Kazakhstan`s sciencers proposed to salt the Ocean

In the study^[7] of the main oceanic carbon sinks, unicellular planktonic foraminifera and their suborder Globigerinina, in experiments on the deposition of calcite shells (called "tests") was studied the ratio of boron to calcium (B/Ca). These results suggest that borate [B(OH)₄^–] and carbonate [CO₂^3–] ions may compete for the same site in the calcite lattice. B/Ca has no significant temperature dependence, but increases with salinity.

The non-proportional increase B component in calcite tests with a proportional increase in salinity reflects the chemistry of the ancient oceans, their higher total ion concentration or ionic strength, and influence of "effective concentration" or thermodynamic activity of borate ions, drivers of carbonate sedimentation . Planktonic foraminifera are the main component of "calcite rain" in the sea and the largest sinks of carbon. Today they, together with benthic species, account for almost 25 % of the carbonate production in the oceans [23]. Because they are buoyant, their life cycles depend on the density of sea water, which is determined by temperature and salinity. Since the Mesozoic, foraminifera have evolved in a tense regime of decreasing aqueous and atmospheric CO2 from tens of percent to today's 0.03...0.0417 % and sinked a huge amount of carbon in solid inorganic carbonates. In particular, they did a good job in the Cretaceous period (from the Latin creta, "chalk", CaCO3). In total, sedimentary carbonates in the form of limestone and dolomite accumulated more than 60 million gigatons, which is more than three orders of magnitude greater than the amount of carbon contained in the oceans, the biosphere and fossil organics combined.

In laboratory culture experiment “Effect of salinity induced pH changes on benthic foraminifera”^[9]

the life activity of foraminifera was studied depending on the degree of salinity.

The graphs of the life and death of this microorganism show that these foraminifera practically do not live in an environment with a salinity of less than 20 ‰ and poorly at 25 ‰. Therefore, for clarity, we have excluded these values from the combined third plot, which shows that the greatest development occurs at high salinity, with final maximum values of 40 ‰. This is despite the fact that at the bottom of the Indian Ocean, where this foraminifera was taken from, the salinity is lower. Bottom waters from the equator to the arctic latitudes have a salinity of 34.7–34.8 ‰.

This preference for high salinity is for foraminifera not only an evolutionary memory, but mainly a direct adherence to the laws of chemical thermodynamics. Increased salinity shifts the chemical equilibrium towards the formation of a new solid phase – calcium carbonate.

All foraminifera and most other calcite-fixing organisms use biological catalysts, enzymes like carbonic anhydrase to increase the pH of the internal environment (up to 9.0)^[11] relative to sea water (modern pH 7.4–8.2 from lysocline to surface) by actively pumping out protons H⁺.

The pH and salinity of seawater have an almost linear relationship, so the preference for salinity corresponds to a proportional increase in the thermodynamic potential, or Gibbs free energy, available for calcification.

This heterogeneous equilibrium can be described by a system of nonlinear equations, the values of which constitute the equilibrium constants of all individual elements of seawater. Knowing the exact thermodynamic values of all elements of the system and their relationship, it is possible to calculate the salt-carbon balance, find the solution (root) of the system of equations by Newton's method.

Microorganisms affect the kinetics of reactions, accelerate it. Their biological catalysts reduce the activation energy of chemical reactions or activation barrier, reduce the amount of energy required for the reaction.

Without enzymes, the reaction of precipitation CaCO₃ takes place at a higher temperature, pH, and salinity of seawater. In the ocean, there are such natural conditions for the abiotic precipitation of solid carbonates. For example, spontaneous precipitation of "lime powder" (also called "whitening") occurs in the Persian Gulf during the hot season, when salinity in surface waters reaches 41–42 ‰ due to evaporation. This rule is also confirmed by the deposits of the Bahama Banks and other shallow carbonate factories, where in the presence of a crystallization grain, aragonite (a less stable phase of calcium carbonate than calcite, with the same formula CaCO₃) precipitates from seawater on a regular basis. ^[6]

 

Spontaneous precipitation ^[22] of CaCO₃ occurs at high supersaturation of seawater with respect to calcium and magnesium carbonates (from 7 to 50 times^[6]), high pH (the threshold for the beginning of precipitation is set at pH 8.60) and high salinity.

