IChO 1981 · Theory problem 4

Thermochemical cycle for the decomposition of water at moderate temperature

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The thermal decomposition of water

Figure 1

can be traced (\(\alpha = 10^{-3}\)) at temperature above 1700 K. This process can be realized at temperatures 800 – 900 K as well as through subsequent stages carried out in a cycle. Suggest such a process on the basis of the reactions:

Figure 2

and

Figure 3

satisfying the following requirements:

a) Only water should be consumed during the process.

b) Oxygen and hydrogen alone should be the end products of the process.

c) In addition to the above substances, a 25 % ammonia solution is needed for the cycle.

d) The temperature for each step in the cycle should not exceed 840 K.

Official English text of the problem.

Answers

  • a) Regenerate the copper(II) oxide, magnesium chloride, silver, and ammonia using the cycle below. Its net reaction is \[ \boxed{\ce{2H2O -> 2H2 + O2}}. \]
  • b) The only net products are hydrogen, [H][H], and oxygen, O=O, in the molar ratio \(2:1\).
  • c) Aqueous ammonia, N, enables copper(I) chloride to reduce silver chloride to silver, forming a copper(II) ammine complex. Removing ammonia in the presence of magnesium oxide regenerates the copper oxide and magnesium chloride.
  • d) Use \(840\,\mathrm{K}\) for the first supplied reaction and \(430\,\mathrm{K}\) for the second. Complex formation and the regeneration operations can be conducted below \(840\,\mathrm{K}\).

Names and SMILES for the remaining species are collected in the solution.

Solution

a) Constructing a closed cycle

First balance the supplied oxygen-producing reaction:

\[ \ce{4CuO(s) + 4MgCl2(s) + 2H2O(g) -> 4CuCl(s) + 4MgO(s) + 4HCl(g) + O2(g)}. \tag{1} \]

This step takes place at \(840\,\mathrm{K}\). Four copper centres change from oxidation state \(+2\) to \(+1\), accepting four electrons in total. Formation of one molecule of oxygen from oxygen in oxidation state \(-2\) releases four electrons.

Separate the hydrogen chloride from the oxygen and use it in the second supplied reaction, at \(430\,\mathrm{K}\):

\[ \ce{2Ag(s) + 2HCl(g) -> 2AgCl(s) + H2(g)}. \tag{2} \]

To close the cycle, the copper(I) chloride and silver chloride must regenerate copper(II) and metallic silver. Their reaction in aqueous ammonia accomplishes this:

\[ \ce{CuCl(s) + AgCl(s) + 4NH3(aq) -> [Cu(NH3)4]Cl2(aq) + Ag(s)}. \tag{3} \]

Here copper(I) supplies the electron needed to reduce silver(I); ammonia stabilizes the resulting copper(II) complex.

Next add the magnesium oxide from reaction (1) and remove ammonia by warming. As the ammine complex dissociates, magnesium oxide supplies the basic conditions needed to precipitate copper(II) hydroxide. The overall equation is

\[ \ce{[Cu(NH3)4]Cl2(aq) + MgO(s) + H2O(l) -> Cu(OH)2(s) + MgCl2(aq) + 4NH3(g)}. \tag{4} \]

Capture the ammonia in recycled water to restore the ammonia solution. On warming, copper(II) hydroxide gives copper(II) oxide:

\[ \ce{Cu(OH)2(s) -> CuO(s) + H2O(l)}. \tag{5} \]

Filter off the copper(II) oxide and recover magnesium chloride from the solution. For its return as an anhydrous solid, dehydration should use a circulating hydrogen chloride atmosphere to suppress hydrolysis. Hydrogen chloride is already an intermediate in the cycle and is recovered for reuse.

Thus reactions (4) and (5), taken together, regenerate both oxides/chlorides needed for closure:

\[ \ce{[Cu(NH3)4]Cl2 + MgO -> CuO + MgCl2 + 4NH3}. \]

Add the reactions in the proportions

\[ (1)+2(2)+4(3)+4(4)+4(5). \]

After ammonia recovery and the solvent/phase-recovery operations, every auxiliary substance cancels:

\[ \boxed{\ce{2H2O -> 2H2 + O2}}. \]

Only water is consumed.

b) Identifying the final products

Reaction (1) releases oxygen; reaction (2) releases hydrogen. Collect these streams separately, retaining hydrogen chloride and ammonia within the process.

