Identification of Nano-Metal Oxides That Can Be Synthesized by Precipitation-Calcination Method Reacting Their Chloride Solutions with NaOH Solution and Their Application for Carbon Dioxide Capture from Air—A Thermodynamic Analysis

Several metal oxide nanoparticles (NPs) were already obtained by mixing NaOH solution with chloride solution of the corresponding metal to form metal hydroxide or oxide precipitates and wash—dry—calcine the latter. However, the complete list of metal oxide NPs is missing with which this technology works well. The aim of this study was to fill this knowledge gap and to provide a full list of possible metals for which this technology probably works well. Our methodology was chemical thermodynamics, analyzing solubilities of metal chlorides, metal oxides and metal hydroxides in water and also standard molar Gibbs energy changes accompanying the following: (i) the reaction between metal chlorides and NaOH; (ii) the dissociation reaction of metal hydroxides into metal oxide and water vapor and (iii) the reaction between metal oxides and gaseous carbon dioxide to form metal carbonates. The major result of this paper is that the following metal-oxide NPs can be produced by the above technology from the corresponding metal chlorides: Al2O3, BeO, CaO, CdO, CoO, CuO, FeO, Fe2O3, In2O3, La2O3, MgO, MnO, Nd2O3, NiO, Pr2O3, Sb2O3, Sm2O3, SnO, Y2O3 and ZnO. From the analysis of the literature, the following nine nano-oxides have been already obtained experimentally with this technology: CaO, CdO, Co3O4, CuO, Fe2O3, NiO, MgO, SnO2 and ZnO (note: Co3O4 and SnO2 were obtained under oxidizing conditions during calcination in air). Thus, it is predicted here that the following nano-oxides can be potentially synthesized with this technology in the future: Al2O3, BeO, In2O3, La2O3, MnO, Nd2O3, Pr2O3, Sb2O3, Sm2O3 and Y2O3. The secondary result is that among the above 20 nano-oxides, the following five nano-oxides are able to capture carbon dioxide from air at least down to 42 ppm residual CO2-content, i.e., decreasing the current level of 420 ppm of CO2 in the Earth’s atmosphere at least tenfold: CaO, MnO, MgO, CdO, CoO. The tertiary result is that by mixing the AuCl3 solution with NaOH solution, Au nano-particles will precipitate without forming Au-oxide NPs. The results are significant for the synthesis of metal nano-oxide particles and for capturing carbon dioxide from air.


Introduction
Metal oxide nanoparticles have been produced from different reagents by different synthesis techniques, including precipitation [1], combustion [2], sol-gel [3], microwave [4], mechanochemical [5], and hydrolysis [6]. Metal oxides nanoparticles can be used as catalysts or toxic-waste remediation agents for their activity, biological toxicity in pharmaceuticals, or as additives in refractory and paint industries, etc. Al 2 O 3 nanoparticles were synthesized using the precipitation technique from various reagents, including aluminum isopropoxide, Al(NO 3 ) 3 ·9H 2 O and AlCl 3 ·6H 2 O [7] as well Table 1 is a summary of nano-oxide synthesis from metal chlorides and NaOH solutions as reagents. One can see that altogether, nine different metal oxide nano-particles have been synthesized so far experimentally using these two types of reagents. One of the goals of this paper is to analyze theoretically, which other nano-oxides can be synthesized in a similar way.
Carbon dioxide CO 2 is a major contributor to the greenhouse effect. Most CO 2 emission is due to the combustion of fossil fuel, especially from coal power plants and industrial processes. Metal oxides nanoparticles have been used for the capture of carbon dioxide from air. FeO, Fe 2 O 3 and Fe 3 O 4 iron oxides have been investigated for CO 2 capturing processes [62]. KO 2 transforms to K 2 CO 3 in a water and CO 2 environment [63]. BeO nanotube has been used for CO 2 absorption [64,65]. Li 2 O transforms to Li 2 CO 3 under a CO 2 environment at low temperatures at 600 • C [66]. MgO particles have been produced for carbonation at room temperature to 316 • C and decarbonation process at 320-460 • C [67]. Na 2 O has a better CO 2 absorption ability than Li 2 O and K 2 O [68]. The second goal of this paper is to find the list of possible metal oxide nano-particles that (i) can be produced by the above explained method and at the same time, (ii) can also absorb carbon dioxide from air efficiently, i.e., reducing the current CO 2 level of air at least by ten times.

