, \text{V}\)
\(Cr^{3+} + e^− \rightleftharpoons Cr^{2+}\) \(E^o = −0.41 \, \text{V}\)
(i) An electrochemical cell is constructed with the following half-cells (electrodes):
• An acidified solution of \(H_2O_2\), a platinum wire
• \(Cr^{2+}\) mixed with \(Cr^{3+}\), a platinum wire.
Identify the positive half-cell and calculate the standard cell potential, \(E^o_{cell}\).
(ii) Calculate the value of \(ΔG^o\) for the cell reaction that occurs, per mole of \(H_2O_2\).

(f) The \(E^o\) values for two electrode reactions are given.
\(H_2O_2 + 2H^+ + 2e^− \rightleftharpoons 2H_2O\) \(E^o = +1.77 \, \text{V}\)
\(Co^{3+} + e^– \rightleftharpoons Co^{2+}\) \(E^o = +1.82 \, \text{V}\)
An electrochemical cell is constructed with the following half-cells.
Half-cell 1: An acidified solution of \(H_2O_2\) under standard conditions, a platinum wire
Half-cell 2: A solution containing \(0.020 \, \text{mol dm}^{-3} \, Co^{3+}\) and \(2.0 \, \text{mol dm}^{-3} \, Co^{2+}\), a platinum wire
(i) Use the Nernst equation to calculate the value of \(E\), the electrode potential of half-cell 2 under these conditions.
(ii) Write an equation for the cell reaction that occurs in this cell under these conditions.

(g) (i) Define enthalpy change of hydration, \(\Delta H_{hyd}\).
(ii) Aluminium fluoride, \(AlF_3\), is an ionic solid.
Complete and label the energy cycle to show the relationship between:
● The enthalpy change of solution of \(AlF_3\), \(\Delta H^o_{sol}\)
● The lattice energy of \(AlF_3\), \(\Delta H^o_{latt}\)
● The enthalpy changes of hydration of \(Al^{3+}\) and \(F^-\), \(\Delta H^o_{hyd}\). Include state symbols for all substances and ions.

(iii) Relevant data for this question are given.

Use these data and your energy cycle in (g)(ii) to calculate the \(\Delta H^o_{latt}\) of \(AlF_3\).