tokens: governed by the equilibrium with SI clathrate hydrates of CO 2 (Levi et al. 2017 ). For convenience, we have cast into a cubic polynomial form the first and second dissociation constants of carbonic acid, as derived from the revised-HKF equation of state:where P is in GPa and K is in molal. For each isotherm, the polynomial is valid for the pressure range spanning from the surface of the ocean to the ocean floor. The coefficients for the polynomials are tabulated in Table 4 . Table 4 Polynomial Coefficients to Be Used with Equation ( 55 ) In Figure 14 , we give the speciation of the carbonate system as a function of depth, for the 280 K isotherm. We find that freely dissolved CO 2 is the most abundant form of DIC, in water-planet oceans, at any depth. This is opposite to the case of Earth, where freely dissolved CO 2 is the least abundant DIC component in the ocean (Zeebe Wolf-Gladrow 2001 ). Also, we find no substantial difference between the concentrations of hydrogen complexes, H + , and bicarbonate (both are represented by the red curve). Carbonate and hydroxide ions are found to exist in the ocean only in trace amounts. We note that the errors we have suggested above for the values of K 1 and K 2 do not have any considerable effect on our results. Figure 14. Speciation of the carbonate system as a function of depth in the ocean. Here we consider the ocean thermal profile to be an isotherm, set at 280 K. The black curve is the concentration of freely dissolved CO 2 . The red curve is the concentration of H + and . The green curve is the concentration of . The cyan curve is the concentration of OH − . The curves terminate at the pressure representing the bottom of the ocean, for the given isotherm. From Figure 14 we see that the different chemical species making up the carbonate system have a concentration gradient with depth. We argue that these concentration gradients with depth are stable against vertical mixing in an ocean world. First, we wish to point out that the concentration of freely dissolved CO 2 , the most abundant component of the DIC, is constant to a good approximation throughout the ocean. This is a consequence of the nature of solubility when in equilibrium with the clathrate phase, rather than due to efficient vertical mixing in the ocean (Levi et al. 2017 ). Thus, the concentration gradients with depth are most pronounced for the chemical species that are least abundant. If a parcel of ocean water migrates from the ocean floor upward, this parcel would be supersaturated with carbonate with respect to the shallower depth. The value for K 2 decreases with decreasing pressure. Consequently, carbonate would transform to bicarbonate, and then to freely dissolved CO 2 . However, this newly formed CO 2 is added to an ocean likely saturated with CO 2 , at equilibrium levels with respect to its clathrate hydrate phase (Levi et al. 2017 ). Therefore, the additional dissolved CO 2 forms grains of clathrate hydrates, which tend to
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