Composition of the Primordial Ocean Just after Its Formation: Constraints from the Reactions between the Primitive Crust and a Strongly Acidic, CO 2 -Rich Fluid at Elevated Temperatures and Pressures

: The Hadean was an enigmatic period in the Earth’s history when ocean formation and the emergence of life may have occurred. However, minimal geological evidence is left from this period. To understand the primordial ocean’s composition, we focused on the ocean’s formation processes from CO 2 - and HCl-bearing water vapor in the high-temperature atmosphere. When the temperature of the lower atmosphere fell below the critical point, high-temperature rain reached the ground surface. Then, hydrothermal reactions between the subcritical ﬂuid and primordial crust started. Eventually, a liquid ocean emerged on the completely altered crust as the temperature decreased to approximately 25 ◦ C. Here, we conducted two experiments and modeling to simulate the reactions of hypothetical primordial crustal rock (basalt or komatiite). The results indicate that the primordial ocean was mildly acidic and rich in CO 2 , Mg, and Ca relative to Na, irrespective of the rock type, which is different from the modern equivalents. Therefore, unlike the present seawater, the primordial seawater could have been carbonic, bitter, and harsh rather than salty.


Introduction
The Hadean was an enigmatic period in the Earth's history when ocean formation and the emergence of life occurred [1][2][3]. However, minimal geological evidence is left from this period. The oldest zircon grains with ages extending to~4.4 Ga [4] were found from the clastic rocks in Australia. Their oxygen isotopic evidence indicates the incorporation of low-temperature weathering products under liquid water at~4.3 Ga (e.g., [5]), indicating that the Earth's surface temperature had cooled down enough to stabilize the liquid ocean at this age.
Regarding the ocean in the early Earth, previous research indicates that seawater had weak acidity (pH 4-7) because the carbon dioxide concentration in the atmosphere was high compared to today [6][7][8][9][10], or it was strongly acidic (pH 1-2) because a large amount of halogen substance in the high-temperature vapor atmosphere eventually dissolved into seawater [11]. Previously, pH levels, and concentrations of CO 2 and other elements were considered [6], but these estimations did not provide information about the quantitative chemical compositions of seawater. Furthermore, the specific compositions of the ocean have not been reported from experiments or thermodynamic calculations simulating fluidrock reactions.
The entire surface of the Hadean Earth was covered by a magma ocean in the late stage of accretion (e.g., moon-forming impact event) [12][13][14][15]. After Earth's cooling, the solidified proto-crust was formed. The continuous cooling of the Earth's surface led to (Table 2; Figure 1a), whereas the komatiite consists of olivine, Cr-spinel, magnetite, and glass (Table 2; Figure 1b). Furthermore, we adjusted the sulfur contents in these rocks to about 2850 ppm, assuming that the sulfur contents were close to those of volcanic minerals and glass in Hawaii and mid-ocean ridge basalt (MORB) in the modern Earth (~3000 ppm) [42][43][44]. Sulfur was additionally mixed as FeS (purity >99.9%) in the rocks after heating at 600 • C with the electric furnace under an anoxic condition to remove organic components, as reported previously [45]. The Fe content in the rocks was maintained identically to the objective compositions of basalt and komatiite. The solution's HCl concentration was adjusted to approximately 1000 mmol/kg because the Cl concentration in seawater in the early Earth was estimated to be twice the modern value from the total amount of Cl included in seawater and continental halite in the present Earth [46]. Thus, HCl with this concentration was assumed to have been present as HCl in the supercritical early atmosphere. We assumed the CO 2 concentration in the initial fluid to be approximately 5.9 mol/kg, which was roughly estimated from the total water and carbon (CO 2 ) inventory in the atmosphere, biosphere, hydrosphere, and crust currently. The amounts of water and CO 2 are~8 × 10 22 moles (1.41 × 10 21 kg H 2 O) and 8.3 × 10 21 moles (~1.0 × 10 20 kg C), respectively [7,47,48]. The dark gray strip-shaped structure is composed of plagioclase, while the light gray structure that spreads to fill the space is augite. Therefore, the strip-shaped structure in which the space between the plagioclase constituting the matrix is filled with pyroxene, called the intersertal texture, a peculiar basalt structure. (b) The dark gray strip-shaped structure is composed of olivine (spinifex texture), while the light gray structure that spread to fill the space is glass. Abbreviations: Spi-Cr spinel; Pl-plagioclase; Ol-olivine; Mtmagnetite; Aug-augite; Gl-glass.