Theoretical Calculations of the Formation of Metal Oxide Nano-Particles through Precipitation-Calcination Method Reacting Metal Chlorides with NaOH
In this paper the following technology is considered. Take a given volume of a 2 M NaOH water solution. Take the equal volume of a metal chloride solution in water with the equal amounts of Cl − and OH − ions. Mix the two solutions and let a precipitate form. Wash the precipitate in water to dilute the Cl − ions to about zero concentration. Filtrate the precipitate and dry it at least to 400 K. If needed, calcine the dry precipitate at a higher temperature. All calculations in this paper are based on the physico-chemical (such as solubility) data taken from the CRC Handbook of Chemistry and Physics [87] and on thermodynamic (such as standard molar Gibbs energy of formation) data taken from the compilation by Barin [88].
There are several reasons to select NaOH as a reagent with this technology: 1. NaOH is a bulk and cheap reagent.

2.
NaOH has a good solubility in water: 100 g/100 g of H 2 O at 25 • C. Using its molar mass of 40.0 g/mol, its solubility in water can be re-calculated to molarities as follows: it changes from 10.5 M at 0 • C to 86.8 M at 100 • C. So, a 2 M NaOH solution is a stable and cheap reagent. 3.
One of the products of the reaction of metal chlorides with NaOH is NaCl. From the initial 2 M NaOH solution, a maximum of 1 M NaCl solution is formed during the reaction with the equal volume of metal chloride solution. Its solubility in water is 36 g/100 g of H 2 O at 25 • C. From its molar mass of 58.4 g/mol, its solubility can be re-calculated to 6.10 M at 0 • C and 6.70 M at 100 • C in water. Therefore, the maximum concentration of 1 M NaCl that can form during the technology remains in the solution even if the effects of other chlorides are taken into account. 4.
During the reaction, NaOH is converted into NaCl; it can be done efficiently, if the difference between their molar standard Gibbs energies is as negative as possible.
The molar standard Gibbs energy of formation of NaCl is −383.9 kJ/mol (300 K) and −374.6 kJ/mol (400 K). The molar standard Gibbs energy of formation of NaOH is −379.5 kJ/mol (300 K) and −363.8 kJ/mol (400 K). Thus, the molar standard Gibbs energy change accompanying the transformation of NaOH into NaCl is −4.4 kJ/mol (300 K) and −10.8 kJ/mol (400 K). This negative standard molar Gibbs energy change will help to convert metal chlorides into their hydroxides or oxides.

Condition I Existence and Sufficient Solubility of Stable Chloride for Given Metal
The reaction takes place between an aqueous solution of the metal chloride (MCl x ) and NaOH. Thus, the first condition is that a given metallic ion should have a stable chloride with a high enough solubility in water. In order to make proper use of the planned 2 M NaOH reagent, the solubility of the metal chloride should be equal or larger than its stoichiometric concentration with this 2 M NaOH considering same volumes of the two solutions. Thus, the required minimum solubility of MCl x is expressed as: where s min,MClx (molarity) is the required minimum solubility of the metal chloride to obey condition I and x is the oxidation number of the metal ion. For M(x) = Ca(II) let us substitute the value of x = 2 into Equation (1): s min,CaCl2 = 2/2 = 1 M is obtained. Thus, the solubility of CaCl 2 in water should be higher than 1 M to obey condition I. The actual solubility of CaCl 2 in water is S CaCl2 = 81.3 g/100 g of H 2 O at 20 • C. This solubility unit should be re-calculated to molarity as: where, s MClx (molarity = mol/dm 3 ) and S MClx (g/100 g water) are the actual solubilities of the metal chloride in water in two different units, M MClx (g/mol) is the molar mass of the metal chloride. Note that Equation (2)   As follows from Table 2

