IChO 2022 · Theory problem 3

Capture and Transformation of Carbon Dioxide

Download PDFIChO 2022

Climate change is one of the most critical global challenges nowadays. The increase of \(\ce{CO2}\) concentration in the atmosphere has been recognized as the primary driver of global warming. The study of the capture and transformation of \(\ce{CO2}\) has attracted considerable attention.

Direct air capture (DAC) technology which aims to extract \(\ce{CO2}\) directly from ambient air is promising. The conventional method of DAC is wet scrubbing with alkaline hydroxide solutions (typically \(\ce{NaOH}\)), where \(\ce{CO2}\) in air is absorbed till pH ≈ 10 (step 1). The spent sorbent is regenerated by dosing calcium hydroxide into the system (step 2). The white precipitate A received in step 2 decomposes at \(700\,^\circ\mathrm{C}\), giving rise to \(\ce{CO2}\) and another white compound B (step 3). Finally, calcium hydroxide can be generated by the hydration of B. This process is highly energy-demanding. (\(\ce{H2CO3}\): \(K_{\mathrm{a1}}=4.5\times10^{-7}\), \(K_{\mathrm{a2}}=4.7\times10^{-11}\)).

3.1 Write the formulas for A and B respectively.

3.2 Write the balanced equations of all possible reactions in steps 1-3. \(\ce{NaOH}\) solution is used as sorbent.

Recently, an electrochemical process was developed for regenerating the alkaline solution in the wet scrubbing process for DAC application, and pure \(\ce{CO2}\) gas could be recovered that is suitable for storage or utilization. The process is based on a \(\ce{H2}\)-recycling electrochemical system (HRES), as shown in Figure 3.1.

Figure 1

Figure 3.1 Schematic drawing of the experimental setup

The electrochemical cell contains three compartments: an anode region (A), an acidifying region (B), and a cathode region (C). They are separated by ion-selective permeable membranes M1 and M2. During the operation, protons produced from \(\ce{H2}\) oxidation at the anode are transported to the acidifying compartment where the spent solution (\(\ce{Na2CO3}\)-\(\ce{NaHCO3}\)) coming from the air contactor is fed. The decreasing pH of the solution leads to the conversions of carbonate to hydrocarbonate (reaction 1) and hydrocarbonate to carbonic acid (reaction 2). When the solution is saturated by dissolved \(\ce{CO2}\) (solubility: \(0.033\ \mathrm{mol\,L^{-1}}\)), a further pH decrease leads to the release of \(\ce{CO2}\) gas (reaction 3). \(\ce{H2}\) generated in the cathode is introduced to the anode and the solution from the cathode can be reused as a DAC absorbent.

3.3 Write the electrode reactions in the anode (A) and the cathode (C) respectively.

3.4 Write the balanced equations for the reactions 1–3 in the acidifying region (B).

3.5 Check all that correctly describe the movement of cations during the system operation.

(a) \(\ce{H+}\) ions permeate through M1 from A to B.

(b) \(\ce{H+}\) ions permeate through M2 from B to C.

(c) \(\ce{Na+}\) ions permeate through M1 from B to A.

(d) \(\ce{Na+}\) ions permeate through M2 from B to C.

(e) Both \(\ce{H+}\) and \(\ce{Na+}\) ions can permeate through M1and M2.

The cell works at a steady state when the current passing through the cell is \(2.00\ \mathrm{A}\) and the flow rate of the solution (\(0.050\ \mathrm{mol\,L^{-1}}\ \ce{Na2CO3}\) - \(0.10\ \mathrm{mol\,L^{-1}}\ \ce{NaHCO3}\)) into the region B is \(10.0\ \mathrm{mL\,min^{-1}}\). The pH in the anode compartment is maintained at 1 in the steady state.

3.6 Calculate the generation rate of \(\ce{CO2}\) gas (in \(\mathrm{mmol\,min^{-1}}\)).

Zeolitic imidazolate frameworks (ZIFs), a sub-class of metal–organic frameworks (MOFs) are promising materials for the capture and utilization of \(\ce{CO2}\). The structures of ZIFs resemble zeolites. They form 3D frameworks with tetrahedrally coordinated metal ions (e.g. \(\ce{Zn^2+}\), \(\ce{Co^2+}\)) bridged by imidazolate (\(\ce{Im-}\)) and its derivatives. As the conjugated base of imidazole (\(\ce{HIm}\)), imidazolate anion binds to metal cations (M) by its two N atoms. The fact that the \(\ce{M-Im-M}\) angle is similar to the \(\ce{Si-O-Si}\) angle (145°) preferred in zeolites (as shown below) has led to the synthesis of a large number of ZIFs with zeolite-type tetrahedral topologies.

