IChO 1989 · Theory problem 3

Removal of sulphur dioxide from power-station flue gases

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Sulphur dioxide is removed from waste gases of coal power stations by washing with aqueous suspensions of calcium carbonate or calcium hydroxide. The residue formed is recovered.

3.1 Write all reactions as balanced equations.

3.2 How many kilograms of calcium carbonate are daily consumed to remove 95 % of the sulphur dioxide if 10000 \(\mathrm{m^3/h}\) of waste gas (corrected to 0 °C and standard pressure) containing 0.15 % sulphur dioxide by volume are processed? How many kilograms of gypsum are recovered thereby?

3.3 Assuming that the sulphur dioxide is not being removed and equally spread in an atmospheric liquid water pool of 5000 \(\mathrm{m^3}\) and fully returned on earth as rain, what is the expected pH of the condensed water?

3.4 If a sodium sulphite solution is used for absorption, sulphur dioxide and the sulphite solution can be recovered. Write down the balanced equations and point out possible pathways to increase the recovery of sulphur dioxide from an aqueous solution.

Note:

Protolysis of sulphur dioxide in aqueous solutions can be described by the first step dissociation of sulphurous acid. The dissociation constant \(K_{a,1}(\ce{H2SO3})=10^{-2.25}\).

Assume ideal gases and a constant temperature of 0 °C at standard pressure.

\(M(\ce{CaCO3})=100\ \mathrm{g\,mol^{-1}};\ M(\ce{CaSO4})=172\ \mathrm{g\,mol^{-1}}\).

Official English text of the problem.

Answers

  • 3.1 Absorption forms calcium sulphite, which is oxidized and recovered as gypsum. The overall equations are \[ \ce{2CaCO3 + 2SO2 + O2 + 4H2O -> 2CaSO4.2H2O + 2CO2} \] \[ \ce{2Ca(OH)2 + 2SO2 + O2 + 2H2O -> 2CaSO4.2H2O}. \]

  • 3.2 Calcium carbonate consumed: approximately \(1.53\times10^3\ \mathrm{kg}\) per day. Gypsum recovered: approximately \(2.63\times10^3\ \mathrm{kg}\) per day.

  • 3.3 For one hour’s untreated emissions, \(\mathrm{pH}\approx3.88\).

  • 3.4 \[ \ce{Na2SO3 + SO2 + H2O <=> 2NaHSO3}. \] Absorption proceeds to the right; regeneration proceeds to the left. Heating and lowering the sulphur dioxide partial pressure promote recovery. Acidification also releases sulphur dioxide, but subsequent neutralization is needed to restore the absorbent.

Solution

The species used below have the following names and SMILES. For salts, disconnected SMILES components specify composition; they do not describe the crystal lattice or coordination of water in gypsum. Sulphurous acid is the formal aqueous species used in the problem’s dissociation model.

Species Name SMILES
\(\ce{SO2}\) Sulphur dioxide O=S=O
\(\ce{H2O}\) Water O
\(\ce{H2SO3}\) Sulphurous acid OS(=O)O
\(\ce{CaCO3}\) Calcium carbonate [Ca+2].[O-]C(=O)[O-]
\(\ce{Ca(OH)2}\) Calcium hydroxide [Ca+2].[OH-].[OH-]
\(\ce{CaSO3}\) Calcium sulphite [Ca+2].[O-]S(=O)[O-]
\(\ce{CO2}\) Carbon dioxide O=C=O
\(\ce{O2}\) Oxygen O=O
\(\ce{CaSO4}\) Calcium sulphate [Ca+2].[O-]S(=O)(=O)[O-]
\(\ce{CaSO4.2H2O}\) Gypsum; calcium sulphate dihydrate [Ca+2].[O-]S(=O)(=O)[O-].O.O
\(\ce{H3O+}\) Hydronium ion [OH3+]
\(\ce{HSO3^-}\) Hydrogen sulphite ion; bisulphite ion OS(=O)[O-]
\(\ce{Na2SO3}\) Sodium sulphite [Na+].[Na+].[O-]S(=O)[O-]
\(\ce{NaHSO3}\) Sodium hydrogen sulphite; sodium bisulphite [Na+].OS(=O)[O-]

3.1 — Absorption and gypsum formation

Dissolved sulphur dioxide behaves as an acid, represented formally by \[ \ce{SO2(aq) + H2O(l) <=> H2SO3(aq)}. \]

Neutralization by calcium carbonate releases carbon dioxide: \[ \ce{CaCO3 + H2SO3 -> CaSO3 + CO2 + H2O}. \] Combining this with the formal hydration step gives \[ \ce{CaCO3 + SO2 -> CaSO3 + CO2}. \]

Neutralization by calcium hydroxide gives \[ \ce{Ca(OH)2 + H2SO3 -> CaSO3 + 2H2O}, \] or, after combining with hydration, \[ \ce{Ca(OH)2 + SO2 -> CaSO3 + H2O}. \]

Oxygen from the flue gas or supplied air oxidizes calcium sulphite to calcium sulphate: \[ \ce{2CaSO3 + O2 -> 2CaSO4}. \] The sulphur oxidation state increases from \(+4\) to \(+6\). The recovered hydrated solid is gypsum: \[ \ce{CaSO4 + 2H2O -> CaSO4.2H2O}. \]