Usually, precipitation is triggered by an increase in temperature, but it also happens in the case of an increase in salinity. For example, in winter in northern latitudes, when ice freezes, the salinity of the underlying water layers can increase sharply and, according to the laws of thermodynamics and the Ostwald's rule, precipitate ikaite, most unstable form calcium carbonate. However, due to its high solubility, it is not sedimented.

The salinity effect is cognate with salting out (also known as salt-induced precipitation) due to a combination of increased ionic strength and common-ion effect.

 

If we compare the carbonate sediment map on the ocean floor, the salinity map (satellite modeled image (surface salinity changes seasonally)) and the depth map, we can see a correlation between surface salinity and bottom sediments. Depths below the lysocline ~3.5 km (dark blue on depth map) preclude carbonate accumulation due to pressure and temperature effects on CaCO₃ dissolution.

Tops of seamounts are covered with calcite sediments, like snow-capped peaks on land.

ΔS% / 2.9% Sr ratio

  Anthropogenic CO₂ leads to an increase of DIC but does not change TA because the charge balance is not affected. The formation of CaCO₃ decreases both DIC and TA. For each mole of CaCO₃ precipitated, one mole of carbon and one mole of double positively charged Ca²⁺ ions are taken up which leads to a decrease of DIC and TA in a ratio of 1:2. As a result, the system shifts to higher CO₂ levels and lower pH.^[3]

Formation CaCO₃ sediments occurs in the so-called carbonate factories, the functioning of which is well studied in marine carbonate sedimentology. ^{[1] [12] [13]}

 

 

The productivity of these carbonate factories directly depends on the TA and pH of seawater, so anthropogenic ocean acidification shifts the balance of the system towards carbonate dissolution.

Until now, in all books on oceanology, this was called a carbonate system with the obligatory representation of the borate component. It's time to call it by its true name: the carbonate-borate system. Because, despite the low concentration borate ions (average 4.5 mg/L), are the key elements of the system, the trigger in the carbonate precipitation reaction.

The concentration of borate ions in sea water depends on pH and increases with its increase, forming a kind of fixing wedge or cline that supports balance, which is associated with the thermodynamic concept of degrees of freedom. We called this the "third leg effect".

Black-and-white diagram from the "Carbonate sediments and their diagenesis", 1994, Robin Bathurst, University of Liverpool.^[1] Our comments are colored.

 

 

The carbonate-borate system of the ocean determines the rate of carbonate sedimentation. It has a negative feedback on seawater acidity and a positive feedback on salinity.

For precipitation from a solution of salts, including carbonates, salts of carbonic acid, it is necessary that the solution be supersaturated. Seawater becomes supersaturated with respect to CaCO₃ when the ion product exceeds the solubility product Ksp or Ω > 1.

In the depths of the oceans, water is undersaturated, while surface waters are in a state of significant supersaturation. In tropical areas, the solubility product Ksp of calcite is exceeded by 7–8 times.

There is evidence of exceptional stability of this condition.^[6]

 

Thus, Lyakhin et al. (1968)^[6] showed that for the spontaneous precipitation of CaCO₃ from seawater, it is necessary 50-fold supersaturation. When the solution is supersaturated with calcium carbonate, the Ostwald rule is valid, according to which, by purely chemical means, the metastable component, i.e., aragonite, precipitates first, and after reaching the aragonite solubility product (Ksp_aragonite = 10^-8.22), precipitate of calcite (Ksp_calcite = 10^-8.35). For example, on the Bahama Bank, as a result of overheating and increasing salinity from evaporation, precipitation occurs mainly of aragonite, which then gradually recrystallizes slowly into more stable calcite.