Figure 2

ZIF-8 is one of the representative ZIFs, which adopts a sodalite framework (SOD), as shown in Figure 3.2. ZIF-8 was firstly synthesized by Chinese scientists Xiao-Ming Chen et al. (they named it as MAF-4) by the reaction of \(\ce{Zn^2+}\) with 2-methylimidazole (\(\ce{CH3(C3N2H3)}\), \(\ce{HmIm}\)). It crystalizes in the cubic system with the cell parameter \(a=1.632\ \mathrm{nm}\) for a solvent-free phase with the effective pore diameter (shown by the inside virtual sphere in Figure 3.2d) of \(1.16\ \mathrm{nm}\).

Figure 3

Figure 3.2 Topology of SOD and structure of ZIF-8

(a) Topology of SOD cage;

(b) SOD cage in ZIF-8 formed by \(\ce{Zn^2+}\) (at the centers of the tetrahedra) and imidazolate (H atoms are omitted for clarity);

(c) Framework of SOD with the unit cell shown by the square box;

(d) Some of the pores are highlighted by virtual spheres in ZIF-8.

Note: .If you wish, you may use the symbol "HmIm" and "mIm" representing 2-methylimidazole and 2-methylimidazolate respectively in solving the following questions.

3.7 Write the formula of the single sodalite cage.

3.8 Write the composition of the unit cell of ZIF-8.

3.9 Calculate the inner surface area (\(S\)) of the pores (modeled by the virtual spheres) of 1 g ZIF-8 (in \(\mathrm{m^2}\)). If you failed to get the composition of the unit cell, use 3500 as the formula weight of the unit cell.

3.10 Calculate the porosity \(R\) of ZIF-8 (\(R\) is the ratio of pore volume to the actual volume of the material) and the pore volume of 1 g ZIF-8 (\(V_p\), in \(\mathrm{cm^3}\)).

ZIF-8 can also act as a catalyst to promote the conversion of \(\ce{CO2}\) to high value-added chemicals. One of the most promising routes for \(\ce{CO2}\) fixation is the preparation of cyclic carbonates via \(\ce{CO2}\) cycloaddition. An example is shown as below:

Figure 4

A mechanism of catalytic conversion of \(\ce{CO2}\) to cyclic carbonate over ZIF-8 catalyst is proposed:

Figure 5

3.11 If ZIF-8 provides acid sites in the above catalytic process, complete the mechanism by choosing the reasonable intermediates from the following species:

Figure 6

Choose the intermediates corresponding to I and II respectively.

ZIF-8 shows a relatively high thermal stability. However, a recent study revealed that its structure would be destroyed if applied in a wet acidic environment. The co-existence of \(\ce{CO2}\) and \(\ce{H2O}\) with ZIF-8 resulted in the formation of \(\ce{ZnCO3}\).

3.12 Write the balanced equation of ZIF-8 with \(\ce{CO2}\) and \(\ce{H2O}\).

Official English text of the problem.

Answers

  • 3.1 A: calcium carbonate, \(\ce{CaCO3}\), [Ca+2].[O-]C(=O)[O-]. B: calcium oxide, \(\ce{CaO}\), [Ca+2].[O-2].

  • 3.2 The principal reactions are: \[ \begin{aligned} \text{Step 1:}\quad& \ce{CO2 + 2NaOH -> Na2CO3 + H2O}\\ &\ce{Na2CO3 + CO2 + H2O -> 2NaHCO3}\\[2pt] \text{Step 2:}\quad& \ce{Na2CO3 + Ca(OH)2 -> CaCO3 v + 2NaOH}\\ &\ce{NaHCO3 + Ca(OH)2 -> CaCO3 v + NaOH + H2O}\\[2pt] \text{Step 3:}\quad& \ce{CaCO3 -> CaO + CO2 ^} \end{aligned} \] Equivalent net reactions and the final hydration are included in the solution.

