Exergy analysis of a bio-system: Soil–plant interaction

entropy Article Exergy Analysis of a Bio-System: Soil–Plant Interaction Masoomeh Bararzadeh Ledari 1, Yadollah Saboohi 1,* , Antonio Valero 2and Sara Azamian 1   Citation: Bararzadeh Ledari, M.; Saboohi, Y.; Valero, A.; Azamian, S. Exergy Analysis of a Bio-System: Soil– Plant Interaction. Entropy 2021,23, 3. https://dx.doi.org/10.3390/e23010 003 Received: 11 October 2020 Accepted: 19 November 2020 Published: 23 December 2020 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). 1Department of Energy Engineering of Sharif University of Technology, Tehran 11365-8639, Iran; [email protected] (M.B.L.); [email protected] (S.A.) 2Department of Mechanical Engineering, University of Zaragoza, ETSII, 50015 Zaragoza, Spain; [email protected] *Correspondence: [email protected] Abstract: This paper explains a thorough exergy analysis of the most important reactions in soil– plant interactions. Soil, which is a prime mover of gases, metals, structural crystals, and electrolytes, constantly resembles an electric field of charge and discharge. The second law of thermodynamics reflects the deterioration of resources through the destruction of exergy. In this study, we developed a new method to assess the exergy of soil and plant formation processes. Depending on the types of soil, one may assess the efficiency and degradation of resources by incorporating or using biomass storage. According to the results of this study, during different processes from the mineralization process to nutrient uptake by the plant, about 62.5% of the input exergy will be destroyed because of the soil solution reactions. Most of the exergy destruction occurs in the biota–atmosphere subsystem, especially in the photosynthesis reaction, due to its low efficiency (about 15%). Humus and protonation reactions, with 14% and 13% exergy destruction, respectively, are the most exergy destroying reactions. Respiratory, weathering, and reverse weathering reactions account for the lowest percentage of exergy destruction and less than one percent of total exergy destruction in the soil system. The total exergy yield of the soil system is estimated at about 37.45%. Keywords: soil–plant system; exergy analysis; soil–plant exergy loss; soil–plant exergy destruction 1. Introduction All ecosystem processes are irreversible and are accompanied by entropy production and exergy destruction. Exergy analysis is a method for analyzing energy systems based on the second law of thermodynamics. Exergy is a driving force for the conversion of energy and chemical substances for the further development of ecosystems [ 1 ]. Green plants convert exergy from the sunlight into exergy-rich biomass, via photosynthesis. The exergy content of biomass passes through different food chains in the ecosystems. At every trophic level, exergy is consumed and decomposing organisms dominate the last level in this food chain [ 2 ]. Most of the exergy is destroyed in the irreversible interaction of solar radiation with the surface, and only a tiny fraction of about 2.5% of global cosmic exergy consumption is used in transforming earth materials [ 3 ]. Exergy is stored in the form of biomass in soil. Increased inputs (more solar radiation is captured) mean more biomass, more exergy stored, and more exergy degraded [ 4 ]. Schneider and Kay [ 4 ] expressed an extended second law. The findings of ecosystem tend toward dissipating solar exergy because of different processes in the earth. They concluded that an increase in exergy storage and through-flow describe ecosystem development based on all three growth forms. The results referred to above can be used to formulate a general law for the development of ecosystems: if a system receives a through-flow of exergy (energy), it will move away from thermodynamic equilibrium and select the components and the organization that yield useful energy through the system (maximum power principles) and the most exergy stored in the system. Ecological exergy analysis and environmental effects follow different approaches. Some researchers studied ecological integrity and the effects of environmental hazards. Entropy 2021,23, 3. https://dx.doi.org/10.3390/e23010003 https://www.mdpi.com/journal/entropy Entropy 2021,23, 3 2 of 28 They focused on the effect of changing environmental conditions on the system, moving away from the original optimum operating point [ 5 , 6 ]. Some authors were interested in the information exergy and the eco-exergy methods. They analyzed ecosystems considering conservation [ 7 ] (Patten, Straškraba, and Jörgensen 1997), dissipation [ 8 ], openness [ 9 ], growth [ 10 ] (Sven E Jørgensen, Patten, and Straškraba 2000), constraints [ 11 ], and differentiation [ 12 ] toward an ecology of complex systems in a complex future [ 13 ]. They tried to find a method to illustrate ecosystems evolution considering the adjustment and compensation of human activity effects on the quality of ecosystems. This means the quality of ecosystems depends on the amount of exergy storage in the earth. Moreover, thermodynamic analysis of biological systems based on exergy analysis of photosynthesis [ 14 ], plant exergy efficiency [ 15 ], and exergy analysis of different biological reactions has been followed up. For instance, Lems [ 16 ] and Moura [ 17 ] demonstrated a method for biochemical reactions that can indicate a change in the quality of soil and plants. They introduced some methods for exergy analysis of different phenomena in the ecosystem by using exergy analysis of different reactions. In addition, according to Keller [ 18 ], the first and second laws of thermodynamics were used for a classical