Recrystallization of carbonates as a movement of the system towards thermodynamic equilibrium is possible because the dissolution↔precipitation reactions are reversible and they are influenced by many other seawater ions: Mg²⁺, К⁺, Sr²⁺, H₂BO₃^–, SO₄^2– etc. that form ion pairs among themselves, as well as fluctuations in their general concentration – the ionic strength of the solution. For example, the association reactions for calcium Ca²⁺ and magnesium Mg²⁺ cations are not only with carbonate anions CO₃^2– and HCO₃^– but also with sulphate ions: Ca²⁺ + SO₄^2– = CaSO₄⁰ and Mg²⁺ + SO₄^2– = MgSO₄⁰

Calcium and magnesium sulphates exists as both contact and solvent-shared ion-pairs in seawater.

The high stability of supersaturation of seawater with calcium carbonate is explained by the complexity, multistage and mobility of the carbonate-borate system together with the presence of numerous foreign ions in the solution make it difficult approach and orientation of Ca²⁺ and CO₃^2– ions, necessary for the formation of nuclei of the solid phase. Complexation processes cause the existence of more than 90% CO₃^2– in ion pairs with Mg²⁺ and Na⁺ and about 9 % Ca²⁺ in ion pairs with SO₄^2– and HCO₃^–, resulting in activity concentration Ca²⁺ and CO₃^2– are greatly reduced.

Any salt has its own value of the solubility product constant, for example, K_sp(CaMg(CO₃)₂ dolomite, which is coupled with the constants of other sea salts: K_sp(MgSO₄) magnesium sulfate, K_sp(CaSO₄) gypsum, K_sp(SrCO₃) strontianite, etc., and with their ionic complexes.

The system of non-linearly coupled elements of seawater has an electrical nature. The activity of individual ions and complexes depends on the Ionic strength, a quantity representing the strength of the electric field in the solution:

 

 where I is equal to half the sum of the products of the molar concentration c_i of each ion (M, mol/L) and the square of its charge z_i. The sum is taken over all ions in the solution. Due to the square of z_i, multivalent ions (Mg²⁺, Ca²⁺) contribute particularly strongly to the ionic strength.

Quadraticity in this equation follows from Coulomb's law, according to which the force of interaction of two point charges is proportional to their magnitudes and inversely proportional to the square of the distance between them. However, water molecules as a dielectric weaken the Coulomb interactions of ion pairs, triplets, and clouds. These ion clouds shield the charge of the central ion, which is the reason for introducing activity as an "effective concentration" in ions.

Typical values the Ionic strength:

potable and groundwater I = 0.001 – 0.02M,

seawater I = 0.67 – 0.71M .

Seawater as a solution with significant ionic strength has large deviations from ideality, which are described by the Debye-Hückel theory. This theory gives equations that use an individual dimensionless activity coefficient γ_i can be calculated as a function of the concentration, temperature and permittivity of the solvent. The basic equation of this theory (Debye–Hückel limiting law) shows the relationship between the activity coefficient of the ion z_i and the Ionic strength of the solution, I, in dilute solutions in the form:

 

First approach		I ≤ 0.01M	A ≈ 0.51 at 25°C in water
Second approach		I ≤ 0.1M	a - average effective ion diameter, B - parameter radius of ionic cloud
Third approach		I ≤ 2M	C - parameter takes into account the polarization of molecules

 

where γ is the activity coefficient, A is a constant independent of the charge of the ion and the Ionic strength of the solution, but dependent on the dielectric constant of the solvent and temperature.

The classical Debye-Hückel theory is applicable only at very low values of ionic strength in dilute electrolytes. Therefore, for high ionic strength solutions often found in nature, extensions have been developed. The main theory extensions are the Davies equation (for I ≤ 0.5M, not acceptable for seawater), and two extensions acceptable for our purposes: Specific ion interaction theory (SIT theory) and Pitzer equations.