  • 3.3 \[ \begin{aligned} \text{Anode:}\quad&\ce{H2 -> 2H+ + 2e-}\\ \text{Cathode:}\quad&\ce{2H2O + 2e- -> H2 + 2OH-} \end{aligned} \]

  • 3.4 \[ \begin{aligned} (1)\quad&\ce{CO3^2- + H+ -> HCO3-}\\ (2)\quad&\ce{HCO3- + H+ -> H2CO3}\\ (3)\quad&\ce{H2CO3 -> CO2(g) + H2O} \end{aligned} \]

  • 3.5 (a) and (d) under the intended ideal transport model.

  • 3.6 \(\boxed{\dot n_{\ce{CO2(g)}}\approx0.41\ \mathrm{mmol\,min^{-1}}}\), with an unrounded stoichiometric result of \(0.4137\ \mathrm{mmol\,min^{-1}}\).

  • 3.7 One geometric cage contains \(\boxed{\ce{[Zn24(C4H5N2)36]^{12+}}}\), conventionally written \(\ce{[Zn24(mIm)36]^{12+}}\).

  • 3.8 \(\boxed{\ce{Zn12(C4H5N2)24}}\), or \(\ce{Zn12C96H120N48}\), per unit cell.

  • 3.9 \(\boxed{S=1.86\times10^3\ \mathrm{m^2}}\) for 1 g.

  • 3.10 \(\boxed{R=0.376=37.6\%}\) and \(\boxed{V_p=0.360\ \mathrm{cm^3}}\) for 1 g.

  • 3.11 \(\boxed{\mathrm{I}=(b),\qquad \mathrm{II}=(d)}\). Names and schematic SMILES are given below.

  • 3.12 \[ \boxed{\ce{Zn(C4H5N2)2 + CO2 + H2O -> ZnCO3 + 2C4H6N2}} \] The released organic compound is 2-methylimidazole, Cc1ncc[nH]1.

Solution

The following names and SMILES identify the species used throughout the equations. Dot-separated SMILES for salts specify their constituent ions; they do not describe the crystal lattice.

Species SMILES
Carbon dioxide, \(\ce{CO2}\) O=C=O
Water, \(\ce{H2O}\) O
Sodium hydroxide, \(\ce{NaOH}\) [Na+].[OH-]
Sodium carbonate, \(\ce{Na2CO3}\) [Na+].[Na+].[O-]C(=O)[O-]
Sodium hydrogencarbonate, \(\ce{NaHCO3}\) [Na+].O=C(O)[O-]
Calcium hydroxide, \(\ce{Ca(OH)2}\) [Ca+2].[OH-].[OH-]
Calcium carbonate, \(\ce{CaCO3}\) [Ca+2].[O-]C(=O)[O-]
Calcium oxide, \(\ce{CaO}\) [Ca+2].[O-2]
Hydrogen, \(\ce{H2}\) [H][H]
Proton, \(\ce{H+}\) [H+]
Hydroxide ion, \(\ce{OH-}\) [OH-]
Carbonate ion, \(\ce{CO3^2-}\) [O-]C(=O)[O-]
Hydrogencarbonate ion, \(\ce{HCO3-}\) O=C(O)[O-]
Carbonic acid, \(\ce{H2CO3}\) O=C(O)O
Sodium ion, \(\ce{Na+}\) [Na+]
Zinc(II) ion, \(\ce{Zn^2+}\) [Zn+2]
2-Methylimidazolate, \(\ce{C4H5N2-}\), abbreviated \(\ce{mIm-}\) Cc1ncc[n-]1
2-Methylimidazole, \(\ce{C4H6N2}\), abbreviated \(\ce{HmIm}\) Cc1ncc[nH]1
Zinc carbonate, \(\ce{ZnCO3}\) [Zn+2].[O-]C(=O)[O-]

3.1

The precipitate contains calcium supplied by calcium hydroxide and carbonate obtained from absorbed carbon dioxide. Thus A is calcium carbonate, \(\ce{CaCO3}\).

Its thermal decomposition releases carbon dioxide and leaves calcium oxide, \(\ce{CaO}\), as B. Hydration of this oxide regenerates calcium hydroxide.