Condition II Spontaneous Reaction between Metal Chloride and NaOH
One of the possible reactions of metal chloride with NaOH with the 1:1 molar ratio of chlorine and hydroxide ions leads to the formation of metal hydroxide and NaCl, the latter being fully soluble in the mixed water solution: However, the same reagents in the same molar ratio can lead also to the following reaction with the formation of a metal oxide with NaCl and water, the latter two being fully soluble in the mixed water solution: As the left-hand sides of Equation (3) and Equations (4) and (5) are identical, the reaction with a more negative standard molar Gibbs energy change will be preferred by Nature. Moreover, any of reactions (3)-(5) are considered fast (leading to a nano-precipitate) only if they are accompanied by at least −50 kJ/mol-MCl x standard molar Gibbs energy change at 300 K, calculated as: NaCl (J/mol) is the ssame for NaCl (their difference equals −4.4 kJ/mol at T = 300 K), ∆ f G 0 H2O (J/mol) is the same for liquid water (=−236.8 kJ/mol at 300 K), Note that the above requirement (the standard molar Gibbs energy change of reactions (3)-(5) at 300 K should be at least −50 kJ/mol-MCl x ) is also sufficient to ensure the formation of nano-particles, which are thermodynamically less stable compared to particles larger than 100 nm in diameter [89].
3 kJ/mol. Substituting these and the above given values into Equations (6) and (7): ∆ r3 G 0 = −158.9 kJ/mol, ∆ r4a G 0 = −101.1 kJ/mol. There are two conclusions from the latter two values: (i) ∆ r3 G 0 = −158.9 kJ/mol is more negative than ∆ r4a G 0 = −101.1 kJ/mol and so the formation of Ca(OH) 2 according to reaction (3) is more probable than the formation of CaO according to reaction (4), (ii) ∆ r3 G 0 = −158.9 kJ/mol is more negative than the above given −50 kJ/mol threshold value, so for M(x) = Ca(II) the formation of Ca(OH) 2 will be preferred by nature. For another 28 metal ions that passed condition I, the results of calculations are given in Table 3.
The following conclusions can be drawn from Table 3:  (3) and (5), see Table 3 (for experimental proof see [90,91]). That is why M(x) = Au(III) is also excluded from further consideration, as it cannot provide oxide nano-particles, mostly because Au 2 O 3 is the only oxide in Table 3 that has positive standard molar Gibbs energy of formation. Finally, conditions I-II are obeyed only by 29 − 5 − 1 = 23 metal ions of 22 metals. .

Condition III Fast Precipitation of Metal Hydroxides or Metal Oxides
The metal hydroxide (or oxide) formed in the previous step should precipitate fast in order to form nano-crystals. For that, the solubility of metal hydroxide (or oxide) in water should be much lower than its actual concentration in the water solution. The maximum concentration of metal hydroxide is about 1/x M, supposing that the same volume of NaOH solution was added to the same volume of the metal chloride solution with concentrations discussed above. To make sure the precipitation is fast, we need at least ten times less solubility compared to the maximum concentration, i.e., where, s max,M(OH)x (molarity) is the maimum allowed solubility of the metal hydroxides to satisfy condition III. Substituting x = 2 into Equation ( Table 4 for those metal ions that satisfied both conditions I and II above. The metal ions satisfying conditions I-II but not obeying condition III are listed at the bottom of Table 4: M(x) = Ba(II), Li(I), Sr(II). These metal ions are excluded from further consideration. As follows from Table 4, all other metal ions that passed conditions I-II also pass condition III. As was mentioned above, some of the metal ions that passed conditions I-II preferably form oxides. The above precipitates are dispersed in a water solution and can be contaminated by dissolved NaCl. That is why they should be washed by water to remove NaCl, so when the precipitates are dried, NaCl would not co-precipitate and would not contaminate them.
Those metal ions that passed the above conditions I-II-III as oxides, should be dried only, preferably at around 400 K, i.e., somewhat above the boiling point of water. As a result, oxide nano-particles can be obtained for the following 12 metal ions M(x) = Fe(III), In(III), La(III), Mn(II), Nd(III), Ni(II), Pr(III), Sb(III), Sm(III), Sn(II), Y(III) and Zn(II). As follows from the above, there are further six metal ions that are precipitated at least partly as oxides: M(x) = Al(III), Be(II), Cd(II), Co(II), Cu(II) and Fe(II). For the oxide part of the precipitates from these six metal ions it is also sufficient to dry the system at around 400 K to obtain the desired nano-particles. However, the hydroxide part of those six metal ions should be calcined to obtain oxide nano-particles. The same is true for the two metal ions that are precipitated in the form of hydroxides: M(x) = Ca(II) and Mg(II). Therefore, for these eight metal ions, condition IV is considered below.