The Pitzer equations have more parameters than the SIT equations. Because of this, the Pitzer equations provide more accurate modeling of mean activity coefficient data and equilibrium constants. The Pitzer equations are based on rigorous thermodynamics.^[26][27] While the SIT theory approaches are based on pairwise interactions between oppositely charged ions, Pitzer's approach also allows interactions between three ions. Determining the Pitzer parameters is more laborious, but this is justified by the accuracy of the results and their adequacy to real conditions, since it is based on numerous data from practical measurements.

For the average activity coefficient of the i-th ion species, the Pitzer equations, with slight simplifications, can be written as

where

 is the Debye-Hückel coefficient for the osmotic function, equal to 0.3921 at 298.15K or 25 °C;

 b = 1.2 is the parameter of the Pitzer model; m_j, m_k are the molalities of the ions salt background, index _j refers to background cations, index _k to anions; NK is the number of types of background cations; NA is the number of types of background anions; N is the total number of types of ions that make up the background electrolytes;

Ionic strength is expressed in units of molality m_l (mol/kg) thermodynamically independent of temperature. z_l is the charge of ions of the lth kind (in atomic units);

and are the parameters of the interaction of the i-th species with the l-th ion;

α = 2 is a constant parameter of the Pitzer model;

 is the interaction parameter of the j-th and k-th types of ions.

If the reagents are uncharged, then

the limiting form of which at high values of the Ionic strength is the Sechenov equation.

 

The activity equations for all salts dissolved in seawater and the activity of the water itself, as well as their thermal and volumetric properties, are derived from a single expression for the excess Gibbs energy of solutions. The equations contain sets of two kinds of parameters: "pure" solutions containing single electrolytes (for example, NaCl, MgSO₄); and "mixture" parameters, the values of which are determined from measurements containing two different electrolytes with a common ion (NaCl and Na₂SO₄).

To solve such a complex system as seawater, data are used: activities γ gamma, apparent molar enthalpies and heat capacities, apparent molar volumes and compressibilities, solubilities of all sea salts and equilibrium partial pressure of CO₂.

We created a model with major ions (99.9 %) in seawater: Na⁺, K⁺, Mg²⁺, Ca²⁺, Sr²⁺, Cl ^–, SO₄^2–, H₂BO₃^–, Br^–, F ^–, HCO₃^–, CO₃^2–, OH ^– and H ⁺.

The Pitzer parameter matrix for these major ions is significant: 38 sets of cation-anion interactions and potentially 210 ternary or "mixture" parameters that express the interactions between two different ions with same type of charge and one with the opposite type of charge.

System of 65 equations with unknowns,

11 of them are key, the rest are less significant,

however, neutral ions such as Na⁺, Cl ^– set significant contribution to

the value of ionic strength due to their high concentration.

The dissolution/deposition balance of calcium carbonates determines the Saturation index, SI, which is determined by the difference between the measured pH_actual of the water and the calculated pH_s of the water if it were in equilibrium with CaCO₃ at the existing calcium ion and bicarbonate ion concentrations.

     

SI = pH_actual – pH_s,   and   pH_s = f(T) + f(TDS) – f(Ca) – f(TA),

 

where function of temperature f(T) = -13.12 log₁₀ (°C + 273) + 34.55, function of water TDS = (log₁₀[TDS] – 1)/10 is a correction for the ionic strength and it is determined using the table value, factor calcium hardness of water value, f(Ca) = log₁₀[Ca²⁺], and factor the measured value for total alkalinity, TA, in mol/kg water.

Saturation index is widely used to control scale deposition, for example, in water supply systems. If SI > 0, than water is oversaturated with CaCO₃, scale forming.

If SI < 0, water is undersaturated, corrosive, and dissolved solid carbonates.

  

 

  

Saturation index is calculated by comparing the chemical activities of the dissolved ions of the mineral (ion activity product, IAP) with their solubility product (Ksp). In equation form,

SI = log(IAP/Ksp).