biological system (plant). Next, Petela [ 14 ] determined a system boundary of a leaf surface layer, in which biomass is created at temperature T and undertook an exergy balance of the leaf. Silva [ 15 ] decomposed the photosynthesis process into three main processes (photosynthesis I and II and Calvin cycle) and analyzed the changing quality of these processes. In this regard, Silow et al. [ 19 ] used and proposed the eco-exergy approach to analyze an open system that receives solar exergy as input, captures energy, as well as analyzes decomposer activities and the cycle’s waste, This method uses some coefficients, such as capacity of packaging information at the molecular level (DNA) that differs from one organism to another and can be taken into account using the eco-exergy function. This method can be applied to problems of a theoretical nature and does not have a practical application in ecosystems. Fath et al. [ 20 ] analyzed a bio-system including interactions between solar exergy, autotroph levels, and heterotroph levels. Their research used the eco-exergy method, considering different stages of growth and biomass storage. According to them, such analysis does not provide a better understanding of the transformation path [ 20 ]. In Ecoinvent Life Cycle Analysis, solar exergy absorbed directly by the soil is not considered by the functional unit, since its category is classified as “occupation, pasture and meadow, extensive”; this deficiency actually forgets the solar exergy the ecosystem needs to sustain its natural cycles [ 21 ]. Rocco et al. use exergy indicators for environmental impact assessment, which supplies a wider framework and deeper insights into the environmental performance of production processes and products. They used exergy-based indices for studying changes in soil quality [22]. Different types of nutrient loss and degradation reactions in ecosystems not only change the nutrient availability in the plant but also compromise soil microorganisms’ habitat. Moreover, the soil quality can decrease or increase due to nutrient uptake reactions such as mineralization by plants (microorganisms’ biochemical reactions in soil). In the present paper, we have utilized Moura and Lems’ exergy analysis in the plant–soil system [16]. In summary, there is a lack of systematic exergy analysis of the most important reactions in soil–plant interactions. Therefore, the primary objectives are: • Evaluate the exergy performance of the bio-system (plant–soil system) by overall exergy efficiency. • Identify the most significant source of exergy destruction and exergy losses in the bio-system (plant–soil system) and their location of occurrence. • Evaluate the effect of various natural phenomena (weathering, acid rain, etc.) on the bio-system exergy efficiency. Entropy 2021,23, 3 3 of 28 2. Materials and Methods We may consider soil as an energy system, in which the main purpose of this system is nutrient supply. As in any energy system consisting of different subsystems, in the soil system, numerous reactions occur that supply nutrients for plant growth [23]. Biogeochemical processes in the terrestrial environment dominate the hydrochemical response of small catchments because stream water is largely made up of drainage water from soils. Biogeochemical processes can be categorized into three major groups (cf. van Breemen et al., 1983): 1. Biochemical processes, including interactions between biota and the atmosphere (e.g., photosynthesis, respiration, N2 fixation), and interactions between biota and soil solution (e.g., assimilation and mineralization). 2. Geochemical and soil chemical processes, including interactions between solution and the soil solid phase (e.g., cation exchange, adsorption, chemical weathering). 3. Chemical reactions in solution (e.g., hydrolysis, complexation reactions) or between solution and atmosphere (e.g., degassing of CO2). In this study, these reactions are classified into five categories: plant to the soil, biota to the solution, atmosphere to biota, the solution to the atmosphere, solid to the solution, and other reactions (related to fertilizers, pollution, and acidification). The relationship between different parts of the ecosystems, including the hydrosphere, atmosphere, and biosphere, is shown in Figure 1. Figure 1. Mutual interactions between atmosphere, lithosphere, and biosphere leading to accretion or decrease in nutrient content in the soil. Entropy 2021,23, 3 4 of 28 The effects that lead to the generation of nutrients and increase their availability are considered positive and those that reduce the availability of nutrients and the degradation of nutrients in the soil are considered negative. However, the negative effects are those reactions that occur in the soil to compensate the entropy increasment; for example, in power plants, a condenser plays an important role to discharge the entropy increasment in the power plantsBy managing and controlling the soil system, these negative effects could be reduced to some extent, but cannot be eliminated (denitrification, de-complexation, and respiration). These interactions are associated with some main reactions including chemical formation, concentration change, electrical potential change, and mixing reactions. As mentioned, the main objective of the soil system is food production and the photosynthesis reaction. In order to achieve this goal, the main reactants of these reactions could come from minerals, manure/compost, and the atmosphere. The important elements, such as nitrogen, phosphorus, carbon, and sulfur, enter the soil from the atmosphere. Part of the reactions originate from the atmosphere to the soil or vice