Experimental Procedure
This study used the Inconel alloy autoclave modeled for the hydrothermal experiment [49]. The reaction cell is made of a gold bag with a titanium head. However, in this experiment, the titanium head was covered with gold to prevent the reaction between the head and strongly acidic fluids. The contamination of organic matter was reduced by baking all apparatus in contact with the sample fluid in a muffle furnace at 450 °C for 8 h.
The synthetic basalt and komatiite were crushed in a tungsten mill and sieved to obtain a < 100 μm powder. Any contamination of organic materials during sample preparation was removed by washing both powdered rocks with Milli-Q water and acetone several times. The initial solution was prepared by adding HCl (99.5% purity) and liquid CO2 to Milli-Q water (about 44 g) that was degassed to remove dissolved oxygen. A HCl solution was introduced into the reaction cell with the rock powder, then liquid The dark gray strip-shaped structure is composed of plagioclase, while the light gray structure that spreads to fill the space is augite. Therefore, the strip-shaped structure in which the space between the plagioclase constituting the matrix is filled with pyroxene, called the intersertal texture, a peculiar basalt structure. (b) The dark gray strip-shaped structure is composed of olivine (spinifex texture), while the light gray structure that spread to fill the space is glass. Abbreviations: Spi-Cr spinel; Pl-plagioclase; Ol-olivine; Mt-magnetite; Aug-augite; Gl-glass.

Experimental Procedure
This study used the Inconel alloy autoclave modeled for the hydrothermal experiment [49]. The reaction cell is made of a gold bag with a titanium head. However, in this experiment, the titanium head was covered with gold to prevent the reaction between the head and strongly acidic fluids. The contamination of organic matter was reduced by baking all apparatus in contact with the sample fluid in a muffle furnace at 450 • C for 8 h.
The synthetic basalt and komatiite were crushed in a tungsten mill and sieved to obtain a < 100 µm powder. Any contamination of organic materials during sample preparation was removed by washing both powdered rocks with Milli-Q water and acetone several times. The initial solution was prepared by adding HCl (99.5% purity) and liquid CO 2 to Milli-Q water (about 44 g) that was degassed to remove dissolved oxygen. A HCl solution was introduced into the reaction cell with the rock powder, then liquid CO 2 was directly injected into the reaction cell from a gas cylinder to set the initial ΣCO 2 concentration to be around 6.1-8.0 mol/kg. Note that even such a high CO 2 amount is completely dissolvable under the initial experimental conditions (350 • C and 500 bars) [50].
The basalt and komatiite powers were reacted with the strongly acidic fluid in the reaction cell for 6970 and 4864 h at 500 bars, respectively. During the experiments, the temperature decreased stepwise from 350 • C to 250 • C, 175 • C, 100 • C, and 25 • C, simulating the decrease in the surface temperature of the primitive crust. The initial water/rock (W/R) mass ratio was adjusted to 2.25, corresponding to the reactions between 2.7-km-thick water (modern seawater volume) and 0.4-km-thick proto-crust. During the experiments, fluid samples were collected eight times before (and after) the temperature changed via a gold-coated sampling tube. Because of the eight-time fluid samplings, the W/R ratio in the reaction cell decreased to about 1 at the end of the experiments. Hereafter, the experiments using basalt and komatiite are represented as Exp-B and Exp-K, respectively.

Analytical Methods
Quantitative analyses of CO 2 and H 2 were performed using a gas chromatograph (Nexis GC-2030; Shimadzu, Kyoto, Japan) with a barrier discharge ionization detector (BID), while analysis of H 2 S was performed using a gas chromatograph (Agilent 7890B; Agilent Technology, Santa Clara, CA, USA) with a sulfur chemiluminescence detector (SCD). Gas present at the headspace in the vials was injected into the GC using a gas-tight syringe. After measuring the H 2 concentrations, for determination of the ΣCO 2 and ΣH 2 S concentrations in the fluid, the sampled fluid was acidified (pH < 2) with HCl to completely extract the dissolved bicarbonate, carbonate and bisulfide ions. The procedural precision of the ΣCO 2 and ΣH 2 S concentrations in the fluid analyses was better than 20%, whereas that of H 2 was better than 5%.
The Na, K, and Cl concentrations in the fluid samples were determined using an ion chromatograph (Dionex ICS-1600/2100; Thermo Fisher Scientific, Waltham, MA, USA). Mg, Si, Ca, Mn, and Fe concentrations were obtained by introducing the sampled solutions into an inductively coupled plasma-optical emission spectrometry (ICP-OES) (Spectro ARCOS; AMETEK, Berwyn, PA, USA) instrument at JAMSTEC (Yokosuka, Japan) after adding~1 M HNO 3 or NaOH to avoid mineral precipitation. The analytical reproducibility (2σ) was better than 5% for all species. For pH measurement, another sample solution was placed in contact with the atmosphere at least 1 h after sampling, allowing the pH to stabilize against CO 2 degassing. The pH of the fluid samples was measured using a pH meter (LAQUAtwin; HORIBA, Kyoto, Japan) at room temperature. The pH in-situ in the fluids was calculated using a Geochemist's Workbench using the same method, as reported in [39,40].
The compositions of minerals and glass in the rock powders before and after the experiments (Exp-B and Exp-K) were determined using a field emission-electron probe microanalyzer (FE-EPMA) (JXA-8500F; JEOL, Tokyo, Japan) at JAMSTEC. The analytical conditions for the FE-EPMA were an accelerating voltage of 15 kV, a specimen current of 12 nA, and a counting time of 10-20 s.