  

SI is only a qualitative indicator of CaCO₃ deposition, it indicates the direction and intensity of the dissolution and precipitation processes. The quantitative indicator of calcium carbonate that needs to be precipitated or dissolved from water to reach equilibrium with CaCO₃ is the Calcium Carbonate Precipitation Potential, CCPP.

To find CCPP, the PHREEQC program allows multiple all pure phases in seawater, that to exist in equilibrium with the aqueous phase, subject to the limitations of the Gibbs' Phase Rule. This equilibrium is found using heterogeneous equations of mass action and is termed a “phase assemblage”.

17

Math Chem

 

 

Salinity		34	Salinity		35	Salinity		36
Temperature		25	Temperature		25	Temperature		25
pH		8.0	pH		8.1	pH		8.2
Alkalinity		0.00223	Alkalinity		0.0023	Alkalinity		0.00237
B		0.000403764	B		0.000416	B		0.000427885
Br		0.000819176	Br		0.000844	Br		0.000886811
Ca		0.009997058	Ca		0.0103	Ca		0.010594285
Cl		0.529941176	Cl		0.546	Cl		0.561599999
F		0.000066000	F		0.000068	F		0.000069942
K		0.009900000	K		0.0102	K		0.010491429
Mg		0.051247058	Mg		0.0528	Mg		0.054308571
Na		0.481411764	Na		0.496	Na		0.510171428
S(6)		0.027370588	S(6)		0.0282	S(6)		0.029005714
Sr		0.000088323	Sr		0.000091	Sr		0.000093599
EQUILIBRIUM_PHASES
CO2(gas)		-3.4				CO2(gas)		-3.4
Calcite		-7.0				Calcite		-7.0
Equilibrium with atmospheric CO2(gas) with logariphm partial pressure -3.4 (411 ppm).
Equilibrium with solid phase calcite with account 7-fold subsurface supersaturation.

 

Proceeding in a similar manner, we created an array of proportionally calculated of major ions for each salinity value in the range of 25-45 ‰, and calculated the CCPP for each of them

. The results of these large calculations are presented in the table and graph. From which it can be seen that the dependence of the precipitation potential of calcite increases linearly over the entire range of salinities. Whereas, the CO2 gas associated with it in the phase assemblage has a non-linear dependence, with acceleration decreasing from the average salinity of the world ocean to more salty semi-closed and closed reservoirs (salt lakes).

Using the methods of chemical thermodynamics, we investigated what happens when salt is dissolved in seawater and the solution is diluted. We looked into the abyss of the ocean one order of magnitude, as much as the mathematical "lantern" allows.  

We assume that the reason for the annulment of the values of CCPP at large stages of dilution is an integer overflow, when the value of the arithmetic operation is out of range. In-depth calculations with an increase in the bit depth, the number of digits after the decimal point, show that the linear trend of the precipitation potential continues. This is also indicated by the linear nature of the dependence of CCPP on salinity, which also linearly depends on the mass of the solution.

If this is the case, then the CCPP of 1 kg of seawater is equal or nearly equal to the CCPP of 1 ton of water or perhaps 1000 tons, 1 mln kg. But in 1000 kg of seawater, there is a thousand times more not only calcium, and also all other ions, and in particular carbonate ones.

That is, carbonate precipitation reactions do not have any limiting factors of reactant concentrations, and at a constant temperature and pressure, the change in the reaction rate can be carried out only in a catalytic way. The change in salinity affects the change in rate of precipitation. This means that salt is the catalyst.

It is the main “engine” in the carbonate factory. It sounds paradoxical, but in a generalized sense it is true, all the properties of a catalyst are present in salinity. Individual elements in this system behave differently. For example, Mg²⁺ and SO₄^2–, which are believed ^[29] to inhibit calcite precipitation, decrease the reaction rate. On the contrary, Na⁺ and Cl ^– increase the rate of calcite precipitation. And the general increase in the totality of sea salt ions leads to a significant increase in speed of carbonate sedimentation..