versa, which are considered to be positive, and reversing these reactions leads to the reduction in nutrients availability (negative effects). The most important part of the soil is the soil solution, which includes the organic and inorganic phases (Figure 2). Variations in key electron donors and acceptors ( NO2− 3 , N2 , NH+ 4 , SO2− 4 , CH4 , and dissolved organic carbon (DOC)) closely follow the predictions of thermodynamics. Transformations of N and other elements result from the response of microbial communities to two dominant hydrologic flow paths: (1) horizontal flow of shallow subsurface waters with high levels of electron donors (i.e., DOC, CH4 , and NH+ 4 ), and (2) near-stream vertical upwelling of deep subsurface waters with high levels of energetically favorable electron acceptors (i.e., NO2− 3 , N2O , and SO2− 4 ). Thermodynamic constraints on microbial metabolism depend on the use of electron donors and electron acceptors in redox reactions that generate energy for growth and maintenance. While organic matter ( CH2O ) dominates as the electron donor in many natural environments, other electron donors (e.g., CH4 , H2S , Fe(II), NH+ 4 , and Mn(II)) can be locally important. Similarly, O2 dominates as the electron acceptor in oxic environments, while NO2− 3 , N2O , Mn(IV), Fe(III), SO2− 4 , CO2 , and CH2O can be locally important in anoxic environments. Different combinations of electron donors and electron acceptors, in expression, release different amounts of free energy that, in turn, can be harnessed for microbial growth and maintenance. For example, aerobic respiration ( CH2O as an electron donor, O2 as an electron acceptor) generates almost five times more free energy (501 kJ) per mole of oxidized CH2O than sulfate reduction does (102 kJ; CH2O as electron donor and SO2− 4 as an electron acceptor) at pH 7 and molar concentrations of reactants [ 24 ]. The environment becomes increasingly reduced due to microbial consumption of electron acceptors following the sequence: (1) loss of O2 (aerobic respiration); (2) loss of NO2− 3 (denitrification); (3) loss of SO2− 4 (sulfate reduction); and (4) accumulation of CH4(methane fermentation) [24]. Entropy 2021,23, 3 5 of 28 Figure 2. Soil–plant interactions. Entropy 2021,23, 3 6 of 28 2.1. Exergy Analysis of Electron Transport Chain Exergy transferred through an electron carrier is passed to the next carrier i − 1, used to do workwithin the living system, and partially lost to the environment as low-grade waste heat (exergy destruction). These carriers can move from the nucleus in channels to make energy carrieravailable for other reactions such as the carbon cycle (more detail about these reactions in photosynthesis process has been explained in the Supplementary Materials) [15]: Bcarriers,i=Bcarriers,i−1+W+δB(1) where Bcarriers,iis the exergy of carrier i(high-energy electrons proceed in photosynthesis reactions), Wis the work performed by the electron transfer, and δ Bis the exergy destroyed. The standard reduction potentials can be expressed as: ∆G0=−nF∆ε0(2) where ∆ G 0 is the standard Gibbs free energy change (Here, the initial concentration of each component is 1.0 M, the pH is 7.0, the temperature is 25 C, and the pressure is 101.3 kPa.), nis the number of moles of electrons, Fis the Faraday constant (96,485 Coulomb/mole e-), and ∆ε0 is the standard change in reduction potential. It can be modified to account for the effects of intracellular concentrations and used to calculate the exergy difference between electron carriers [16]. NADPH carries added protons in the last biosystem in photosynthesis processes. This process is a proton–electron that originated from the NADPH reaction. This reaction helps to reach a level of thermodynamic stability: ∆ε0 is 1.140 V [ 25 ]. The energy level difference compared to the reference responses of the intracellular proton–electron system in the exchange process is estimated as (detail of the reactions is presented in the Supplementary Materials): ∆Belec =Bcarriers,i−Bcarriers,i−1=nF∆ε0+RT0Ln(∏[A]−ϑi i)(3) where ∆ B elec is the exergy difference between carriers iand i − 1, Ris the universal gas constant (8.3143 J/moleK), T0 is the dead-state temperature (298.15 K), [A]i is the activity of carrier i, and ϑiis the stoichiometric coefficient of carrier i. For each molecule in the reactions, its chemical exergy is estimated using the method of Lems et al. [16]: Bchem ≈∑ k (ϑkBelement,i) + ∆G0 f+RT0Ln[A]+RT0Ln1+∑ i ∏l=1Kl [H+]i +RT0∑ j Ln(1+n ∑ 1 ∏ i=1 Ki)[Mj]i)(4) where B chem is the chemical exergy of a species (per mole), Belement,i is the number of times that atom k occurs in the species (stoichiometric coefficient when forming the species from reference atoms), [A] is the activity of the species, Kl is the chemical equilibrium constant (for either acid, base, or metal ion dissociation) for reaction l, [H]+ is the hydrogen ion concentration, [Mj] is the concentration of metal ion j,kis the atom counter, iand lare the reaction counters, and jis the metal ion counter [15]. To determine the exergy of a mole of photons, a modified form of Planck’s Law is applied [ 16 ]. Note that the only difference between Planck’s Law and the factor (1−Tearth Tsun ) , which accounts for a 5 percent difference between the energy and exergy of photons (the data required for this reaction are presented in the Supplementary Materials): Bphoton(λ)=NA hc λ(1−Tearth Tsun )(5) Entropy 2021,23, 3 7 of 28 where B photon is the photon exergy (J/mole photons) at a given wavelength ( λ ), N A is Avogadro’s number (6.023 × 1023), his Planck’s constant (6.626 × 10 − 34 J × s), cis the speed of light (3 × 108 m/s), λ is the wavelength (m), T earth is the ambient temperature of the earth (298.15 K), and Tsun is the temperature of the sun’s surface (5762 K) [16]. Applying the mean-value theorem to exergy of the photon equation yields (the data required for this reaction are presented in the Supplementary Materials): Bphoton,avg =NAhc(1−Tearth Tsun )Lnλhigh−Ln(λlow) λhigh −λlow (6) An exergy analysis of systems is the introduction of exergy cost analysis. This is based on the second law of thermodynamics regarding the concept of exergetic cost [ 26 ], the average cost approach [ 27 , 28 ], and specific exergy costing method [ 29 ]. In the present paper, we use the average exergy cost for bio-systems analysis. 