Thermodynamic Modeling of Water-Rock Reactions
The thermodynamic modeling of water-rock reactions was conducted using the EQ3/6 version 8.0 software (Lawrence Livermore National Laboratory, Livermore, CA, USA) package for geochemical modeling [51] with a customized thermodynamic database. The database was assembled using SUPCRT92 [52], with thermodynamic data for minerals, aqueous species, and complexes taken from [53][54][55][56][57][58][59][60][61][62] or calculated using estimation techniques used in [63]. In the calculations, the B-dot activity model was used [64,65], whereas activity coefficients were assumed to be unity for neutral species, except for CO 2 [66]. As solid solutions, Fe-Mg substitution was considered for olivine, chlorite, Fe layer -saponite, tremolite, spinel, and talc, while a solid solution of plagioclase was assumed to consist of albite and anorthite. Meanwhile, carbonate was assumed to be ideal for mixing among four endmembers (calcite, magnesite, siderite, and rhodochrosite). The reaction model simulates the reactions between the rock (basalt or komatiite) and a highly acidic, CO 2 -rich fluid at 25-400 • C at 500 bars. The initial W/R ratios of the modeling with each rock were adjusted to those at the beginning (2.25) and end (1) of the experiments (hereafter represented as Model-B WR2 and -B WR1 , and Model-K WR2 and -K WR1 , respectively). The initial compositions of the rocks (except Cr, Ni, Ti, and P) and fluids were identical to those assumed for the experiments. All organic carbon species were suppressed because of the kinetically limited CO 2 reduction at laboratory timescales (e.g., [67]).
After the modeling of reactions between single-phase fluid and rock, we further simulated a re-equilibration among a gas phase, solution, and rock to estimate the partial pressure of CO 2 (pCO 2 ) in atmosphere and the composition of the ocean, using the results at 25 • C in each model. In the calculations, a simulation of CO 2 degassing from the solution (originally a single-phase fluid) to a hypothetical gas phase was continued until the pCO 2 of the gas phase reached the value of the fluid, assuming the ocean depth as 2.7 km and a mass balance of CO 2 in the atmosphere, ocean, and crust.

Carbonate and Other Secondary Minerals
In Exp-B, the solid run product includes carbonate, quartz, and a montmorillonitebeidellite mixture as secondary major minerals, whereas magnetite and pyrite occur as  Table 3). In addition, subordinate amounts of augite and plagioclase were also recognized as relict igneous minerals. Among these minerals, the abundance of carbonate is clearly much higher than others (Figure 2a,b). Therefore, it is suggested that the composition of carbonate strongly affected and reflected the compositions of coexisting fluids.
sampling (350 °C); therefore, the formation of the Mg-rich core of the type I carbonate was already terminated at that time (Figures 3b and 4b,c,e). The hydrothermal fluid just after the beginning of the experiment presumably had a reasonably high Mg concentration. Next, the decrease in Fe content and the increases in Mg contents outward recognized in both type I and type II carbonates are consistent with the drastic decrease in the Fe concentration and the slight increase in Mg concentration in the fluid by the end of the 175 °C period (Figures 3b and 4d,f). Then, although the Ca enrichment in the rims of both carbonate types is not reflected in the increase in Ca concentration in the fluid (Figures 3b and 4e,f), this compositional change in carbonates was probably caused by the temperature decrease to ≤100 °C, because calcite is much more stable than Mg-bearing carbonates, even in solutions with high Mg/Ca ratios at low temperatures (e.g., <100 °C) [68].     Almost all carbonates in the run product have a high Fe content with clear zoning textures (Figure 2c,d). The carbonate Fe content decreases, whereas the Mg and Ca contents increases from the core to the rim (Figure 2c,d), although the Mn content is kept low throughout the crystal (Figure 2d). The second most abundant element in carbonate changes from Mg in the core to Ca in the rim. Meanwhile, the ΣCO 2 concentration in the fluid drastically decreased before the first fluid sampling (Table 4 and Figure 3a), indicating that the carbonate formation mainly occurred at 350 • C. Furthermore, considering that the Fe content in the montmorillonite-beidellite mixture (only one major silicate bearing Fe) is quite low (Table 3), this indicates that most of the Fe in the basalts was fixed into carbonates at the earliest stage of the experiment. Then, the outer parts of carbonates presumably grew slowly in the periods at 250 and 175 • C because the outward increases in the contents of Mg and Ca relative to Fe in carbonates are consistent with the drastic decrease in Fe concentrations by the end of the 175 • C period and gradual increases or conservation of Mg and Ca concentrations in fluid by the beginning of the 175 • C period (Figures 2c,d and 3a). Although the ΣCO 2 concentration in the fluid irregularly fluctuated at these temperatures (e.g., a temporal increase at 665 h), it is highly possible that dissolution of preexisting (metastable) carbonate drove the growth of other zoned carbonates.     In Exp-K, carbonate and saponite predominantly occur as secondary minerals, whereas pentlandite and magnetite are also included in the run product as minor minerals. In addition, the primary igneous olivine and Cr-spinel are also partially preserved in Exp-K (Figure 4a,b,d). Similar to Exp-B, carbonate abundantly exists and shows clear zoning textures in the run product of Exp-K (Figure 4), whereas the drastic decrease in ΣCO 2 concentration before the second sampling indicates the dominant formation of carbonate at 350 • C (Table 4 and Figure 3b). The EPMA analyses revealed that the carbonate minerals can be classified into two types, based on the zoning pattern-type I carbonates have a Mg-rich core (Figure 4c,e), whereas the less abundant type II carbonates have a Fe-rich core (Figure 4d,f). From core to rim, the most abundant element of the type I carbonate changes from Mg, through Fe, and Mg again to Ca, whereas that of the type II carbonate changes from Fe through Mg to Ca. Moreover, the second most abundant element of the type I carbonate changes from Fe through Mg and Fe to Mg, whereas that of the type II carbonate changes from Mg through Fe to Mg outward. The zoning pattern of the type II carbonate is completely consistent with that in the middle to the outer parts of the type I carbonate, indicating that the type II carbonate started to form when the composition of the preexisting type I carbonate changed from Mg-rich to Fe-rich.   By comparing the zoning patterns of carbonate to the fluid compositions, the Mg-rich core of the type I carbonate cannot be explained using the obtained fluid data because the ΣCO 2 concentration had been already sufficiently decreased at the timing of the first fluid sampling (350 • C); therefore, the formation of the Mg-rich core of the type I carbonate was already terminated at that time (Figures 3b and 4b,c,e). The hydrothermal fluid just after the beginning of the experiment presumably had a reasonably high Mg concentration. Next, the decrease in Fe content and the increases in Mg contents outward recognized in both type I and type II carbonates are consistent with the drastic decrease in the Fe concentration and the slight increase in Mg concentration in the fluid by the end of the 175 • C period (Figures 3b and 4d,f). Then, although the Ca enrichment in the rims of both carbonate types is not reflected in the increase in Ca concentration in the fluid (Figures 3b and 4e,f), this compositional change in carbonates was probably caused by the temperature decrease to ≤100 • C, because calcite is much more stable than Mg-bearing carbonates, even in solutions with high Mg/Ca ratios at low temperatures (e.g., <100 • C) [68].