For every \(2\,\mathrm{mol}\) of water consumed,

\[ n(\ce{H2})=2\,\mathrm{mol}, \qquad n(\ce{O2})=1\,\mathrm{mol}. \]

Silver, copper compounds, magnesium compounds, chloride, and ammonia all circulate within the cycle.

c) Explaining the role of the 25 % ammonia solution

Ammonia dissolves the sparingly soluble copper(I) and silver(I) chlorides through ammine-complex formation:

\[ \ce{CuCl(s) + 2NH3(aq) <=> [Cu(NH3)2]+(aq) + Cl-(aq)}, \]

\[ \ce{AgCl(s) + 2NH3(aq) <=> [Ag(NH3)2]+(aq) + Cl-(aq)}. \]

The dissolved complexes undergo the electron-transfer reaction

\[ \ce{[Cu(NH3)2]+ + [Ag(NH3)2]+ -> [Cu(NH3)4]^2+ + Ag(s)}. \]

The copper centre changes from \(+1\) to \(+2\), while the silver centre changes from \(+1\) to \(0\). Ligand redistribution provides four ammonia ligands around copper(II). Adding the two dissolution equations gives reaction (3).

Ammonia therefore enables silver regeneration and stabilizes the copper(II) intermediate. It is subsequently released in reaction (4), captured, and reused.

d) Meeting the temperature limit

Operation Temperature or suitable condition
Oxygen evolution, reaction (1) \(840\,\mathrm{K}\), as supplied
Hydrogen evolution, reaction (2) \(430\,\mathrm{K}\), as supplied
Ammine formation and silver recovery, reaction (3) Ordinary temperature
Ammonia removal and hydroxide precipitation, reaction (4) Warming the aqueous mixture
Copper(II) hydroxide decomposition, reaction (5) Gentle heating, readily below \(840\,\mathrm{K}\)
Magnesium chloride recovery Evaporation and dehydration below \(840\,\mathrm{K}\), with recycled hydrogen chloride suppressing hydrolysis

The ammonia and water vapours are recovered by cooling and absorption. No step requires a temperature above the stated maximum.

The following SMILES identify the species used. For ionic solids, disconnected-ion SMILES represent composition and formal charges, not the crystal lattice.

Species Name SMILES
\(\ce{H2O}\) Water O
\(\ce{H2}\) Hydrogen [H][H]
\(\ce{O2}\) Oxygen O=O
\(\ce{HCl}\) Hydrogen chloride Cl
\(\ce{NH3}\) Ammonia N
\(\ce{CuO}\) Copper(II) oxide [Cu+2].[O-2]
\(\ce{CuCl}\) Copper(I) chloride [Cu+].[Cl-]
\(\ce{MgO}\) Magnesium oxide [Mg+2].[O-2]
\(\ce{MgCl2}\) Magnesium chloride [Mg+2].[Cl-].[Cl-]
\(\ce{Ag}\) Silver [Ag]
\(\ce{AgCl}\) Silver chloride [Ag+].[Cl-]
\(\ce{Cu(OH)2}\) Copper(II) hydroxide [Cu+2].[OH-].[OH-]
\(\ce{Cl-}\) Chloride ion [Cl-]
\(\ce{[Cu(NH3)2]+}\) Diamminecopper(I) ion [NH3]->[Cu+]<-[NH3]
\(\ce{[Ag(NH3)2]+}\) Diamminesilver(I) ion [NH3]->[Ag+]<-[NH3]
\(\ce{[Cu(NH3)4]^2+}\) Tetraamminecopper(II) ion [NH3]->[Cu+2](<-[NH3])(<-[NH3])<-[NH3]
\(\ce{[Cu(NH3)4]Cl2}\) Tetraamminecopper(II) chloride [NH3]->[Cu+2](<-[NH3])(<-[NH3])<-[NH3].[Cl-].[Cl-]

The two-coordinate copper(I) and silver(I) ammine complexes are approximately linear. In aqueous copper(II) solution, the four ammonia ligands occupy approximately equatorial positions, with axial water coordination omitted from the shorthand formula. The SMILES do not specify these coordination geometries or oxygen’s triplet electronic ground state.

The solution was checked against the official solution. Where this solution differs from the official solution, the official solution contains an error or a misprint.