2.2. The Exergy of Biochemical Reactions In standard biochemical conditions, the medium is considered to be pure water of neutral acidity at standard pressure and temperature, and the compound is considered to be at unit concentration, or actually at the unit chemical activity. Gibbs free energies of formation in standard biochemical conditions have been determined for a wide range of biochemical compounds, and the exergy of these compounds at the given conditions can then be calculated following [16]: Ex00 A=∑ i ϑiEx0 element,i+∆fG00 A(7) where Ex00 A and Ex0 i are the stoichiometric number and the exergy in standard chemical conditions (superscript 0) of element iin compound A, respectively, and where ∆fG00 A is the Gibbs free energy of formation of compound A in standard biochemical conditions (superscript 0 0 ). For the exergy of the elements, we refer to Szargut et al. (1988) [ 30 ], who also give a detailed description of how these exergy values are calculated. The cellular concentrations of the compounds are far from the 1 M which is considered in Gibbs free energy, and since the environment can be considered water, the concept of an ideal solution can be applied, where the activity coefficient is considered to be equal to 1. Such an effect is very important as some reactions only occur due to differences in concentration. Exconcentration =RT0ln[C/C0](8) The metabolic compounds suffer ionic dissociations with cations (H + ) and anions (OH−), since the environment is active, forming different compounds, for example: C0→ K1 C1+H+→K2C2+2H+. . . →KnCn+nH+ The exergy due to acid dissociation is: Exdissociations =−RT0[1+ n ∑ i=1 ∏i j=1Kj [H+]i](9) Some compounds bound to metallic ions forming metallic compounds and act as catalysts of the reactions. Similarly, an equation for the exergy effect of the metal compound is: Exmetallic =−RT0ln[1+ n ∑ i=1 ( i ∏ j=1 Kj[M]i)] (10) Entropy 2021,23, 3 8 of 28 The new equilibrium constant is known as the apparent equilibrium constant: Kapparent =∏ i (Ciγi)ϑi=∏ i (Ci)ϑi∏ i (γi)ϑi=KΓ(11) where γ is the activity coefficient and Γ is a global factor. The extended Debye–Hückel Law is used to evaluate Γby re-evaluating the activity coefficient: lnγi=−az2 iI1/2 1+BI1/2 (12) where z i is the ion electrical charge, Iis the ionic force, and α and Bare constants. The new equilibrium constants can now be re-evaluated using the definition of pK = log(k): pK(I)=pK(I=0)−αlog(e)I1/2 I+BI 1 2∑ i ϑiz2 i(13) The total exergy of the compound is then the sum of all effects above. Ex =Ex0+Exconcentration +∑(Exdissociations)+Expotential (14) In some reactions, the proton and electron transfer can change the energy level of the product ( Expotential) . With the exergy value of the compounds evaluated, chemical reactions such as A+B→C+Dcan be analyzed through the exergy balance [17]: Exreactants =Exproducts +Exdestroyed +Exlost (15) Moreover, the exergetic efficiency can be defined by: ε=Exproducts Exreactants (16) 3. Results 3.1. Exergy Loss and Destruction of Different Ecosystems Interactions 3.1.1. Weathering The weathering of rocks leads to the formation of sand, silt, and clay. Based on their mechanisms, the following are the three types of weathering: physical weathering, chemical weathering, and biological weathering. Chemical weathering (chemical erosion) is the decomposition of rocks by a change in the chemical and mineralogical composition, through a combination of several chemical processes. It is a slow but more intense process than physical weathering. Chemical weathering takes place mainly at the surface of rocks and minerals, leading to the disappearance of certain minerals and the formation of new products and secondary minerals. Chemical weathering is more intense in areas where it is preceded by physical weathering, which causes a decrease in particle size and an increase in surface area. Chemical weathering is therefore aided and abetted by physical weathering. During the process of chemical weathering, one or more of the following minerals in solution (cations and anions) are formed: oxides of iron and alumina (sesqui-oxides Al 2 O 3 , Fe 2 O 3 ), various forms of silica (silicon oxide compounds), and stable wastes such as very fine silt (mostly fine quartz) and sand (coarser quartz) [31]. In sedimentary rocks, which are made up of primary and secondary minerals, weathering acts initially to destroy any relatively weak bonding agents (FeO), and the particles are freed and can be individually subjected to weathering. Based on the results, the greater exergy destruction in chemical weathering is caused by hydrolysis reactions. Such exergy destruction is caused by the chemical reaction and the change in concentration (Table 1). Entropy 2021,23, 3 9 of 28 Table 1. Exergy destruction of various chemical weathering (kJ/mole). Reaction ∆G1(kJ/mole) Exdestruction (KJ/mole) Ein 2(KJ/mole) Oxidative weathering of mineral 4FeO +O2→2Fe2O3−287.856 287.856 503.36 Reverse weathering Fe2++1 4O2+3 2H2O→Fe(OH)3+2H+151.92 171.59 376.59 FeS +9 2O2+5 2H2O→Fe(OH)3+SO2− 4+2H+−960.22 73.19 393.47 Rainfall 2Fe3++3SO− 4+6H2O→2Fe(OH)3+6H++3SO2− 4856.42 856.42 2582.8 Soil acidity adjustment H+2+CaCO3→Ca2++ +CO2+H2O443 240.12 678.9 1Difference of Gibbs free energy; 2Exreactants. The main effects of these reactions in the soil are imbalanced creation in the number of cations and anions in the soil. Microorganisms have spent part of their activities on these reactions. Therefore, it can easily reflect the effects of human activities on the soil balance reactions. Among these general reactions, chemical weathering reactions cause the 9% of total exergy destruction in the soil system. 