Fluid Chemistry
The Cl concentrations of the fluids in both experiments were kept relatively constant throughout the experiments because Cl-bearing minerals generally rarely form during the alteration of basalts and komatiites (Table 4 and Figure 3) [69,70]. Nevertheless, most of the fluid compositions changed as water-rock reactions proceeded in both experiments. As discussed above, the ΣCO 2 concentrations in the fluids decreased from 6000-8000 mmol/kg to 970 mmol/kg in Exp-B and 839 mmol/kg in Exp-K (Figure 3) because of the formation of abundant carbonate minerals (details above). Meanwhile, other cations also dissolved in the fluid from rocks through the reactions with the strongly acidic fluid. These water-rock reactions probably affected the pH in-situ of fluid. The pH in-situ values of fluids increased and converged to 4.6 in Exp-B and 3.9 in Exp-K through both experiments ( Table 4), indicating that the neutralization effect of water-rock reactions (especially carbonate formation) efficiently elevated the pH in-situ from 0.
The H 2 concentrations in the fluids in Exp-B and Exp-K increased up to 0.30 mmol/kg and 2.42 mmol/kg just after the beginning of the experiments, then eventually decreased down to 0.05 mmol/kg and 0.02 mmol/kg, respectively (Table 4 and Figure 3). The difference in H 2 concentrations in the fluid between Exp-B and Exp-K was likely caused by the compositional difference between basalt and komatiite, as the modern peridotitehosted hydrothermal systems generate more H 2 -rich fluid than basalt-hosted systems [71]. Thereafter, the H 2 concentrations in both experiments rapidly decreased the values to lower than 0.1 mmol/kg. Such fluctuations in H 2 concentrations under CO 2 -rich conditions are generally caused by Fe redox reactions in metastable minerals (including Fe-carbonate) before reaching a near-equilibrium state [40,72]. Thus, similar processes could occur in our experiments.
The other element concentrations (Na, K, Ca, Mg, Fe, Mn, SiO 2 and H 2 S) increased just after the beginning of the experiments, then changed as the water-rock reactions proceeded (Table 4; Figure 3). As discussed in Section 3.1.1, the concentrations of carbonateforming elements (Ca, Mg, Fe, and Mn) in the fluids are closely related to the formation of carbonates in both experiments. Among these elements, most importantly, Ca in Exp-B had the highest concentration, whereas the most abundant cation in the fluid was Mg in Exp-K at low temperatures, which is completely different from Na-rich modern seawater and seafloor hydrothermal fluids (Table 4 and Figure 3). Although it is known that Ca and Mg are frequently released from mafic and ultramafic rocks into hydrothermal fluid under CO 2rich conditions [39,40,72,73], this is likely because the Na content in basalt and komatiite is generally not high enough to elevate a fluid Na concentration from zero to the highest values, in contrast to the Mg and Ca abundantly contained in these mafic and ultramafic rocks. Therefore, considerable amounts of Na (and also K) in the rocks were dissolved into the fluids, whereas their residuals were fixed as minor elements in the secondary minerals (mainly phyllosilicates) in the experiments. Therefore, the rates of change of the Na and K concentrations in fluids in both experiments were not significant compared with those of Fe and Mn (Table 4 and Figure 3). It is, therefore, obviously suggested that the more Naand K-rich basalt generated high concentrations of these cations in the fluid than komatiite in the experiments.
The SiO 2 concentrations significantly fluctuated during both experiments. However, considering that the concentrations at the end of the period of each temperature were more stable than that just after the temperature drop, the changes in SiO 2 concentrations should be tracked using the last values in the period of a temperature. In this case, it seems that the SiO 2 concentrations in the fluid decreased in Exp-B, whereas the concentrations in Exp-K irregularly fluctuated with decreasing temperatures (Table 4 and Figure 3). The different behaviors may have been caused by the numbers of minerals buffering the SiO 2 concentrations in the fluid. In Exp-B, two minerals (quartz and montmorillonite-beidellite mixture at least at low temperatures) should affect the fluid SiO 2 concentration (Figure 2), indicating that the decreasing SiO 2 concentration with decreasing temperature was presumably controlled mainly by the temperature dependency of equilibrium constants among SiO 2 and minerals in the experiments. However, the only SiO 2 -bearing mineral in Exp-K was saponite, as far as the solid run product was observed using EPMA ( Figure 4). Considering that saponite is basically influenced by not only SiO 2 activity but also other components such as Al, Mg, and Fe, the SiO 2 concentration in Exp-K was strongly affected by the behavior of the activities of other species during the experiments.
Regarding H 2 S concentrations in the experiments, they were drastically elevated just after the beginning of the experiments (sampling #0 to #1) and then basically decreased to <0.1 mmol/kg with minor fluctuations (Table 4 and Figure 3). These compositional changes were likely caused by the dissolution of FeS originally contained in the rocks just after the beginning and formation of pyrite in Exp-B and pentlandite in Exp-K with decreasing temperature (Figures 2 and 4).