Condition IV the Ability of Metal Hydroxides to Convert into Metal Oxides upon Calcination at a Reasonably Low Temperature
The following chemical reactions are expected upon heating a metal hydroxide: For example, for M(x) = Ca(II) and x = 2 Equation (11) is simplified to: Ca(OH) 2 = CaO + H 2 O. As the only gaseous component of reactions (11) and (12) is on their righthand sides (water vapor), these reactions will be shifted to the right with increasing temperature. Therefore, it is expected that all metal hydroxides will thermally decompose at a sufficiently high temperature. Those metal ions will pass condition IV, for which the normal decomposition temperature is much below the melting points of their oxides and hydroxides, and so after calcination the nano-size of the oxide particles will be similar to the nano-size of the hydroxide particles before calcination.
The normal decomposition temperature will be the temperature at which the partial pressure of water vapor reaches 1 bar, i.e., when the standard molar Gibbs energies of reactions (11) and (12) will be zero (at a lower temperature this will be positive, while at a higher temperature this will be negative). This is demonstrated in Figure 1 for M(x) = Ca(II). As follows from Figure 1, the normal decomposition temperature of Ca(OH) 2 to CaO is found at about T d = 785 K. Data obtained in a similar way as shown in Figure 1 are collected in Table 5 for other metal hydroxides. After Ca(OH)2 the second highest decomposition temperature is obtained for Mg(OH)2, being equal to 542 K. As follows from Table 5, the decomposition temperatures of all other hydroxides are in the interval of 300 … 400 K. Moreover, all the decomposition temperatures found in Table 5 are much below the corresponding melting points of the hydroxides and oxides of the same metals. Therefore, we can conclude that nano-oxide particles can be obtained by calcination of the hydroxides of all the eight metal ions of Table 5 at reasonably low calcination temperatures: M(x) = Al(III), Be(II), Ca(II), Cd(II), Co(II), Cu(II), Fe(II) and Mg(II). Thus, all these eight metal ions obey condition IV. Note: calcination should be performed at least at 400 K (or above) even for metal hydroxides with lower decomposition temperatures to make sure that dry oxide nano-particles are obtained.  Data obtained in a similar way as shown in Figure 1 are collected in Table 5 for other metal hydroxides. After Ca(OH) 2 the second highest decomposition temperature is obtained for Mg(OH) 2 , being equal to 542 K. As follows from Table 5, the decomposition temperatures of all other hydroxides are in the interval of 300 . . . 400 K. Moreover, all the decomposition temperatures found in Table 5 are much below the corresponding melting points of the hydroxides and oxides of the same metals. Therefore, we can conclude that nano-oxide particles can be obtained by calcination of the hydroxides of all the eight metal ions of Table 5 at reasonably low calcination temperatures: M(x) = Al(III), Be(II), Ca(II), Cd(II), Co(II), Cu(II), Fe(II) and Mg(II). Thus, all these eight metal ions obey condition IV. Note: calcination should be performed at least at 400 K (or above) even for metal hydroxides with lower decomposition temperatures to make sure that dry oxide nanoparticles are obtained. These eight metal . Thus, the chloride solutions of these metal ions mixed with a NaOH solution leads to oxide or hydroxide precipitates that lead to the formation of oxide nano-particles upon heating to at least 400 K to dry the system or to a somewhat higher temperature for calcination. These findings are confirmed by Table 1.