3.1.2. Dissolution and Precipitation Solids can either be formed by precipitation and crystallization or dissolved depending upon the conditions of the solution. Some of the most influential conditions affecting dissolution/precipitation in soils are ionic composition and concentration, pH, and temperature. In addition, solution species that form strong complexes with the constituents of a solid may enhance the dissolution of such solids. In this section, we will discuss the process of solid phase formation and destruction [32]. Based on the thermodynamic prediction, mineral dissolution reactions are represented in Table 2. Table 2. Thermodynamic analysis of mineral dissolution. Reaction log(K) Exdestruction (kJ/mole) CaSO4(gypsum)↔Ca2++SO42−−4.6 11.40 CaCO3(calcite)↔Ca2++CO32−−8.35 20.6 Fe(OH)3(amorphous)↔Fe3++3OH−−38.7 95.93 Al(OH)3(gibbsite)↔Al3++3OH−−33 81.80 Fe(OH)2H2PO4(strengite)↔Fe3++2OH−+H2PO4−35 86.75 As can be seen in Table 2, we only have some electrolysis reactions, which are dissolution reactions. These types of reactions are useful in the soil solution quality. The soil solution needs some ionic interactions to prepare nutrient that they have the proper condition to uptake by plant. The most important precipitation reactions take place with H2SO4 and HNO3 . The exergy analysis of the reactions is shown in Table 3[32]. Entropy 2021,23, 3 16 of 28 this exergy input can be lost as leaching and atmospheric influx, as well as different exergy destruction in soil. Eventually, only 71,568 kJ/mole of total exergy input will be available as a nutrient resource for the photosynthesis process (Figure 6). Figure 6. Different interaction of soil reactions (exergy efficiency and destruction). 5. Conclusions Different interactions between soil, atmosphere, lithosphere, and biota can greatly affect the efficiency of exergy absorption from the sun and the amount of biomass exergy storage in the earth. Biological activities in soil supply the nutrients required by the plant; however, they could have unpleasant effects on microorganism life. In the present research work, the main biogeochemical reactions have been taken into account. The plant nutrients make up the inorganic elements required for plant growth, most of which are also essential for microflora and fauna to continue living. The main energy resources in soil include organic compounds—which are subject to biological attacks—serve as energy sources for the soil fauna and microflora rather than the few bacteria that can live. Although, these processes can form nitrogenous, phosphoric, and potassium compounds, they can cause about 17.8% of total exergy destruction in the soil. These organic and inorganic materials, after mineralization, are absorbed within ion exchanges. In general, different processes through mineralization to nutrient uptake destruct about 17.8% of total exergy input. A major amount of these resources are used by microorganism activities through biological reactions. Nutrient uptake involves different biological and chemical reactions, in which great portions of nutrients are lost into the atmosphere (similar to heat loss in energy systems). These reactions can deplete material resources in the soil through its interaction with water (equivalent to the discharge of waste and sewage in energy systems). In general, these losses are divided into two categories—losses of natural activities such as acid rain, erosion, etc., and the direct discharge of waste into the soil. Different biota–atmosphere reactions lead to high levels of exergy destruction in the soil system. One of the most important reactions in this pathway is photosynthesis (with a low amount of efficiency which is about 15%). After that, the next greatest amounts of exergy destruction occur in the biota–solution pathway. Given that, the most important reactions in this group force exergy destruction through chemical reactions. After photosynthesis, which accounts for up to 21% of total exergy destruction, the second and third places go to plant to soil reactions and protonation reactions with 14% and 13% of total exergy destruction, respectively. Respiration, weathering, and reverse weathering processes account for the lowest percentage of exergy destruction, with even less than one percent Entropy 2021,23, 3 17 of 28 of total exergy destruction in the soil system. The lack of nutrients in the soil is supplied through adding fertilizer/compost (similar to energy carriers in energy systems). Plants use a part of resources through mineralization to uptake processes. Another part of resources compensates for the losses that occurred in the soil. In the neutral pH range (6 to 8), eventually, only 7.16E05 of 1.91E05 kJ/mole of the exergy input will be available as a nutrient resource for the photosynthesis process because the rest is lost due to leaching and atmospheric influx, as well as different exergy destruction in soil. Supplementary Materials: The following are available online at https://www.mdpi.com/1099-430 0/23/1/3/s1, Figure S1: Qualitative Exergy-Flow Diagram of the plant. The Color Key describes the type of exergy flows between the different biological operations, Figure S2: Transfer of high energy electrons through photosystem II (PSII) and photosystem I (PSI). Two chemical reactions are described in this figure. All of the reactions are explained here. In the first step, water is split into protons, oxygen, and electrons. The electrons are excited to the high-level energy (P680*). NADP þ is reduced to NADPH. Intermediate carriers are various functional groups in the protein complexes of PSII and PSI, Table S1: The assumption for the average photon exergy, Table S2: Exergies and reduction potentials of PSII, Table S3: Exergies and reduction potentials of PS, Table S4: Exergy losses in the dark reactions, Table S5: Overall chloroplast efficiency. Author Contributions: Conceptualization: M.B.L. and Y.S.; methodology: M.B.L. and Y.S.; software: M.B.L.; validation: M.B.L. and Y.S., and A.V.; formal analysis: M.B.L. and Y.S., and A.V.; investigation: M.B.L.; resources: M.B.L., S.A.; data curation: M.B.L., S.A.; writing—original: M.B.L.; writing— review: Y.S., A.V.; visualization: M.B.L.; supervision: Y.S.; project adm.: Y.S., M.B.L.; funding acq.: Y.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science, Research and Technology of Iran, SET. Conflicts of Interest: The authors declare no conflict of interest. Appendix A. Soil Reactions and Exergy Analysis Table A1. Exergy analysis of soil to plant interactions. Reaction ∆G(kJ/mole) Exin (kJ/mole) Exout (kJ/mole) NH3+CH3OH →CH3NH2+H2O−51.87 1057.90 211.00 NH3+C2H5OH →C2H5NH2+H2O 57.72 1694.80 426.10 H2S+CH3OH →CH3SH +H2O−728.05 1532.00 119.87 H2S+C2H5OH →C2H5SH +H2O−649.12 2168.90 957.85 SO2+CH3OH →CH3SH +1 2O2514.29 1033.40 120.96 SO2+C2H5OH →C2H5SH +1 2O2593.22 1670.30 958.94 NH+ 4+CH3OH →CH3NH2+H2O+H+−846.98 1389.20 542.30 NH+ 4+C2H5OH →C2H5NH2+H2O+H+−737.38 2026.10 757.40 H++CH3NO− 3+2OH−→2O2+CH3NH21063.26 1461.30 218.04 H++C2H5NO− 3+2OH−→2O2+C2H5NH22063.07 1461.30 433.14 CH3OH +SO2− 4+2H+→1 4O2+3 2H2O+CH3SH 2793.47 1500.70 121.31 C2H5OH +SO2− 4+2H+→1 4O2+3 2H2O+C2H5SH 2872.40 2137.60 959.29 Table A2. Glucose oxidation versus other important oxidation reactions carried out by chemolithotroph levels. Reaction ∆G(kJ/mole) Exin (kJ/mole) Exdestruction (kJ/mole) CH2O+O2→CO2+H2O−287 542.37 234.99 CH4+2O2→CO2+2H2O−871 839.14 1688.86 S+1 2O2+H2O→SO− 4+2H+−587 614.47 703.73 NH+ 4+1 2O2→NO− 2+2H++H2O−275 673.17 177.77 H2+1 2O2→H2O−237 240.07 476.17 HS−+H++1 2O2→S+H2O−209 1478.57 112.77 NO− 2+1 2O2→NO− 3−76 110.87 53.39 2Fe2++2H++1 2O2→2Fe3++2H2O−31 1417.39 698.59 Entropy 2021,23, 3 18 of 28 Table A3. Exergy analysis of biota solution (mineralization). Reaction ∆G(kJ/mole) Exin (kJ/mole) Exdestruction (kJ/mole) CH3NH2+2O2→OH−+2 3NO− 3+CH3OH −705.82 218.04 130.25 C2H5NH2+2O2→2OH−+2 3NO− 3+H++C2H4−2223.46 433.14 396.72 CH3SH +3 2H2O+1 4O2→CH3OH +SO2− 4+2H+−1125.80 121.31 66.89 C2H5SH +3 2H2O+1 4O2→C2H5OH +SO2− 4+2H+−1032.98 959.29 356.43 C3H7H2PO4+H2O→CH3OH +H2PO− 4+H+406.84 151.10 43.66 NH3+2H++O2+e−→NH2OH +H2O−251.95 1004.47 916.72 NH2OH +H2O→NO− 2+4e−+SH+−232.05 339.70 232.05 2H++1 2O2+2e−→H2O → NH+ 4NH3+H+1253.57 664.59 588.98 NO− 2+H2O→NO− 3+2H++2e−−159.72 107.80 267.52 3(CH2O)+2N2+3H2O+4H+→3CO2+4NH+ 42504.86 1867.74 637.12 NH3+2O2→H++NO− 3+H2O−746.27 1281.90 88.07 CH2O+O2→CO2+H2O+cellular material −876.91 542.37 334.54 C6H12O6→CH3CH2OH +2CO2−2512.99 2930.00 2512.99 H++H2O+CH3NH+ 2→CH3OH +NH+ 4739.00 542.30 196.70 Humic acid : C20H15(CO2H)(OH)5(CO2)2: Carboxyle(−COOH) CH2O+1 2SO2− 4+1 2H+=CO2+1 2HS−+H2O494.53 1008.85 514.32 SO2+HCO− 3=CO2+HSO− 3−96.97 1523.59 1426.62 CH2O+2MnO2+4H+=CO2+2Mn2++3H2O3691.34 1916.60 1774.74 2H++SO2− 4→H2S+2O21164.40 1272.20 107.80 2NO− 3+SO2− 4→2NO− 2+H2O+CO269.60 1272.20 1202.60 2H++SO2− 4→H2O+SO2+1 2O22249.43 1272.20 977.23 2NO− 2+3CH2O+4H+→2NH+ 4+3CO2+H2O3013.02 3154.20 141.18 Ca2++2CO2+2H2O→H+2+Ca2++2HCO− 3−120.91 770.26 649.35 FeS2+15 2H2O2→Fe3++2H++7H2O+2SO2− 4−3592.54 2435.35 1157.19 FeS2+7 2O2+H2O→Fe2++2H++2SO2− 4−2271.66 1440.66 831 Table A4. Exergy analysis of amorphous hydroxides. Amorphous Hydroxides ∆G(kJ/mole) Exout (kJ/mole) Exdestruction (kJ/mole) Al(OH)3−1141.76 1154.00 7617.78 Fe(OH)3−695.86 40.47 210.98 Mn(OH)2−663.14 . . . . . . sum 1194.47 7828.76 Silicates ß-CaSiO 3(wollastonite) + 2 H++ H2O = Ca2++ H4SiO4 −75.74 75.74 663.50 CaSiO3(pseudowollastonite) + 2 H+ + H2O = Ca2++ H4SiO4−81.22 81.22 663.50 ß-Ca2SiO4(larnite) + 4 H+↔2 Ca2+ + H4SiO4−226.14 226.14 1325.20 ?- Ca2SiO4(Ca olivine) + 4 H+↔2 Ca2+ + H4SiO4−215.86 215.86 1325.20 Aluminosilicates CaAl2SiO6(pyroxene) + 8 H+↔Ca2+ + 2 Al3+ + H4SiO4+2 H2O−201.20 201.20 2650.40 CaAl2Si2O8(Ca-glass) + H+↔Ca2+ + 2 Al3+ +2H4SiO4−193.55 193.55 2650.40 CaAl 2 Si 2 O 8 (hexagonal anorthite) + 8 H +↔ Ca 2+ + 2 Al 3+ +2H 4 SiO 4−148.97 148.97 2650.40 CaAl2Si2O8(anorthite) + 8 H+↔Ca2++ 2 Al3+ + 2 H4SiO4o −133.16 133.16 2650.40 CaAl2Si2O82 H2O (lawsonite) 8 H+↔Ca2+ + 2 Al3+ +2H4SiO4+ 2 H2O−100.11 100.11 2650.40 CaAl 2 Si 2 O 4 O 12 i2 H 2 O (wairakite) + 8 H +↔ Ca 2+ + 2 Al 3+ +2H 4 SiO 4−91.61 91.61 2650.40 Ca2Al4Si8O24i7 H2O (leonhardite) + 16 H++ H2O↔2 Ca2++4 Al3+ + 8 H4SiO4 −98.69 98.69 5301.70 CaMg(SiO3)2(diopsite) + 4 H++2H2O↔Ca2++ Mg2+ +2H4SiO4−120.77 120.77 1327.00 Entropy 2021,23, 3 19 of 28 Table A5. Exergy analysis of biota-atmosphere (Photosynthesis). Photosynthesis Exin (kJ) Exout (kJ) Exdestruction (kJ) Efficiency PAR Reflection 9977 9977 0 100 Non-PAR Reflection 13,226 661 12,564 50 Photosystem II absorption 5319 4193 1126 78.8 Photosystem I absorption 5319 4074 1246 76.6 Photosystem II ETC 4209 2200 2009 52.3 Photosystem I ETC 4901 2401 2500 49 ATP synthase 1372 992 381 72.2 Calvin cycle (dark