Secondary Minerals
The secondary minerals in the experiments were not completely but well reproduced by thermodynamic modeling. Both Model-B WR2 and Model-B WR1 show that the assemblage of major minerals changes from beidellite + saponite + talc + carbonate at 350 • C, through beidellite + carbonate + quartz at intermediate temperatures, to carbonate + kaolinite + quartz at <100 • C ( Figure 5). Therefore, the low-temperature mineral assemblage of carbonate + kaolinite + quartz is expected for the solid run product in Exp-B if complete equilibrium was achieved during the experiment. In this regard, carbonate and quartz were also included as major minerals in Exp-B (Table 3; Figure 2). However, the montmorillonite-beidellite mixture was the most abundant phyllosilicate in the experiment, instead of kaolinite as predicted in the modeling. Although these phyllosilicates are commonly SiO 2 -rich hydrous minerals, this discrepancy of the mineral species could be due to the kinetic effects at the laboratory timescale. In this experiment, the solid run product experienced the reactions at temperatures decreasing from 350 • C to 25 • C, meaning it is highly likely that traces of the minerals formed at higher temperatures were compositionally conserved in the newly formed minerals or preserved as relict metastable minerals at lower temperatures.
In the modeling of the komatiite system, Model-K WR2 and Model-K WR1 commonly show that the major minerals consist of talc + carbonate + saponite + chlorite at around 350 • C ( Figure 6). However, Model-K WR2 indicates that the assemblage of carbonate + quartz + beidellite at 300-100 • C changes to carbonate + quartz + kaolinite, whereas the assemblage in Model-K WR1 is carbonate + talc + saponite + quartz + beidellite at <300 • C. This difference in stable silicate minerals at temperatures below 300 • C between the two komatiite models means that phyllosilicates are generated more abundantly in the system with a low initial W/R ratio (Model-K WR1 ). The abundant occurrence of various phyllosilicates in Model-K WR1 indicates that carbonate-forming elements (Mg and Fe) are incorporated not only into carbonate but also into the phyllosilicates (Figure 6). Such elemental partitioning between carbonates and silicates is closely related to the drastic decrease in ΣCO 2 concentrations in the fluid with decreasing temperature from~300 • C in Model-K WR1 (see details below), indicating that the lowered ΣCO 2 concentration can no longer form more carbonate minerals, in contrast to Model-K WR2 (Figure 6a). Therefore, the CO 2 fixation capacity still remains for the komatiite at these temperatures in this model (see details below). coudlMinerals 2021, 11, x FOR PEER REVIEW 14 of 22  Model-B WR1 (e-h) as functions of temperature. In each panel, the results of the re-equilibration simulation for the gas phase, solution, and rock at 25 • C are shown on the right.
As described above, Exp-K shows that the carbonate and saponite are the predominant secondary minerals in the run products (Table 5 and Figure 4). These minerals are included as major minerals even at low-temperatures in Model-K WR1 (Figure 6), indicating that the alteration minerals in Exp-K could be reproduced by thermodynamic modeling, at least partially. However, the mineral assemblage of carbonate + saponite indicates that the run product includes neither quartz nor talc (Table 5 and Figure 4), which are the second major minerals in Model-K WR2 and Model-K WR1 , respectively. In general, there are some minerals for which formation or precipitation is kinetically limited despite their thermodynamic stability. However, the formation of quartz and talc is rather common in altered rocks, as observed for natural carbonated serpentinites and experimentally serpentinized ultramafic rocks (e.g., [72,74,75]). Therefore, the inconsistency between the experiment and modeling might be explained by the effective bulk composition for silicates (whole-rock composition, excluding carbonate). If the amount of carbonate formed in the experiment is lower than the amounts predicted in the models, the effective bulk composition for silicates in the experiment should be more SiO 2 -poor than those of the models, which might stabilize saponite rather than more SiO 2 -rich talc and quartz. Conversely, if the saponite formation in Exp-K is faster than talc at 350 • C, where both saponite and talc are thermodynamically stable, the selective formation and the preservation of saponite, including carbonate-forming elements (e.g, Mg and Fe), could cause the slight suppression of carbonate formation. In addition, the small amount of igneous minerals left in the experiment could also affect the effective bulk composition.