Thus the overall equations are \[ \boxed{\ce{2CaCO3 + 2SO2 + O2 + 4H2O -> 2CaSO4.2H2O + 2CO2}} \] and \[ \boxed{\ce{2Ca(OH)2 + 2SO2 + O2 + 2H2O -> 2CaSO4.2H2O}}. \]

3.2 — Daily calcium carbonate consumption and gypsum recovery

At \(0\,^\circ\mathrm C\) and conventional standard pressure, the ideal-gas molar volume is \[ V_m\approx22.4\ \mathrm{L\,mol^{-1}} =22.4\ \mathrm{m^3\,kmol^{-1}}. \]

The volume of sulphur dioxide entering per hour is \[ \dot V_{\ce{SO2}} =(10000\ \mathrm{m^3\,h^{-1}})(0.0015) =15.0\ \mathrm{m^3\,h^{-1}}. \]

The volume captured per day is therefore \[ V_{\mathrm{captured}} =(15.0\ \mathrm{m^3\,h^{-1}}) (24\ \mathrm{h\,day^{-1}})(0.95) =342\ \mathrm{m^3\,day^{-1}}. \]

Its amount is \[ n_{\mathrm{captured}} =\frac{342\ \mathrm{m^3\,day^{-1}}} {22.4\ \mathrm{m^3\,kmol^{-1}}} =15.27\ \mathrm{kmol\,day^{-1}}. \]

The overall reaction shows that one mole of captured sulphur dioxide consumes one mole of calcium carbonate and produces one mole of gypsum. Hence \[ m_{\ce{CaCO3}} =(15.27\ \mathrm{kmol\,day^{-1}}) (100\ \mathrm{kg\,kmol^{-1}}) \approx\boxed{1.53\times10^3\ \mathrm{kg\,day^{-1}}}. \]

Gypsum is \(\ce{CaSO4.2H2O}\); the supplied molar mass \(172\ \mathrm{g\,mol^{-1}}\) applies to this dihydrate. Thus \[ m_{\mathrm{gypsum}} =(15.27\ \mathrm{kmol\,day^{-1}}) (172\ \mathrm{kg\,kmol^{-1}}) \approx\boxed{2.63\times10^3\ \mathrm{kg\,day^{-1}}}. \]

3.3 — pH of the rainwater

Taking one hour of untreated emissions as the basis, the entire \(15.0\ \mathrm{m^3}\) of sulphur dioxide enters the water: \[ n_{\ce{SO2}} =\frac{15.0\ \mathrm{m^3}} {22.4\times10^{-3}\ \mathrm{m^3\,mol^{-1}}} =669.6\ \mathrm{mol}. \]

The water volume is \[ 5000\ \mathrm{m^3}=5.000\times10^6\ \mathrm L. \] Consequently, the analytical concentration of dissolved sulphur dioxide, expressed as sulphurous acid, is \[ C=\frac{669.6\ \mathrm{mol}}{5.000\times10^6\ \mathrm L} =1.339\times10^{-4}\ \mathrm{mol\,L^{-1}}. \]

The prescribed dissociation equilibrium is \[ \ce{H2SO3 + H2O <=> H3O+ + HSO3^-}, \qquad K_{a,1}=10^{-2.25}=5.623\times10^{-3}. \]

Neglecting water’s self-ionization and using only the stipulated first dissociation, let \[ x=[\ce{H3O+}]=[\ce{HSO3^-}], \qquad [\ce{H2SO3}]=C-x. \]

Using numerical concentrations in \(\mathrm{mol\,L^{-1}}\), \[ K_{a,1}=\frac{x^2}{C-x}. \] The physically meaningful root is \[ x=\frac{-K_{a,1}+\sqrt{K_{a,1}^{\,2}+4K_{a,1}C}}{2} =1.309\times10^{-4}\ \mathrm{mol\,L^{-1}}. \]

Therefore \[ \boxed{\mathrm{pH} =-\log_{10}\!\left( \frac{[\ce{H3O+}]}{1\ \mathrm{mol\,L^{-1}}} \right) =3.88}. \]

Approximately \(97.7\%\) undergoes the first dissociation. Thus the usual weak-acid approximation \(x\ll C\) is inappropriate here; the quadratic is needed.

3.4 — Reversible absorption in sodium sulphite

Sodium sulphite absorbs acidic sulphur dioxide to form sodium hydrogen sulphite: \[ \boxed{\ce{Na2SO3(aq) + SO2(g) + H2O(l) <=> 2NaHSO3(aq)}}. \]

Heating and removing the evolved gas reverse the absorption, regenerating sodium sulphite: \[ \boxed{\ce{2NaHSO3(aq) <=> Na2SO3(aq) + SO2(g) + H2O(l)}}. \]

Sulphur remains in oxidation state \(+4\), allowing recovery through this reversible absorption process.

The following changes increase sulphur dioxide release:

  • Raise the temperature. Heating reduces gas solubility and promotes regeneration from sodium hydrogen sulphite.
  • Lower the sulphur dioxide partial pressure above the solution. Vacuum operation or continuous removal by steam or an inert gas promotes desorption and shifts the regeneration equilibrium toward the products.
  • Acidify the solution. Protonation converts hydrogen sulphite into dissolved sulphur dioxide, which can escape: \[ \ce{HSO3^- + H3O+ -> SO2(g) + 2H2O}. \] This consumes the absorbent’s alkalinity, so additional neutralization is required before sodium sulphite can be reused.

The solution was checked against the official solution.