reaction) 3509 2848 661 81.2 overall 23,334 2848 20,487 12.2 Table A6. Exergy analysis of biota-atmosphere (Aerobic Respiration). Reaction Exin (kJ/mole) Exdestruction (kJ/mole) Efficiency 1 2O2+H++e−→1 2H2O335.27 169.78 49.36 Table A7. Exergy analysis of biota-atmosphere (volatilization). Reaction ∆G (kJ/mole) Exdestruction (kJ/mole) Exin (kJ/mole) H2O+CH3NH2→CH3OH +NH355.87 55.87 211.00 H2O+CH3SH →H2S+CH3OH −72.80 72.80 119.87 3 2O2+CH3SH →CH3OH +SO2−514.29 514.29 638.90 H2O+CH2CH3NH2→CH2CH3OH +NH3−57.70 57.70 426.10 H2O+CH2CH3SH →H2S+CH2CH3OH 649.12 649.12 957.85 3 2O2+CH2CH3SH →CH2CH3OH +SO2−593.22 593.22 962.59 Surface Volatilization 5S +6KNO3+2H2O→3N2+K2SO4+4KHSO4−1243.65 1243.65 2933.40 5K2S2O3+8KNO3+H2O→4N2+9K2SO4+H2SO4−3106.80 310.00 1358.70 Table A8. Exergy analysis of biota-atmosphere (ion exchange). Ion Exchange ∆G(KJ/mole) Exin (kJ/mole) 2F +2e−→2F−325.70 504.90 Cl2+2e−→2Cl−179.60 175.80 NO− 3+6H++5e−→1 2N2+3H2O169.95 2413.00 O2+H++4e−→4H2O169.78 335.06 N2+6H++6O−→2NH359.77 1988.52 2H++2e−→H251.08 662.60 Fe2++2e−→Fe 7.62 376.40 Zn2++2e−→Zn −23.26 339.20 K++e−→K−233.42 366.60 NO− 3+2H++4e−→NO− 2+H2O. . . Fe3++e−→Fe2+125.39 376.40 SO2− 4+10H++8e−→H2S+4H2O78.99 78.99 CO2+4H++4e−→C+2H2O71.35 1344.68 Al3++3e−→Al −109.40 888.20 Mg2++2e−→Mg . . . . . . Na++e−→Na −212.44 336.60 Ca2++2e−→Ca −226.88 729.10 Entropy 2021,23, 3 20 of 28 Table A9. Exergy analysis of biota-atmosphere (carbon cycle). Reaction Exdestruction (kJ/mole) Exin (kJ/mole) Slow Reactions in Carbon Cycle CaSiO3+CO2+2H2O→Ca(OH)2+SiO2+H2CO332.4 44.88 Ca(OH)2+H2CO3→CaCO3+2H2O 81.24 2276.98 CaSiO3+CO2→CaCO3+SiO248.84 60.18 Fast Reactions in Carbon Cycle CO2+H2O→CH2O+O2 510.17 20.38 CO2(atmosphere)=CO2(dissolved) CO2(dissolved)+H2O=H2CO3 CO2+H2O=HCO− 3+H+ HCO− 3=H++CO2− 3 CH2O+1 2CO2=CO2+1 2CH4 Methane formation 105.4 548.14 H2CO3=H++HCO− 3 Soil inorganic carbon 201.16 2206.18 Table A10. Exergy analysis of solution-atmosphere interactions. Reaction Exdestruction (kJ/mole) Exin (kJ/mole) Nitrogen 2H++H2O+NO− 3→NH+ 4+2O257.98 1793.5 NO− 3+H+→1 2H2O+1 4O2+NO2130.39 1461.3 NO− 3+H+→1 2H2O+3 4O2+NO 93.79 1461.3 2NO−3+2H+→H2O+3 2O2+N2169.95 2260 Table A11. Exergy analysis of solution-atmosphere interactions. Complexes Log K ∆G(kJ/mole) Exdestruction (kJ/mole) Exin (kJ/mole) CaF2(fluorite)↔Ca2+ + 2F−−10.41 59.42 70.82 130.23 Ca2 + Cl−↔CaCl+−1.00 5.71 822.31 828.02 Ca2++0/5O2+ 2 Cl−↔CaCl20.00 0.00 903.70 903.70 Ca2++ CO2(g) + H2O↔CaHCO3+H+−6.70 38.24 788.04 826.28 Ca2++ CO2(g) + H2O↔CaCO3+2H+−15.01 85.67 835.47 921.14 Ca2++ NO3−↔CaNO3+−4.80 27.40 763.21 790.61 Ca2++ 2 NO3−↔Ca(NO3)2−4.50 25.68 767.81 793.50 Ca2+ +2H2O↔Ca(OH)2+2H+−27.99 159.76 891.06 1050.82 Ca2++ H2PO4−↔Ca H2PO41.40 −7.99 1058.65 1050.66 Ca2+ + H2PO4−↔CaHPO4+ H+−4.46 25.46 1092.10 1117.56 Ca2+ + H2PO4−↔CaPO4−+2H+−13.09 74.71 1141.36 1216.07 Ca2+ + SO42−↔CaSO42.31 −13.18 1325.62 1312.43 Table A12. Exergy analysis of solution atmosphere (crystal modification dissolution reaction). Crystal Modification Dissolution Reaction Log K ∆G(kJ/mole) Exin (kJ/mole) Exdestruction (kJ/mole) CaSO4i2H2O↔Ca2+ + SO42−+ 2H2O4.60 26.26 26.26 26.26 CaCO3↔Ca2++ CO32−8.35 47.66 48.66 1 Fe(OH)3↔Fe3+ + 3 OH−38.7 220.89 260.49 39.60 Al(OH)3↔Al3+ + 3 OH−33.8 192.92 566.32 373.40 Al(OH)3↔Al3+ + 3 OH−33.0 188.35 3922.75 3734.40 Al(OH)2H2PO4↔Al3+ + 2 OH−+ H2PO4−30.5 −174.08 174.08 174.08 Fe(OH)2H2PO4↔Fe3+ + 2 OH−+ H2PO4−35.0 −199.77 199.77 199.77 Ca2++H2PO− 4=CaHPO4+H+−0.09 0.50 1677.97 0.50 Ca2++H2PO−1 4=CaPO4+2H+13 74.71 1752.18 74.71 Variscite Al(OH)2H2PO4=Al3++2OH−+H2PO430.5 −174.08 2778.65 174.08 Strengite Fe(OH)2H2PO4=Fe3++2OH−+H2PO435.0 −199.77 2238.86 199.77 Entropy 2021,23, 3 21 of 28 Table A12 shows it as a general case, since 0.34% of the total exergy destruction is related to mineral dissolution, and its amount is negligible compared to the total exergy destruction of the soil. Table A13. Exergy analysis of solution atmosphere (protonation). Protonation ∆G(kJ/mole) Exdestruction (kJ/mole) Exin (kJ/mole) OH−+H+→2H2O−5.72 ×10−14 8.94 ×1028.96 ×102 HCO− 3+H+→CO2+H2O1.02 ×1031.02 ×1031.54 ×103 2KAlSi3O8+2H++9H2O→Al2Si2O5(OH)4+2K++4H4SiO46.12 ×1036.12 ×1036.80 ×103 H2SO4+H2O=H3O++HSO− 4−1.32 ×1021.32 ×1021.64 ×102 (CH3)4CH2+HBF4=(CH3)4C++BF− 4−2.19 ×1022.19 ×1029.51 ×102 NH3+HCl →NH4Cl −8.20 ×10 8.20 ×10 4.62 ×102 H2SO4→2H++SO2− 4−3.59 ×1031.16 ×1032.44 ×103 HNO3→H++NO− 3−7.46 ×1028.81 ×1011.28 ×103 Soil Acidification NH+ 4and H+restitution 1.25 ×1035.89 ×1026.65 ×102 Ca2+and 2H+restitution −2.27 ×1022.27 ×1027.29 ×102 Ca2++SO2− 4=CaSO4−1.32 ×10 1.33 ×1031.31 ×103 Al(OH)3↔Al3+ + 3 OH−1.93 ×1025.66 ×1023.73 ×102 Table A14. Exergy analysis of solution atmosphere (soil acidity). Reactions ∆G (kJ/mole) Exout (kJ/mole) Exdestruction (kJ/mole) Soil acidity adjustment −287.86 287.86 503.36 H+2+CaCO3→Ca2+CO2+H2O443.00 240.12 678.90 Acid Rain Limestone Neutralization CaCO3+ H2SO4→CaSO4+ H2CO3−179.70 149.90 179.70 H2CO3→CO2gas + H2O−1019.67 521.82 1019.67 Al(OH)3+ H2SO4→Al2(SO4)3+ H2CO3−1141.76 1154.00 7617.78 Cation Exchange Reactions K++e−→K−233.42 133.18 233.42 Ca2++2e−→Ca −226.88 502.22 226.88 Table A15. Exergy analysis of soil reactions (dissolution and precipitation). Mineral Dissolution Reaction Log (K) ∆G (kJ/mole) Exdestruction (kJ/mole) CaSO4(gypsum)↔Ca2+ + SO42−−4.60 11.40 11.40 CaCO3(calcite)↔Ca2+ + CO32−−8.35 20.70 20.70 Fe(OH)3(amorphous)↔Fe3+ + 3OH−−38.70 95.93 95.93 Al(OH)3(Gibbsite)↔Al3+ + 3OH−−33.00 81.80 81.80 Fe(OH)2H2PO4(Strengite)↔Fe3+ + 2OH−+ H2PO4−35.00 86.76 86.76 Entropy 2021,23, 3 22 of 28 Table A16. Exergy analysis of soil reactions (Dissolution and Precipitation). Reaction Log K ∆G (kJ/mole) Exdestruction (kJ/mole) H2SO4→2H++SO2− 4. . . −3592.54 1157.19 HNO3→H++NO− 3. . . −746.27 88.07 