Fluid Chemistry
There are also many similarities in fluid compositions between the models and experiments. Irrespective of the initial W/R ratios and rock types, the models and experiments show that (1) the major cations are Ca, Mg, and Na; (2) the concentrations of

Fluid Chemistry
There are also many similarities in fluid compositions between the models and experiments. Irrespective of the initial W/R ratios and rock types, the models and experiments show that (1) the major cations are Ca, Mg, and Na; (2) the concentrations of Ca, ΣCO 2 , SiO 2 , ΣH 2 S, and Mn decrease, while (3) that of Mg increases with decreasing temperature (Figures 5 and 6). Furthermore, the Na, K, and Cl concentrations are basically constant at all temperatures, although only the K concentration at < 60 • C in Model-K WR1 is lowered because of the formation of the K-bearing mineral. These consistencies indicate that the experimental results are mostly well reproduced by our thermodynamic modeling (Figures 3, 5 and 6).
The final ΣCO 2 concentration in each model strongly depends on the initial W/R ratio and the rock type; the high initial W/R ratio leads to the high final ΣCO 2 concentration in fluid, whereas the final ΣCO 2 concentrations in the komatiite system (1.4 mmol/kg in Model-K WR1 and 2146 mmo/kg in Model-K WR2 ) are lower than those of the basalt system (502 mmol/kg in Model-B WR1 and 4031 mmo/kg in Model-B WR2 ), respectively ( Figures 5 and 6). The former is well explained by the mass balance of CO 2 in fluid and rocks. At 25 • C in Model-B WR2 , Model-B WR1 , and Model-K WR2 , the abundance of CO 2 in the initial fluid-rock equilibrium system exceeds the CO 2 fixation capacity of the rocks, as carbonate, quartz, and kaolinite are the dominant secondary minerals (no more carbonate could be formed), which is reflected in the results showing that excess CO 2 remains in the fluid as ΣCO 2 in high concentrations (4031, 502, and 2146 mmol/kg, respectively). In contrast, the ΣCO 2 concentration in Model-K WR1 decreases more drastically with decreasing temperature than other models, then reaches a minimum at 1.4 mmol/kg, while talc and saponite are present as major secondary minerals in addition to carbonates at 25 • C ( Figure 6). In this case, the CO 2 fixation ability of komatiite in Model-K WR1 still remains as Fe and Mg in talc and saponite, which sufficiently reduced the ΣCO 2 concentration, in contrast to the Model-B WR1 , despite having the same initial W/R ratio. Therefore, the latter factor (rock type) mainly depends on the contents of the carbonate-forming elements (Ca, Mg, and Fe) in the rocks. Indeed, the sum of these elements is more abundant in the komatiite (10.0 moles/kg) than basalt (5.8 moles/kg). Regarding the final ΣCO 2 concentrations in the experiments (970 mmol/kg in Exp-B and 839 mmol/kg in Exp-K), the value falls within the range between the final ΣCO 2 concentrations with two different initial W/R ratios in each rock type, consistent with the W/R ratios decreasing from 2.25 to 1 during both experiments.
The pH in-situ values of the modeling results are also broadly consistent with those of the experiments (Table 4; Figures 5 and 6). In the basaltic system, the pH in-situ in Exp-B did not show significant fluctuation and changed from 3.6 at 350 • C to 4.6 at 25 • C ( Table 4). Considering that the W/R ratios decreased during the experiment, the pH in-situ in Exp-B is consistent with the calculated pH in-situ value that changes from 4.1 at 350 • C in Model-B WR2 to 4.8 at 25 • C in Model-B WR1 ( Figure 5). In the komatiitic system, the pH in-situ changed from 3.5 to 3.9 in Exp-K (Table 4), which can be considered to be broadly consistent with but slightly lower than that in Model-K WR2 , changing from 3.8 at 350 • C to 4.4 at 25 • C ( Figure 6). This small discrepancy, especially at low-temperatures, might be caused by the difference of phyllosilicate in the secondary minerals between the experiment and model (see above). In addition, in Model-K WR1 , pH in-situ values (changing from 4.1 at 350 • C to 6.7 at 25 • C) are clearly higher than those of the experiment (Figures 5 and 6), which is likely caused by the lower ΣCO 2 concentration of fluid in the model than that of the experiment and by the difference in mineral assemblage between them.
Although most of the fluid compositions could be well explained by the thermodynamic modeling, as discussed above, the Fe and H 2 concentrations in the models clearly differs from those in the experiments (Figure 3, Figure 5, and Figure 6). In both experiments, Fe concentrations decreased from quite high values (~100 mmol/kg) at 350 • C to minimum values at intermediate temperatures, then slightly increased again at 100-25 • C. Nevertheless, the Fe concentrations in the basalt models are kept almost constant at low levels at all temperatures ( Figure 5), whereas the komatiite models show drastic decreases in Fe concentrations with decreasing temperatures from 350 to 300 • C, then the concentration gradually decreased even at low temperatures ( Figure 6). Such discrepancies in the behavior of Fe concentrations between the model and experiment can be derived from several reasons, but the most plausible factor in this case is considered to be the kinetics of the iron redox reactions in the experiments, because there is also a discrepancy in H 2 concentrations that are mainly controlled by the iron redox reactions in rocks.
The H 2 concentrations in the models, except Model-K WR1 , generally increase from 1-5 mmol/kg at 350 • C to 18-40 at 25 • C with decreasing temperature, which are much higher than the experimental values (generally <0.1 mmol/kg) (Figures 4-6). As summarized, H 2 and Fe concentrations in the experiments are lower and higher than those in a thermodynamic equilibrium state, respectively. Given that H 2 is generated by oxidation of FeO and reduction of H 2 O in fluid-rock systems (e.g., [70]), it is suggested that H 2 was not sufficiently generated because the oxidation of ferrous iron in rocks was kinetically slow during the experiments. Indeed, many previous studies have experimentally demonstrated that redox reactions involving Fe(II) and H 2 O in fluid-rock systems are kinetically much slower than non-redox reactions, even at high temperatures [40,76,77]. Therefore, the low H 2 concentrations in the experiments were probably caused by insufficient oxidation of ferrous iron in the rocks, whereas the high activities of Fe(II)-bearing (solid-solution) minerals elevated the Fe concentrations in the experiments. These mechanisms likely account for the higher Fe contents in carbonate minerals in the experiments than thermodynamically expected (Figures 2 and 4-6).

