## 2 What Is Terrestrial Storage of Biomass (TSB)?
### Enhanced Weathering--Adding Olivine to the Ocean  
Adding olivine to ocean waters has been proposed as a NET ([PERSON] et al. [17]). Olivine is a magnesium-rich magnesium iron silicate, (Mg,Fe)\({}_{2}\)SiO\({}_{4}\). Naturally occurring olivine consists, with minor variations, of about 0.92 MgSiO\({}_{4}\) (forsterite) and 0.08 FeSiO\({}_{4}\) (fayalite). The chemistry behind adding olivine to the ocean as a means of pulling CO\({}_{2}\) from the atmosphere is complex. Understanding how adding olivine to the ocean works to pull more CO\({}_{2}\) into the ocean requires an understanding of that chemistry. CO\({}_{2}\) dissolves in the ocean and then reacts with water to form carbonic acid, which lowers the pH of the ocean, leading to the reduced dissolution of CO\({}_{2}\) in ocean waters and the reduced dissolution of calcium carbonate, the primary component of coral reefs and the shells of shellfish. Carbonic acid is a weak acid and, thus, CO\({}_{2}\) dissolution leads to a buffer system (Sturm [28]). CO\({}_{2}\) gas dissolves into ocean water, with the concentration of dissolved CO\({}_{2}\) dictated by [PERSON]'s law. The dissolved CO\({}_{2}\) can react with water to form carbonic acid, which dissociates to form bicarbonate and carbonate ions and protons, which make the water more acidic via the following set of reactions:  
\[ \begin{array}{ccccc}\text{CO}_{2}\left(\text{g}\right)=\text{CO}_{2}\left( \text{aq}\right)+\text{H}_{2}\text{O}=\text{H}_{2}\text{CO}_{3}&=&\text{H}^{+} +\text{HCO}_{3}^{-}=\text{H}^{+}+\text{CO}_{3}^{2}\\ &&\uparrow&\uparrow\\ \text{Henry}^{\prime}\text{s Law}&K_{a1}&K_{a2}\end{array}  \tag{1}\]  
where  
\[ \begin{array}{ccccc}\text{H}_{2}\text{CO}_{3}=\text{ carbonic acid};\\ \text{HCO}_{3}^{-}=\text{bicarbonate ion};\\ \text{CO}_{3}^{2-}=\text{carbonate ion}.\end{array} \]  
\(\text{K}_{a1}\) and \(\text{K}_{a2}\) are equilibrium constants that are temperature-dependent. Thus, the solution of the equilibrium equations depends on the local ocean temperature, which will vary seasonally and by region. The solubility of CO\({}_{2}\) gas (CO\({}_{2}\) (g)) to produce dissolved aqueous CO\({}_{2}\) (CO\({}_{2}\) (aq)) is dictated by Henry's Law, which states that the solubility is directly proportional to the gas concentration. The extent of the dissociation of carbonic acid to form the bicarbonate ion and a proton, and the dissociation of the bicarbonate ion to form the carbonate ion and another proton is determined by the equilibrium constants. At 25 \({}^{\circ}\)C, this leads to the relative concentration of species, as shown in Figure 1.  
Since the ocean pH is in the range of 6 to 8, the dominant species is the bicarbonate ion. The effect of introducing a divalent cation such as Ca\({}^{2+}\) is shown in Figure 2.  
An increase in the pH leads to an increase in hydroxyl ions (OH-), which react with the protons formed by the dissociation of bicarbonate, leading to an increase in the carbonate ion concentration. Carbonate ions can then react with Ca\({}^{2+}\) to precipitate calcium carbonate (middle left). An increase in gaseous CO\({}_{2}\) leads to a decrease in the pH by driving the system of the upper equation, shown in Figure 2 towards the left, which leads to more protons that react with the carbonate ion, which leads to calcium carbonate dissolution. Adding olivine to the system disrupts the system, leading to a higher pH, and, thus, increased mineral precipitation in the following way. Olivine reacts with water (dissolves) to form Mg\({}^{2+}\) and Fe\({}^{2+}\) ions, hydroxyls (OH\({}^{-}\)), and silicic acid (H\({}_{4}\)SiO\({}_{4}\)), as follows:  
\[ \begin{array}{ccccc}\text{(Mg,Fe)}_{2}\text{SiO}_{4}+4\text{H}_{2}\text{O }=2\text{ (Mg,Fe)}^{2+}+4\text{OH}^{-}+\text{H}_{4}\text{SiO}_{4}\end{array}  \tag{2}\]The hydroxyls increase the pH and react with protons, leading to more divalent ion precipitation. This can ultimately lead to increased calcium carbonate formation if the cations are Ca\({}^{2+}\) or magnesium carbonate if the ions are Mg\({}^{2+}\).