CaS04i2H2O↔Ca2+ + SO42- + 2H2O4.6 26.26 26.26 CaCO3↔Ca2+ + CO32−8.35 47.66 48.66 Fe(OH)3↔Fe3+ + 3 OH−38.7 220.89 260.49 Al(OH)3↔Al3+ + 3 OH−33.8 192.92 566.32 Al(OH)3↔Al3+ + 3 OH−33 188.35 3922.75 Al(OH)2H2PO4↔Al3+ + 2 OH−+ H2PO4−30.5 −174.08 174.08 Fe(OH)2H2PO4↔Fe3+ + 2 OH−+ H2PO4−35 −199.77 199.77 Ca2++H2PO− 4=CaHPO4+H+−0.09 0.50 1677.97 Ca2++H2PO−1 4=CaPO4+2H+−13.09 74.71 1752.18 Variscite 30.5 −174.08 2778.65 Strengite 35 −199.77 2238.86 Table A17. Exergy analysis of solid and solution (weathering). Reaction Type Reaction Formula Exdestruction (kJ/mole) carbonation CaCO3+ H2CO3→Ca (HCO3)2527.54 Solution Mineral (Fe, Al, and Mn)+H2O→Anions+ Cations 264.49 Hydrolysis 3KAl4+ Si3Og+ 14H2O→K (AlSi3)4Al24O10(OH)2+ 6Si(OH)4+ 2KOH 6119.50 Hydration Mineral (Mg, Ca, Mn, Fe, and Al)+ H2O→Water enters the mineral Structure of anhydrous mineral 189.13 Oxidation Fe2+ + 2H2O + 1 2O2↔Fe (OH)3+ H+171.59 And similar for Mn2+ . . . Reduction 2Fe2O3(Hematite) −O2→4FeO (Ferrous Oxide) – Reduced form 287.86 Complexation Complexation reaction of Al, Mn, and Fe. 480.87 Table A18. Exergy analysis of solid and solution (rainfall). Reaction ∆G (kJ/mole) Exdestruction (kJ/mole) Exin (kJ/mole) Rainfall 2Fe3++3SO− 4+6H2O→2Fe(OH)3+6H++3SO2− 4856.42 856.42 2582.8 Table A19. Exergy analysis of solid and solution (soil pollution reactions (Pb)). Reaction Log K Exdestruction (kJ/mole) Oxides, Carbonates, and Sulfates PbO(yellow)+2H+↔Pb2+ +H2O12.89 31.95 PbO(red)+2H+↔Pb2+ +H2O12.72 31.53 Pb(OH)2+2H+↔Pb2+ +2H2O8.16 20.23 Pb3O4+8H+↔3 Pb2+ +4H2O73.79 182.91 Pb2CO3Cl2+2H+49.68 123.15 Pb3(CO3)2(OH)2+6H+4.65 11.53 PbCO3.PbO+4H+−1.80 4.46 PbSO417.51 43.40 PbSO4.PbO 17.39 43.11 PbSO4↔Pb2+ + SO4−7.79 19.31 PbSO4.PbO + 2H+−0.19 0.47 PbSO4.2PbO + 4H+11.01 27.29 PbSO4.3PbO + 6H+22.30 55.28 Entropy 2021,23, 3 23 of 28 Table A19. Cont. Reaction Log K Exdestruction (kJ/mole) Silicates PbSiO3+2H++ H2O 5.94 14.72 Pb2SiO4+ 4H+18.45 45.73 phosphates 0.00 Pb(H2PO4)2↔Pb2+ + 2H2PO4−−9.85 24.42 PbHPO4+ H+−4.25 10.53 Pb3(PO4)2+ 4H+−5.26 13.04 Pb4O(PO4)2+ 6H+−2.24 5.55 Pb5(PO4)3OH + 7H+−4.14 10.26 Pb5(PO4)3Br + 6H+−19.49 48.31 Pb5(PO4)3Cl + 6H+−25.05 62.09 Pb5(PO4)3F + 6H+−12.98 32.18 Other Minerals soil_Pb↔Pb2+ −8.50 21.07 PbMoO4↔Pb2+ + MoO4−16.04 39.76 PbS↔Pb2+ + S2−−27.51 68.19 Pb2+ + 2e↔Pb −4.33 10.73 Hydrolysis Species Pb2+ + H2O−7.70 19.09 Pb2+ + 2H2O−17.50 43.38 Pb2+ + 3H2O−28.09 69.63 Pb2+ + 4H2O−39.49 97.89 2Pb2+ + H2O−6.40 15.86 3Pb2+ + 4H2O−23.89 59.22 4Pb2+ + 4H2O−20.89 51.78 6Pb2+ + 8H2O−43.58 108.03 Pb2+ + 4Br−2.30 5.70 Pb2+ + Cl−1.60 3.97 Pb2+ + 2Cl−1.78 4.41 Pb2+ + 3Cl−1.68 4.16 Pb2+ + 4Cl−1.38 3.42 Pb2+ + F−1.49 3.69 Pb2+ + 2F−2.27 5.63 Pb2+ + 3F−3.42 8.48 Pb2+ + 4F−3.10 7.68 Pb2+ + I−1.92 4.76 Pb2+ + 2I−3.15 7.81 Pb2+ + 3I−3.92 9.72 Pb2+ + 4I−4.50 11.15 Pb2+ + NO3−1.17 2.90 Pb2+ + 2NO3−1.40 3.47 Pb2+ + H2PO4−↔PbH2PO4+1.50 3.72 Pb2+ + H2PO4−↔PbHPO4+H+−4.10 10.16 Pb2+ + P2O711.30 28.01 Pb2+ + SO42.62 6.49 Pb2+ + 2SO43.47 8.60 Entropy 2021,23, 3 24 of 28 Table A20. Exergy analysis of solid and solution (soil pollution reactions (Zn)). Reaction Log K Exdestruction (kJ/mole) Zn2+ + H2O−7.69 19.06 Zn2+ + 2H2O−16.80 41.64 Zn2+ + 3H2O−27.68 68.61 Zn2+ + 4H2O−38.29 94.91 Zn2+ + Cl−0.43 1.07 Zn2+ + 2Cl−0.00 0.00 Zn2+ + 3Cl−0.50 1.24 Zn2+ + 4Cl−0.20 0.50 Zn2+ + H2PO4−1.60 3.97 Zn2+ + H2PO4−−3.90 9.67 Zn2+ +NO3−0.40 0.99 Zn2+ + 2NO3−−0.30 0.74 Zn2+ + SO42.33 5.78 Zn(OH)2+ 2H+−25.80 63.95 a-Zn(OH)2+ 2H+12.48 30.94 B-Zn(OH)2+ 2H+12.19 30.22 gamma-Zn(OH)2+ 2H+11.78 29.20 E-Zn(OH)2+ 2H+11.74 29.10 ZnO + 2H+11.53 28.58 ZnCO3+ 2H+11.16 27.66 soil_Zn + 2H+7.91 19.61 ZnFe2O4+ 8H+5.80 14.38 ZnSiO3+2H++ H2O 9.85 24.42 Zn2SiO4+ 4H+13.15 32.60 ZnCl2↔Zn2+ +2Cl−7.07 17.53 ZnSO4↔Zn2+ + SO43.41 8.45 ZnO-2ZnSO4+ 2H+19.12 47.40 Zn(OH)2.ZnSO4+ 2H+7.50 18.59 Zn3(PO4)2.4H2O + 4H+3.80 9.42 Table A21. Exergy analysis of solid and solution (soil pollution reactions (Cd)). Reaction Log K Exdestruction (kJ/mole) Cd2+ + 2e↔Cd −13.64 33.81 CdO + 2H+15.14 37.53 B?_Cd(OH)2+ 2H+13.65 33.84 CdCO3+ 2H+6.16 15.27 CdSiO3+2H++ H2O 7.63 18.91 CdSO4↔Cd + SO4−0.04 0.10 CdSO4.H2O↔Cd + SO4+ H2O−1.59 3.94 CdSO4.2Cd(OH)2+ 4H+22.65 56.15 2CdSO4.Cd(OH)2+ 2H+6.73 16.68 Cd3(PO4)2+ 4H+1.00 2.48 CdS↔Cd2+ + S2−−27.07 67.10 soil_Cd↔Cd2+ −7.00 17.35 Cd2+ + H2O−10.10 25.04 Cd2+ + 2H2O−20.30 50.32 Cd2+ + 3H2O−33.01 81.83 Cd2+ + 4H2O−47.29 117.22 Cd2+ + 5H2O−61.93 153.51 Cd2+ +6H2O−76.81 190.40 2Cd2+ + H2O−6.40 15.86 4Cd2+ + 4H2O−27.92 69.21 Entropy 2021,23, 3 25 of 28 Table A21. Cont. Reaction Log K Exdestruction (kJ/mole) Cd2++ Br−2.15 5.33 Cd2+ + 2Br−3.00 7.44 Cd2+ + 3Br−3.00 7.44 Cd2+ + 4Br−2.90 7.19 Cd2+ + Cl−1.98 4.91 Cd2+ + 2Cl−2.60 6.44 Cd2+ + 3Cl−2.40 5.95 Cd2+ + 4Cl−2.50 6.20 Cd2+ + I−2.28 5.65 Cd2+ + 2I−3.92 9.72 Cd2+ + 3I−5.00 12.39 Cd2+ + 4I−6.00 14.87 Cd2+ + NH4−0.73 1.81 Cd2+ + 2NH4−14.00 34.70 Cd2+ + 3NH4−21.95 54.41 Cd2+ + 4NH4−30.39 75.33 Cd2+ + CO2+ H2O−5.73 14.20 Cd2+ + CO2+ H2O−14.06 34.85 Cd2+ + NO3−0.31 0.77 Cd2+ + 2NO3−0.00 0.00 Cd2+ + H2PO4−−4.00 9.92 Cd2+ + P2O78.70 21.57 Cd2+ + SO42.45 6.07 Table A22. Exergy analysis of solid and solution (soil pollution reactions (Cu)). Reaction Log K Exdestruction (kJ/mole) CuO + 2H+7.66 18.99 Cu(OH)2+ 2H+8.68 21.52 CuCO3+ 2H+8.52 21.12 Cu2(OH)2CO3+ 4H+12.99 32.20 Cu3(OH)2(CO3)2+ 4H+19.57 48.51 a_CuFe2O4+ 8H+10.13 25.11 soil_Cu + 2H+2.80 6.94 CuSo4↔Cu2+ + SO43.72 9.22 CuSo4/5H2O↔Cu2+ + SO5+H2O−2.61 6.47 CuO.CuSO4+ 2H+11.50 28.51 Cu4(OH)6SO4+ 6H+15.35 38.05 Cu4(OH)6SO4.1.3H2O + 6H+17.27 42.81 Cu3(PO4)2+ 4H+2.24 5.55 Cu3(PO4)2.2H2O + 4H+0.34 0.84 Cu2P2O7↔2Cu2+ + P2O7−15.22 37.73 Cu2+ + H2O−7.70 19.09 Cu2+ + 2H2O−13.78 34.16 Cu2+ + 3H2O−26.75 66.31 Cu2+ + 4H2O−39.59 98.14 2Cu2+ + 2H2O−10.68 26.47 Cu2+ + Cl−0.40 0.99 Cu2+ + 2Cl−−0.12 0.30 Cu2+ + 3Cl−−1.57 3.89