3.2

At pH 10, \[ \frac{[\ce{CO3^2-}]}{[\ce{HCO3-}]} =\frac{K_{\mathrm{a2}}}{[\ce{H+}]} =\frac{4.7\times10^{-11}}{10^{-10}} =0.47. \] Both carbonate and hydrogencarbonate must therefore be included.

In step 1, carbon dioxide initially reacts with strongly alkaline solution: \[ \ce{CO2 + 2NaOH -> Na2CO3 + H2O}. \] Further absorption produces hydrogencarbonate: \[ \ce{Na2CO3 + CO2 + H2O -> 2NaHCO3}. \] The corresponding overall equation for hydrogencarbonate formation is \[ \ce{CO2 + NaOH -> NaHCO3}. \]

In step 2, calcium carbonate precipitates, regenerating sodium hydroxide: \[ \ce{Na2CO3 + Ca(OH)2 -> CaCO3(s) + 2NaOH}. \] Hydrogencarbonate also reacts: \[ \ce{NaHCO3 + Ca(OH)2 -> CaCO3(s) + NaOH + H2O}. \] Here hydroxide first removes the hydrogencarbonate proton, \[ \ce{HCO3- + OH- -> CO3^2- + H2O}, \] and the resulting carbonate precipitates with calcium.

For partial regeneration with less calcium hydroxide, an equivalent possible net reaction is \[ \ce{2NaHCO3 + Ca(OH)2 -> CaCO3(s) + Na2CO3 + 2H2O}. \] The remaining sodium carbonate can subsequently undergo the first step-2 reaction.

In step 3, heating causes calcination: \[ \ce{CaCO3(s) -> CaO(s) + CO2(g)}. \]

Finally, the stated hydration closes the calcium cycle: \[ \ce{CaO(s) + H2O -> Ca(OH)2}. \]

3.3

Hydrogen is oxidized at the anode, producing one proton per electron transferred: \[ \boxed{\ce{H2 -> 2H+ + 2e-}}. \]

Water is reduced at the cathode, producing hydrogen for recycling and hydroxide for regeneration of the alkaline absorbent: \[ \boxed{\ce{2H2O + 2e- -> H2 + 2OH-}}. \]

3.4

Successive protonation in B gives: \[ \boxed{\ce{CO3^2- + H+ -> HCO3-}}\qquad(1) \] \[ \boxed{\ce{HCO3- + H+ -> H2CO3}}\qquad(2). \]

Carbonic acid supplies dissolved carbon dioxide; once saturation is reached, carbon dioxide escapes as gas: \[ \boxed{\ce{H2CO3 -> CO2(g) + H2O}}\qquad(3). \]

These reactions represent the acid–base and gas-release processes using the carbonic-acid convention of the problem.

3.5

The productive ion flows are:

  • Protons travel through M1 from A to B, providing the acid needed for reactions 1 and 2.
  • Sodium ions travel through M2 from B to C, carrying positive charge toward the cathode and balancing the hydroxide generated there.

Thus the intended selections are \[ \boxed{(a)\ \text{and}\ (d)}. \]

3.6

Use \(F=96485\ \mathrm{C\,mol^{-1}}\). The proton-generation rate is \[ \dot n_{\ce{H+}} =\frac{I}{F} =\frac{(2.00\ \mathrm{C\,s^{-1}})(60\ \mathrm{s\,min^{-1}})} {96485\ \mathrm{C\,mol^{-1}}} =1.2437\ \mathrm{mmol\,min^{-1}}. \]

The incoming carbonate and hydrogencarbonate rates are \[ \dot n_{\ce{CO3^2-},\mathrm{in}} =(0.050)(0.0100) =0.500\ \mathrm{mmol\,min^{-1}}, \] \[ \dot n_{\ce{HCO3-},\mathrm{in}} =(0.10)(0.0100) =1.00\ \mathrm{mmol\,min^{-1}}. \]

First, approximately \(0.500\ \mathrm{mmol\,min^{-1}}\) of protons converts carbonate to hydrogencarbonate. The remaining proton supply converts hydrogencarbonate into the carbonic-acid/dissolved-carbon-dioxide pool: \[ \dot n_{\text{converted to }\ce{CO2}} =1.2437-0.500 =0.7437\ \mathrm{mmol\,min^{-1}}. \]

