Overview and general comments:

The manuscript of Moras et al. reports results from a laboratory study on magnesium hydroxide additions to seawater, examining the effects of mineral grain size, seawater salinity, and dissolved organic carbon concentrations on the dissolution of magnesium hydroxide and secondary calcium carbonate precipitation. Their results demonstrated that secondary CaCO₃ precipitation was delayed the longest when using medium grain size Mg(OH)₂, and they also found that secondary precipitation was accelerated at lower concentrations of Mg and DOC, both of which are known CaCO₃ precipitation inhibitors. This is an important study with implications for optimizing the efficacy of ocean alkalinity enhancement.

The authors’ conclusions regarding the effects of grain size, Mg, and DOC on delaying secondary precipitation are generally supported by the data, and the manuscript was straightforward to follow. Some major issues that need to be addressed include providing more details on the carbonate chemistry calculations (including uncertainty estimates—especially for Ω, which is an indicator for the secondary precipitation threshold), clearly distinguishing between calculated and measured CO₂ parameters, and the unexplained DIC trends in some of the data (which the authors attribute to ingassing, but does not seem to be well-supported by the data). Additionally, the presentation of the some of the figures and tables can be improved. With minor revisions, I recommend publication.

Major Comments:

Carbonate Chemistry Calculations:

The authors need to provide full details on the carbonate chemistry calculations, such as the choice of constants used in the calculations (Lines 145-146). Additionally, uncertainties should be estimated and reported for calculated CO₂ parameters using the uncertainty propagation routines available on CO2SYS. The uncertainty estimates are especially important when reporting values of Ω, which undoubtedly will inform future research on critical thresholds for CaCO₃ precipitation. Without uncertainty estimates, the results in this study cannot be interpreted. In Table 1, the calculation uncertainty for Ω should be combined in quadrature with the standard deviation of the replicates.

Calculated vs. Measured CO₂ Parameters:

The text and figures are often confusing as to which CO₂ parameters were measured and calculated. Furthermore, the authors do not always specify which input parameters were used in the calculations. In Lines 127-135, it appears that most of the DIC and TA values in the Mg and DOC experiments were calculated values (unlike in the salinity and grain size experiments where each experiment had 9 to 10 DIC and TA measurements). Fig. 5, however, does not make it clear which of the ∆DIC and ∆TA values were measured and calculated (and the input parameters used). Similarly, in Line 133, “the difference between estimated maximum TA and final measured TA” does not specify how TA was calculated.

pH measurements on the “free” scale:

The authors report pH measurements on the “free” scale based on pH electrode measurements calibrated with Metrohm buffer solutions (pH 4, 7, and 9). As the calibration solutions are low-ionic strength solutions, there will be large liquid junction potential errors when making measurements in seawater solutions at high ionic strength, and it is difficult to estimate the uncertainty. While the electrode measurements may still be useful in reporting changes in pH, it seems problematic to use the data to calculate other CO₂ parameters in seawater. One solution may be to calibrate the electrode measurements against pH calculated from measured DIC and TA whenever these measurements coincide. The authors should also make clear which parameters were calculated with pH and how the uncertainty in the pH measurements may affect the interpretation of their results.

Maximum Ω_A attained (Line 288): The authors attribute differences in the maximum Ω_A attained in their Mg(OH)₂ experiments and previous studies with Ca(OH)₂ to differences in the starting water composition. It is difficult for the reader to confirm this without information provided on the starting water composition. I suggest visualizing the results of this and previous studies with Ca(OH)₂ on a DIC and TA diagram with Ω_A isolines, showing the initial water composition and final composition at maximum Ω_A.

Secondary CaCO₃ precipitation thresholds:

The authors chose Ω_A ~ 9 based on their hypothesis that the secondary precipitation threshold would be higher when adding Mg(OH)₂ compared to the threshold when adding CaO and Ca(OH)₂. However, the threshold was not directly investigated in this study. It would be worth discussing how future research might better constrain the threshold for Mg(OH)₂ additions and how secondary precipitation might be mitigated when adding Mg(OH)₂ vs. CaO and Ca(OH)₂. Is it more advantageous to optimize the grain size of the feedstock or to stay below the critical Ω threshold?  

