General Comments:

In recent years, air pollution is seriously threatening the health of millions of people in China. Sulfate is one of the major chemical species in PM_2.5, and play a critical role in human health, and environmental chemistry. However, its formation in the atmosphere remains controversial. In this study, both observational data (δ³⁴S and δ¹⁸O values) and laboratory simulation are used to constrain SO₂ oxidation pathways. The authors found that the sulfate in PM_2.5 was mainly formed from the oxidation of SO₂ by OH, H₂O₂ and TMI. This work provides a valuable dataset of δ³⁴S and δ¹⁸O that add critical constraints for sulfate formation pathways.

Specific Comments:

1. Page 4, Lines 83-84 The authors mention that the sulfur isotopic fractionation factor of SO₂ oxidation by OH determined with laboratory experiments by Harris et al. (2012) was 1.0087. However, they discussed that “It is reported that sulfur isotope fractionation about SO₂ was -9‰ for homogeneous oxidation process (Tanaka et al., 1994)”. The sulfur isotopic fractionation factor for homogeneous pathway (SO₂+OH) obtained by Tanaka et al. (1994) is different from the laboratory results by Harris et al. (2012). The authors need to compare these two values and explain which to be used for their discussion.

Response: Thanks for Reviewer’s rigorous work. Harris et al. (2012) measured sulfur isotopic fractionation factor (αOH) of SO₂ oxidation by OH radicals, which was from the photolysis of water vapor at 30% relative humidity and 184.9 nm. They found that αOH was negatively correlated to the temperature and described as αOH=(1.0089±0.0007)−((4±5)×10⁻⁵)T (◦C). In the revised manuscript, we cancelled αOH values of SO₂ oxidation by OH, O₃/H₂O₂ and iron catalysis and emphasized their differences of αOH values.

  In contrast, Tanaka et al. (1994) estimated αhom to be 0.991 during homogeneous oxidation of SO₂ by OH radicals by Ab initio calculations using transition state theory. The discrepancy between these two values may be explained by different research methods and/or temperature-dependence of fractionation factor. Generally, sulfate enriched light sulfur isotope (αhom<1) during SO₂ homogeneous oxidation for this process was only related to kinetic fractionation. Therefore, we used αhom=0.991 and αhet=1.0165 to study the contribution of SO₂ heterogeneous and homogeneous oxidation to sulfate in our study.

2. Page 17, lines 345-348 Their calculations displayed that the H₂O₂ pathway is predominated during heterogeneous oxidation of SO₂. Could the authors discuss the sources of H₂O₂ in atmosphere if it plays an important role in heterogeneous oxidation of SO₂?

Response: H₂O₂ production in the relatively clean atmosphere is ascribed to self-reaction of HO₂ radicals that mainly come from the reactions of OH with CO and volatile organic compounds. It is favorable for H₂O₂ formation under the conditions of high O₃ concentration, strong solar irradiation, and high temperature. We have added the sources of H₂O₂ in the revised manuscript.

3. The conclusion seems to be a bit dry. I suggest that the important implications for this work should be added, besides summarize the main points.

Response: This is a constructive suggestion, and we have added the following descriptions in Conclusions in the revised manuscript. Sulfur and oxygen isotopes could be used to gain an insight into sulfate formation. Sulfur isotope compositions in SO₂ and sulfate were simultaneously measured to quantify the contributions of SO₂ homogeneous and heterogeneous oxidation. Combining field observations of oxygen isotope in the atmosphere with the linear relationships of δ¹⁸O values between H₂O and sulfate from different SO₂ oxidation processes can obtain an increased understanding of specific sulfate formation pathways. This study is favorable for deeply investigating sulfur cycle in the atmosphere.

Technical corrections:

4. Page 8, Line 163 Please change “The concentrations of PM_2.5, SO₄^2- and SO₂” to “Variations in concentrations of PM_2.5, SO₄^2- and SO₂”.

Response: Thanks for Reviewer’s suggestion. The sentence has been revised in the manuscript.

5. Page 9, Line 197 Please change “Sulfur isotope compositions in sulfate and SO₂” to “Variations in sulfur isotope compositions in sulfate and SO₂”. In addition, the black solid circles represent the δ³⁴S values of sulfate instead of PM_2.5.

Response: Thanks for Reviewer’s suggestion. The sentence has been revised in the manuscript. The black solid circles represent the δ³⁴S values of sulfate in PM_2.5, we have revised it in Fig.3. 

This manuscript quantifies the sulfate formation pathways from 4 to 22 December 2019 in Nanjing by proposing a new method of simultaneously measuring sulfur and oxygen isotope compositions. The authors conclude that sulfate in PM_2.5 is mainly from a secondary source with SO₂ homogeneously oxidized by OH and heterogeneously oxidized by H₂O₂. Overall, the manuscript is well-written, and the method is reasonable. I have a few points that could be addressed to strengthen the manuscript and some minor comments.

General Comments:

1. The method seems applicable, but the authors need to explain the calculations better. I find it hard sometimes to understand how the result is derived. For example, the authors mentioned that the δ¹⁸O value of primary sulfate is about 38 ‰ in Line 296 before they pointed out it was based on Formula (5). That is confusing. Why there are contribution ranges on each day in Table 1, instead of a single number like in Table 2?