The saturated liquid leaving B carries dissolved carbon dioxide at \[ \dot n_{\ce{CO2(aq)},\mathrm{out}} =(0.033\ \mathrm{mol\,L^{-1}}) (0.0100\ \mathrm{L\,min^{-1}}) =0.330\ \mathrm{mmol\,min^{-1}}. \]

Consequently, \[ \begin{aligned} \dot n_{\ce{CO2(g)}} &=0.7437-0.330\\ &=0.4137\ \mathrm{mmol\,min^{-1}}. \end{aligned} \] Thus, to sensible precision, \[ \boxed{\dot n_{\ce{CO2(g)}}\approx0.41\ \mathrm{mmol\,min^{-1}}}. \]

As a consistency check, the residual hydrogencarbonate rate is \[ 0.500+1.00-0.7437=0.7563\ \mathrm{mmol\,min^{-1}}, \] corresponding to about \(0.0756\ \mathrm{mol\,L^{-1}}\). The supplied acid constant then gives \[ [\ce{H+}]_{\mathrm B} \approx K_{\mathrm{a1}}\frac{0.033}{0.0756} =1.96\times10^{-7}\ \mathrm{mol\,L^{-1}}, \] or \(\mathrm{pH}_{\mathrm B}\approx6.71\). At this pH, \[ \frac{[\ce{CO3^2-}]}{[\ce{HCO3-}]} \approx2.4\times10^{-4}, \] so neglecting residual carbonate is justified. The specified pH 1 pertains to the anode compartment A.

3.7

The sodalite cage is a truncated octahedron with six quadrilateral faces and eight hexagonal faces. Every edge belongs to two faces, giving \[ E=\frac{6(4)+8(6)}{2}=36. \] Three cage edges meet at each vertex, so \[ V=\frac{2E}{3}=24. \]

There is one zinc ion at each vertex and one 2-methylimidazolate linker on each edge. Therefore the geometric cage contains \[ \boxed{\ce{[Zn24(C4H5N2)36]^{12+}}} \] or \(\ce{[Zn24(mIm)36]^{12+}}\).

This is a count of the atoms and linkers defining one cage within the extended framework. Each zinc has three connections along that cage and a fourth connection extending into the surrounding network. If only the counted constituents were treated as a separated fragment, their formal charge would be \(24(2)-36=+12\); the cage is not an isolated neutral molecule.

The constituent-ion SMILES are [Zn+2] and Cc1ncc[n-]1. Their periodic Zn–N coordination and tetrahedral geometry are specified by the framework description, rather than by a disconnected molecular SMILES.

3.8

The cubic unit cell contains two equivalent cage centers: \[ 8\left(\frac18\right)+1=2. \]

In the space-filling SOD arrangement, each zinc vertex belongs to four cages, and each linker edge belongs to three cages. Thus the unit-cell contents are \[ N_{\mathrm{Zn}}=\frac{2(24)}{4}=12, \qquad N_{\mathrm{mIm}}=\frac{2(36)}{3}=24. \]

Hence \[ \boxed{\ce{Zn12(C4H5N2)24}=\ce{Zn12C96H120N48}}. \]

The empirical formula is \(\ce{Zn(C4H5N2)2}\). Its ionic-composition SMILES is [Zn+2].Cc1ncc[n-]1.Cc1ncc[n-]1; this string does not encode the periodic coordination bonds.

3.9

Using standard atomic masses \(C=12.01\), \(H=1.008\), \(N=14.01\), and \(Zn=65.38\), \[ M_{\mathrm{mIm}} =4(12.01)+5(1.008)+2(14.01) =81.10\ \mathrm{g\,mol^{-1}}. \] The molar mass of unit cells is therefore \[ M_{\mathrm{cell}} =12(65.38)+24(81.10) =2730.96\ \mathrm{g\,mol^{-1}}. \]

Each cell contains two spherical pores. With \[ N_{\mathrm A}=6.02214076\times10^{23}\ \mathrm{mol^{-1}}, \] the number of pores in 1 g is \[ N_{\mathrm{pores}} =\frac{(1.00\ \mathrm g)(2N_{\mathrm A})}{M_{\mathrm{cell}}} =4.4103\times10^{20}. \]