Seawater ΣCO 2 Concentration and W/R Ratio
The experiments and thermodynamic modeling provided the final ΣCO 2 concentrations in fluids. However, these values methodologically include CO 2 that should remain in the atmosphere after the separation of the ocean from the high-temperature atmosphere (Sections 1 and 2). Therefore, the CO 2 distribution between the atmosphere and ocean at 25 • C was thermodynamically calculated based on a mass balance of CO 2 and re-equilibration of rock, fluid, and gas phases, providing the ΣCO 2 concentration (and other compositions) in seawater and the partial pressure of atmospheric CO 2 (Figures 5 and 6). Consequently, 4031 and 503 mmol/kg of the final ΣCO 2 values in Model-B WR2 and Model-B WR1 provided 550 and 84 mmol/kg of ΣCO 2 in seawater and 39 and 4.4 bars of atmospheric CO 2 , respectively. Likewise, 2146 mmol/kg of the final ΣCO 2 values for Model-K WR2 was calculated to be 320 mmol/kg ΣCO 2 in seawater and 20 bar atmospheric CO 2 , whereas the 1.4 mmol/kg for Model-K WR1 was calculated to be 1.4 mmol/kg ΣCO 2 (unchanged) and 0.006 bar of atmospheric CO 2 . Although these estimates vary depending on the ocean surface temperature, which is still unknown, we discuss the W/R ratios when the primordial ocean formed in comparison with geological records and other theoretical climate models.
Although geological records in the Hadean are quite limited, the Hadean ΣCO 2 concentration can be extrapolated from Archean geological records. The carbonate-bearing mineral assemblage in the high-temperature zone of an Archean-altered oceanic crust [78,79] revealed that ΣCO 2 concentrations in the hydrothermal fluid were much higher than 200 mmol/kg in the early Archean [80]. Furthermore, the depth profile of carbon isotope ratios of carbonate minerals in the altered oceanic crust indicated that most of CO 2 dissolved in hydrothermal fluids was derived from the ambient seawater [81]. Therefore, it is suggested that ΣCO 2 concentrations in seawater were higher than 200 mmol/kg, even in the Archean. Considering the evolution of seawater CO 2 concentrations on geological timescales, the CO 2 fixation into the oceanic crust through hydrothermal alteration at spreading centers and subsequent crustal subduction played significant roles in reducing ΣCO 2 concentrations in seawater from the early Archean to the early Proterozoic [82,83]. In the meantime, previous theoretical modeling of the CO 2 cycles in the early Earth showed that the ΣCO 2 concentration in the 4.4 Ga seawater may have been comparable to that in the early Archean (e.g., 3.5 Ga), although massive meteorite impacts and their ejecta weathering potentially reduced the oceanic and atmospheric CO 2 levels temporarily between the two ages [84][85][86]. These geological and theoretical considerations would imply that the ΣCO 2 concentration when the primordial ocean emerged was higher than approximately 200 mmol/kg. Of course, it should be noted that this estimation involves many uncertainties. However, if this is the case, this lower limit value is inconsistent with the seawater ΣCO 2 concentrations in Model-B WR1 and Model-K WR1 , suggesting that the W/R ratio during the formation of the ocean was at least higher than 1. On the other hand, a mass balance model simulating geochemical CO 2 cycles in the early Earth with a similar amount of total carbon indicated that CO 2 -rich seawater controlled the partial pressure of atmospheric CO 2 at as high as 10 bars (e.g., 8 bars at pH = 6; [7]). Although the assumed geologic ages are later than that assumed in this study, if this value is assumed to be the upper limit of pCO 2 when the stabilized primordial ocean emerged, the estimated values higher than 20 bars in Model-B WR2 and Model-K WR2 contradict the mass balance model. In this case, the W/R ratio can be estimated to be <2.25 during the formation process of the ocean. However, the quantitative constraints on the upper limit of pCO 2 at the time assumed in this study are still uncertain [87].
The constrained W/R ratio (>1) when the primordial ocean formed means that the thickness of the reacted crust should be <0.9 km, given the 2.7 km depth of seawater and a density of carbonated basalt and komatiite of about 3 g/cc. The estimated thickness of the reactive crust in the early Hadean is less than the reactive crustal thickness in modern midocean ridges, where a high-temperature (~400 • C) reaction zone (root zone of hydrothermal circulation cell) is located at a depth of~2 km [88]. This implies that there was an extremely steep geothermal gradient in the primitive crust globally when the steady primordial ocean emerged. This interpretation is consistent with the extremely high heat flow (~160 W/m 2 ) from the Earth's interior when the ocean formed, indicating that the ocean was present on the thin, solidified crust covering the molten mantle [89,90]. Otherwise, almost all CO 2 originally contained in the supercritical atmosphere could be fixed as carbonates into the thick crust with high CO 2 fixation capacity. Furthermore, the underlying molten mantle had no potential to emit CO 2 to the surface because CO 2 in the magma ocean had been already degassed almost completely due to its quite low solubility in melts (e.g., [91]). As such, the CO 2 -poor atmosphere could not keep the Earth's surface temperature above the freezing point of water due to the insufficiency of the greenhouse effects compensating the faint young sun, unless other greenhouse gases were present in the atmosphere (e.g., [92]).