If we translate the range of deposition rates presented by the authors to the mass of seawater (cubic meter ~ ton), then we can see a unified ratio equal to 1.33.

 

removal rate (mol/m2 yr– 1 )	12	9	6	3.75	1.5
depth (meter)	9	6.75	4.5	2.8	1.15
ratio (~mol/ton seawater)	1.33(3)	1.33(3)	1.33(3)	1.33...	1.3...

 

At a constant temperature, the change in CaCO₃ removal rate depends only on the change in salinity. We took the ΔCaCO₃ and Salinity data marked in the table and built a dependency graph in MS Excel.

Pay attention to the similarity of these graphs. But on the graph from the article on the horizontal axis is time (days), and on ours is the salinity (in ‰). Also on the vertical ordinate axis is the scale of calcium carbonate deposition translated to kilograms of seawater instead of square meters of the bottom surface in the original scientific paper. It is obvious that the translation of the resident time of the water on the Bank into its salinity is a linear process. Salinity, as a catalyst, "compresses" time, linearly accelerates the precipitation rate of carbonates. The whole system is reflected in other coordinates.

The nonlinearity of the deposition, the decrease in the precipitation rate with increasing salinity is determined by the consumption of Ca²⁺ ions, which, in fact, is investigated in this article. The authors point out that, despite the increase in calcium with increasing salinity (Ca 1.2 % in sea salt), in the saltiest water (43.6 ‰) in the lagoon near the island, the content of Ca²⁺ is 75 % less than in the water of the Straits of Florida due to the precipitation of CaCO₃.

Under normal conditions (pH 8.1), the distribution of DIC fractions is as follows: CO_2(aq) ~ 1%, carbonate ion CO₃^2– ~ 9% and bicarbonate ion HCO₃^– ~ 90%, precipitation occurs mainly with bicarbonate ion and CO₂ release (see page 33). It follows that the precipitation process is self-sustaining to a certain limit.

The balance that has developed over millions and even billions of years thermodynamically conjugates the process of photosynthesis in picoplankton, the primary food chain, restrictions on its reproduction through viruses, which also stimulate the precipitation of carbonates, which releases CO₂, which in turn stimulates the growth of cyanobacteria, and, accordingly, multiplicative growth in the number of viruses limiting the growth of picoplankton and simultaneously stimulating the precipitation of carbonates. This is the carbon cycle in the oceans.

An increase in the salinity of water moves all this complex of heterogeneous physical and chemical factors towards accelerating the circulation. Salt, or rather its electrical nature – the ionic strength, is a catalyst for the process of natural absorption and sink of carbon in the oceans.

  

  

Under suitable conditions, it is possible not only to stimulate "foraminiferal rain", but also to initiate the "whitening" in the open ocean. The mentioned 23-fold supersaturation in viral lysis allows this.

For every mole of CaCO₃ that precipitate, 0.6 mole of CO₂ is removed in the water, the bank seawater maintains a nearly constant CO₂ partial pressure (here the authors represent the CO₂ partial pressures in water collected by a submersible pump placed about 1 m below the sea surface).

.

  The authors state that "precipitation appears to be a second-order reaction, the rate being proportional to the degree of supersaturation". Using the data from this study, and assuming that the concentration of [Ca²⁺] ions is much higher than the carbonate ions [CO₃^2–] (the excess method), we determined the reaction order by the method of iterating the kinetic equation using the Solver add-in in the Microsoft Excel program. The result is a partial order equal to 2.186.

It should be said here that there are scientific papers in which the dependence of the order of the calcite precipitation rate in seawater on its ionic strength (salinity) is investigated. In work^[33] Mucci et al. investigated the influence of ionic strength on the kinetics of calcite precipitation from seawater. “Results of this study indicate that, when the ionic strength is increased from 0.10 to 0.93 M, the partial reaction order with respect to the [CO₃^2–] concentration increases from 1 to 3 and the forward reaction rate constant k₊₁ increases by several orders of magnitude.