The pore radius is \[ r=\frac{1.16}{2}=0.580\ \mathrm{nm}. \] Thus \[ \begin{aligned} S &=N_{\mathrm{pores}}\,4\pi r^2\\ &=(4.4103\times10^{20}) 4\pi(0.580\times10^{-9}\ \mathrm m)^2\\ &=1.8644\times10^3\ \mathrm{m^2}. \end{aligned} \] Therefore, \[ \boxed{S=1.86\times10^3\ \mathrm{m^2}\text{ for 1 g}}. \]

3.10

The volume of one spherical pore is \[ V_{\mathrm{sphere}} =\frac43\pi(0.580)^3 =0.817283\ \mathrm{nm^3}. \]

The unit-cell volume is \[ V_{\mathrm{cell}}=a^3=(1.632)^3 =4.346708\ \mathrm{nm^3}. \]

Since there are two pores per cell, \[ R=\frac{2V_{\mathrm{sphere}}}{V_{\mathrm{cell}}} =\frac{2(0.817283)}{4.346708} =0.376047. \] Thus \[ \boxed{R=0.376=37.6\%}. \]

Using \(1\ \mathrm{nm^3}=10^{-21}\ \mathrm{cm^3}\), the pore volume in 1 g is \[ \begin{aligned} V_p &=N_{\mathrm{pores}}V_{\mathrm{sphere}}\\ &=(4.4103\times10^{20}) (0.817283\times10^{-21}\ \mathrm{cm^3})\\ &=0.36044\ \mathrm{cm^3}. \end{aligned} \] Therefore, \[ \boxed{V_p=0.360\ \mathrm{cm^3}\text{ for 1 g}}. \]

3.11

A Lewis acid site accepts an electron pair from the epoxide oxygen. This activates the epoxide toward ring opening, corresponding to intermediate (b).

An oxygen atom of carbon dioxide then attacks the terminal epoxide carbon shown in the scheme. The attacked carbon–epoxide-oxygen bond breaks, giving the ring-opened, catalyst-bound intermediate (d).

Finally, the original epoxide oxygen attacks the carbon dioxide-derived carbon. Ring closure and release from the acid site produce the five-membered cyclic carbonate.

Hence \[ \boxed{\mathrm I=(b),\qquad \mathrm{II}=(d)}. \]

For precise schematic SMILES, let [*:1] denote the catalyst acid site and [*:2] denote the substituent R:

Species Name Schematic SMILES
Starting epoxide R-substituted oxirane [*:2]C1CO1
I, option (b) Acid-site-bound epoxide, drawn as an oxonium adduct [*:1][O+]1C([*:2])C1
II, option (d) Catalyst-bound, ring-opened alkoxycarbonyl cation [*:1]OC([*:2])COC#[O+]
Product 4-R-1,3-dioxolan-2-one O=C1OCC([*:2])O1

For II, the carbonyl-cation resonance form can equivalently be written [*:1]OC([*:2])CO[C+]=O.

These SMILES encode the schematic connectivity and formal charges. The wildcard for the catalyst does not specify a particular atom, and the drawings do not fully specify the surface coordination geometry. Electron-pair donation, bond cleavage, and ring closure are the electron-flow steps described above.

In the illustrated phenyl-substituted example, the substrate is styrene oxide (2-phenyloxirane), c1ccccc1C1CO1, and the product is 4-phenyl-1,3-dioxolan-2-one, O=C1OCC(c2ccccc2)O1. No absolute stereochemistry is specified in the problem.

3.12

Each neutral framework formula unit contains one zinc ion and two 2-methylimidazolate anions. Carbon dioxide and water supply the carbonate group and the two protons needed to release two neutral 2-methylimidazole molecules.

Per formula unit, \[ \boxed{\ce{Zn(C4H5N2)2 + CO2 + H2O -> ZnCO3 + 2C4H6N2}}. \]

Equivalently, using the permitted ligand abbreviations, \[ \boxed{\ce{Zn(mIm)2 + CO2 + H2O -> ZnCO3 + 2HmIm}}. \]

Zinc carbonate precipitates, while protonation of the coordinating ligands breaks the Zn–N framework connections.

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.