Concentrations of Cations and pH in Seawater
The four models commonly suggest that the primordial ocean was remarkably enriched in Ca and Mg, in contrast to modern seawater. To keep the consistency with previous geological and theoretical studies (see above), it is highly possible that the concentration of Mg exceeded that of Na in the primordial ocean. Once plate tectonics started, however, a continuous recycling of oceanic crust efficiently provided fresh unaltered basaltic oceanic crust. The newly-created oceanic crust likely supplied Na and K to the ocean and relatively reduced Mg and Ca concentrations through hydrothermal alterations at mid-ocean ridges, as suggested by experiments simulating CO 2 -rich seawater and basalts [39]. Due to this process, the ocean composition would have gradually become NaCl-dominant. Furthermore, later halite formation in association with continental growth probably reduced the salinity to modern values [46].
In contrast, the pH value of the primordial ocean was estimated to be in the range of 4.9-6.7. Such values are consistent with geologically and theoretically estimated values for the early Archean era (>5.7; [8]). Therefore, even if plate tectonics started after ocean formation, a mildly acidic ocean could have been maintained by the Archean era probably because the neutralization effect of the later water-rock reactions in the oceanic crust could be canceled out by the CO 2 -rich atmosphere. Furthermore, Fe concentrations were estimated to be around 1 mmol/kg, consistent with the values in Archean seawater that precipitated banded iron formations (e.g.,~1.8 mmol/kg; [93]). This suggests that the ocean had the capacity to keep Fe concentrations high enough to generate banded iron formations even before the Archean once a continuous supply of Fe from the black smoker-type hydrothermal activities began.

Conclusions
After the last magma ocean, the volatile-bearing supercritical atmosphere cooled down, reacting with the underlying infantile primitive crustal rocks. Once the ocean's temperature stabilized, a mildly acidic Mg-and Ca-rich carbonic ocean eventually emerged on the altered and carbonated thin crust covering a molten mantle. The estimated composition indicates that the modern salty ocean was originally derived from a bitter and fizzy primordial ocean. The ocean's composition likely started to evolve once plate tectonics began on Earth. Funding: This work was partly supported by Grants-in-Aid for Scientific Research from the Japan Society for Promotion of Science (KAKENHI JSPS), grant numbers JP15K13583, JP17H06455, and JP17H06454.

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