Additional Condition V: Ability of Metal Oxides to Capture CO 2 from Air
All the above is performed in order to produce oxide nano-particles. One of their possible applications is to capture CO 2 from air, according to the reactions: As in reactions (13) and (14), the only gaseous component (CO 2 ) is on the left-hand side, the reactions are shifted to the left with increasing T. Thus, the possibility of these reactions will be checked at T = 300 K. If they do not work at T = 300 K, they will not work either at higher temperatures.
The current concentration of CO 2 in the atmosphere is 420 ppm. To call a capturing technology efficient, it should decrease this value at least by ten times. Thus, reactions (13) and (14) should have an equilibrium at a partial pressure of CO 2 of 42 ppm or below, i.e., p CO2 ≤ 4.2 × 10 −5 bar for 1 bar of air pressure. Thus, the equilibrium constant of reactions (13) and (14) should be at least the inverse of this value to the power of x/2:  (13) for M(x) = Ca(II), i.e., that of reaction CaO + CO 2 = CaCO 3 is −129.6 kJ/mol. As this value is more negative than the value of -RTlnK min = −25.1 kJ/mol, one can conclude that CaO nano-particles are able to capture CO 2 from air at T = 300 K below the level of 42 ppm, i.e., M(x) = Ca(II) obeys condition V. Similar calculations are performed for another 19 M(x) ions in Table 6. Note that the thermodynamic instability of the nano-sized oxide particles will move reactions (13) and (14) even somewhat further to the right compared to the results of Table 6 [89]. * Weakly = able to absorb some CO 2 but not able to decrease its level in air to 42 ppm or below at 300 K.
As one can see from Table 6, among the 20 metal nano-oxides that can be produced by the technology described above, the following five oxides are able to capture carbon dioxide from air at least down to 42 ppm residual CO 2 -content (from strongest to weakest absorber): M(x) = Ca(II), Mn(II), Mg(II), Cd(II), Co(II). Additionally, the following three oxides can also capture some CO 2 , but not down to 42 ppm: M(x) = Fe(II), Zn(II), Ni(II).

Conclusions
Although many different nano-oxides have been synthesized as shown above, the complete list of possible nano-oxides to be synthesized by the precipitation-calcination route using metal chlorides and NaOH is missing. In this paper, this knowledge gap is filled by a theoretical method. Moreover, the ability of those oxides to capture carbon dioxide from air is discussed.
The way to synthesize oxide nano-particles by mixing the NaOH solution with a metal chloride solution to form metal hydroxide or oxide precipitates and drying or calcining the latter to form metal oxide nanoparticles is theoretically considered in this paper to select suitable metal chlorides.
The chlorides of the following 20 ions were identified as possible candidates for metal oxide nano-particle synthesis: M(x) = Al(III), Be(II), Ca(II), Cd(II), Co(II), Cu(II), Fe(II), Fe(III), In(III), La(III), Mg(II), Mn(II), Nd(III), Ni(II), Pr(III), Sb(III), Sm(III), Sn(II), Y(III) and Zn(II). These chlorides lead to the following 20 nano-oxide particles, if during the production the oxidation number of the metal is not changed: Al 2 3 have not yet been synthesized experimentally from our list of theoretically possible candidate nano-oxides. We predict that these nano-oxides will be synthesized in the future with the above technology.
Among the above 20 nano-oxides, the following five nano-oxides are able to capture carbon dioxide from air at least down to 42 ppm residual CO 2 -content (from strongest to weakest absorber): CaO, MnO, MgO, CdO, CoO. The following three nano-oxides are somewhat weaker absorbers of carbon dioxide: FeO, ZnO, NiO.
Let us note that mixing the AuCl 3 solution with NaOH solution leads to the immediate precipitation of Au nano-particles without forming Au-oxide NPs.
Author Contributions: E.E.K.: calculations, writing, G.K.: conceptualization, calculations, writing. All authors have read and agreed to the published version of the manuscript.

Funding:
This study was carried out as part of the GINOP-2.3.2-15-2016-00027 "Sustainable operation of the workshop of excellence for the research and development of crystalline and amorphous nanostructured materials" project implemented in the framework of the Szechenyi 2020 program. The realization of this project was supported by the European Union.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.