Response: We are grateful for Reviewer’s suggestions. We mentioned that δ¹⁸O value of primary sulfate was about 38‰, which aimed to calculate the contribution of primary and secondary sulfate in the atmosphere. The δ¹⁸O value of 38‰ was cited from the study of Holt and Kumar (1984), and it was not directly from Formula (5). We have added this reference in the revised manuscript.

In addition, we have further explained the calculation method about the contribution of primary and secondary sulfate in PM_2.5 and the ratios of different SO₂ oxidation pathways in the revised manuscript. We calculated the contribution of primary and secondary sulfate according to the equation: δ¹⁸O_PM2.5=δ¹⁸O_PS×(1-f_SS)+δ¹⁸O_SS×f_SS. It is known that secondary sulfate was mainly ascribed to SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂ and Fe³⁺/O₂ in this study. Therefore, δ¹⁸O_SS can be obtained based on the following three equations, respectively.

δ¹⁸O_SS=0.69×δ¹⁸O_water+9.5 ‰ (OH)

δ¹⁸O_SS=0.65×δ¹⁸O_water+10.6 ‰ (Fe³⁺/O₂)           

δ¹⁸O_SS=0.43×δ¹⁸O_water+12.5 ‰ (H₂O₂)

As a result, data ranges about the contribution of primary and secondary sulfate in PM_2.5 are presented in the original manuscript. To keep consistent with the single ratios of SO₂ different oxidation pathways to sulfate in Table 2, we have calculated the average contribution of primary and secondary sulfate on each dayin Table 1 in the revised manuscript.

2. Is it possible to add more data points in Figure 7? It seems three are not robust enough to rerive the linear relationships.

Response: When simulatively studying the linear relationship of δ¹⁸O values between H₂O and sulfate from SO₂ oxidation by H₂O₂ and Fe³⁺/O₂ in the lab, we selected three kinds of representative water including tap-water, lake water and rainwater. The results showed that the slopes of these two linear curves were 0.43 and 0.65, respectively, which can basically reflect the characteristics of SO₂ heterogeneous oxidation mechanisms by H₂O₂ and Fe³⁺/O₂.

We fully agree with the reviewer, and will provide more data points to precisely study the correlation in the following experimental design.

Minor Comments:

3. Line 69: Define RH here instead of in Line 186.

Response: According to Reviewer’s suggestions, we have defined RH as “relative humidity” in Line 68 and deleted “relative humidity” in Line 187 in the revised manuscript.

4. Line 98/320: I did not find references related to Holt et al.

Response: We are very sorry for our negligence. The reference has been added in the revised manuscript.

Holt, B.D. and Kumar R.: Oxygen-18 study of high-temperature air oxidation of SO₂, Atmos. Environ., 18, 2089-2094, https://doi.org/10.1016/0004-6981(84)90194-X, 1984.

5. Line 168-170: I am not sure why high CO is indicative of local emissions. It can be transported by a long range.

Response: As Reviewer said, CO can be transported by a long range due to its stability, and CO is not indicative of local emissions. In the manuscript, the conclusion “High CO concentration indicates that the pollution was mainly from local emissions” was mainly ascribed to the analysis of meteorological conditions. During the sampling period, the wind speed is lower than 3m/s and there is presence of static weather. Therefore, it is hard for CO to transport a long range. We did not explain clearly in the original manuscript, and we have added the analysis of meteorological conditions in the revised one. The detailed description was as “Based on the wind speed is lower than 3m/s and there is presence of static weather during the sampling period, we believed that high CO concentration was mainly from local emissions.”.

6. Line 192: What does the negative -2.9 mean here? Is it possible to have negative values?

Response: Thanks for Reviewer’s suggestion. The negative -2.9 means that the lighter sulfur isotopes were enriched in SO₂. It is common to have negative δ³⁴S values in the samples.

7. Figure 3: Legend of PM_2.5 is wrong. Should be sulfate.

Response: We are very sorry for our cursoriness. The legend in Figure has been revised.

8. Line 249: The average of 51.6% seems just a little higher than 50%. I suggest to say that most of the days (seems 7 out of 11) have more than 50% contributions from heterogeneous oxidation.

Response: Thanks for Reviewer’s suggestion. The sentence in the manuscript has been revised.

Page 11, Line 249-251: It is observed from Fig. 6 that most of the days (7 out of 11) have more than 50% contributions from SO₂ heterogeneous oxidation, which indicated that SO₂ heterogeneous oxidation was generally dominant during sulfate formation.

9. Figure 7: Are the three dots corresponding to three kinds of water? Better to describe it in the texts or figure title.

Response: Thanks for Reviewer’s suggestion. Three dots are corresponding to three kinds of water in Fig.7, and we have made a detailed explanation as “which aims to make clear the relationship of δ¹⁸O values between product sulfate and three kinds of water at 10 ℃” in Line 278 in the text.

10. Line 324: f_SS-OH+ should be f_SS-OH+

Response: Thanks for Reviewer’s suggestion. The formula has been revised in the manuscript.