CO₂ ingassing in experiments:

In many of the experiments (see Fig. 2, 4, 5, Line 187, Line 227), the data show the DIC increasing after the rapid drop in DIC and TA from CaCO₃ precipitation, yet the cause of this trend is not well-explained. In Fig. 1, the data show the pH of the small grain size experiment  continuously decreasing after reaching its maximum, which the authors attribute to ingassing. Yet, this was not apparent in the medium and large grain size experiments. In Sect. 4.1, the authors claim that ingassing is likely occurring in the other experiments as well, but masked by the stronger pH increase during dissolution. However, their explanation seems to contradict Fig. 1, which shows the strongest pH increase during dissolution for the smallest grain size.

What was the pCO₂ of the seawater samples relative to the laboratory atmospheric pCO₂, and is this consistent with ingassing?

One weakness in the experimental design was that there were no control samples (subjected to the same headspace conditions from the periodic sampling but not the Mg(OH)₂ addition) from which the magnitude of gas exchange can be directly assessed. The authors should address how they can be certain that the changes in DIC not attributable to CaCO₃ precipitation are necessarily due to gas exchange.

Minor Comments:

Line 21: Change “higher alkalinity/pH” to “higher alkalinity and pH.”

Line 83: What was the laboratory pCO₂?

Line 101: Ω_A ~ 9 is not the threshold for CaCO₃ precipitation when adding CaO and Ca(OH)₂. It would be clearer to explain early on that Ω_A ~ 9 was selected based on the suspicion that the precipitation threshold for CaCO₃ precipitation when adding Mg(OH)₂ may be higher than the Ω_A ~ 7 threshold observed when adding CaO and Ca(OH)₂. This was explained later in Lines 304-305.

Line 109: Please reference the specific figures in “see figures.”

Lines 110-111: What was the sample size for the TA and DIC measurements? The description in these two lines sounds like ~150 mL of sample was used for each TA and DIC measurement. However, if 10 samples were taken for TA and another 10 samples for DIC measurements (as suggested in Line 111), there would not be enough sample (1.5 L total). It sounds like most of the sample was consumed by the end of the experiment. Please clarify the measurement process and address how the increasing headspace over the course of the experiment may contribute to the instability of the DIC.

Table 1: The organization of the table needs to be improved for clarity.

Firstly, the initial carbonate composition (e.g., DIC and TA) of the samples should be reported, not just the changes in DIC and TA.

The first three columns after “Experimental details” pertain to the dissolution phase of the experiment and the next three columns pertain to the secondary precipitation phase. It would be helpful to label these columns as such.

Without reading the manuscript text, “Days of stable TA” is an unclear description. Consider including a short explanation in the table caption.

Line 176: The increase in TA for the small grain size experiment was ~428 umol/kg according to Table 1.

Fig. 2: Please specify which input parameter pairs were used to calculate DIC and TA from pH.

Panel figures (Fig. 2, Fig. 4, and Fig. 5):

In general, the panel figures need to be improved for visibility as the font size on the axes may be too small.

Why are the pH measurements not included?                             

Line 244: The text should be 120 μmol kg^-1 DOC.

Fig. 5. Please explain in the caption what the error bars represent in this and other figures.

Line 273: Reference Fig. 1.

Line 275: The text should be “If CaCO₃ precipitation.”

Fig. 6: How were the TA data normalized?

Line 380-382: The mechanism of CaCO₃ precipitation in relation to grain size was not demonstrated in this study, so this conclusion should be stated as a hypothesis rather than a finding.

Marine carbon dioxide removal, and ocean alkalinity enhancement in particular, have the potential to make a significant contribution to the world’s efforts toward avoiding the worst effects of climate change. Mg(OH)2 is a promising alkalinity source, but understanding its dissolution kinetics and how to avoid runaway precipitation of CaCO3 that removes more alkalinity than was added is key to realizing this promise. I recommend “Effects of grain size and seawater salinity on magnesium hydroxide dissolution and secondary calcium carbonate precipitation kinetics: implications for ocean alkalinity enhancement” for publication, but only after the authors address my comments and questions listed below.

Abstract, lines 21-22: “while the slower dissolution of bigger grain size maintained a higher alkalinity/pH at the surface of particles, increasing CaCO3 precipitation rates and making it observable much quicker than for the intermediate grain size” Why would larger size have this effect? in the direction normal to the grain face, should be same in all cases, but is the argument lateral transport makes a parabolic alk/pH distribution with peak at center of grain face?

Line 34: “To mitigate the effects of Ocean Acidification” No CDR process will meaningfully mitigate OA over a global scale, only local scales. I suggest changing to “To locally mitigate…”

Line 83: “laboratory air pCO2” What was the lab CO2 value? if H2O saturated, what was the temperature?

Line 95: “For the grain size experiments, three grain size ranges were produced using two stainless steel sieves with 63 μm and 180 μm mesh sizes. The medium range, i.e., 63-180 μm, was also used for the salinity experiments at ~36, ~28 and ~20.” Did you measure the actual grain size distribution? I suggest making this measurement.

Line 100 and throughout: How was omega determined?

Throughout: Why use free scale instead of total?

Line 166: “After two hours, the maximum pHF recorded for the smaller grain size was 8.76 ±0.04, which continuously decreased to 8.68 ±0.00 between 11 and 12 hours after Mg(OH)2 addition. In contrast, the pHF for the medium and larger grain size increased to 8.72 ±0.00 and 8.68 ±0.03 after about eight hours and remained stable thereafter, respectively (Figure 1).” Why this behavior for small grains? no explanation is given.

Line 184: “Finally, a small drop in DIC was observed after Mg(OH)2 addition in all experiments, of about 80, 30 and 140 μmol kg-1 in the small, medium and large grain size incubations, respectively.” Why? What is the physical mechanism?

Fig. 2: What accounts for the large spread in time among the 3 replicates?

Line 200: “Starting pHF were slightly different, recorded at 7.99 ±0.05, 8.06 ±0.01 and 8.09 ±0.01 in the salinity 20, 28 and 36 incubations, and increased to a maximum of 9.19, ±0.00, 8.91 ±0.00 and 8.72 ±0.00, respectively. In all incubations, similar logarithmic trends were observed for pHF (Figure 3).” Maybe I missed it above. Do you add the same amount of Mg(OH)2 for all experiments (and if so what amount)? Or do you adjust the amount of Mg(OH)2 to target a certain starting pH or omega (and if so, why do you have slightly different starting pH / omega values?)

Fig. 3: From the caption to figure 3, the goal is same starting omega. Do you list somewhere how much Mg(OH)2 is added in each case?

Line 219: “Similarly, following Mg(OH)2 additions, ΩA quickly increased to reach 8.6, 9.3 and 9.1 with increasing salinity.” If targeting same omega, why do you have different values? What exactly determined how much Mg(OH)2 was added in each case? Somewhere the amount of Mg(OH)2 added in each case should be listed.

Line 224: “Finally, DIC also decreased upon Mg(OH)2 additions. An initial DIC drop was observed directly after Mg(OH)2 additions of about 60 μmol kg-1 at the lowest salinity and 30 μmol kg-1 at the highest salinity. At a salinity of 28, a much smaller DIC drop was observed in one replicate. After a period of stable DIC conditions, DIC also dropped in a…” Why? What is the physical mechanism?

Line 279: “Such ingassing is also occurring in the other experiments, but is likely hidden by the stronger pHF increase occurring during Mg(OH)2 dissolution.” This doesn't make sense to me; I think you would see it just as well in the high pH case. Can you justify this statement quantitatively?

Line 281: “For salinity, we did not observe major differences in initial dissolution rates within the range of salinities tested, with dissolution rates for salinities 36, 28 and 20 estimated at 391.6 ±2.6, 359.8 ±0.2 and 301.9 ±0.3 μmol of TA mg-1 min-1…” These differences are quite significant: 25% variation!

Line 320: “Here, it could be higher pH levels and hence ΩA that are reached at a particle’s surface as of having a larger diffusive boundary layer.” Why is this true in a direction normal to the grain surface?

Line 381: “… while the second maintains a higher pH around larger particles due to a larger diffusive

boundary layer compared to smaller particles, which increases precipitation rates.” I think this claim needs to be supported with data and/or modeling.