## 4 Discussion  
### Oxygen Isotope Fractionation between CO\({}_{2}\) and Carbonate Minerals  
The oxygen isotope acid fractionation factors (AFFs) between CO\({}_{2}\) and carbonate minerals have been experimentally determined. For example, calcite ([7] modified after [8]; [3,4,9,10]), dolomite [11], ankerite [11], and siderite [11] were reacted at 25 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, 75 \({}^{\circ}\)C, 100 \({}^{\circ}\)C, and 150 \({}^{\circ}\)C (Table 2). The oxygen isotope fractionation factors between the CO\({}_{2}\) and carbonate minerals were theoretically determined (Figure 3). The magnitude of the fractionation factor appeared to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Carbonate** & **Temperature** & **AFF (\(\alpha\))** & **Reference** \\ \hline Calcite & 25 \({}^{\circ}\)C & 1.01025 & [7] \\ Calcite & 25 \({}^{\circ}\)C & 1.01025 & [3] \\ Calcite & 25 \({}^{\circ}\)C & 1.01025 & [4] \\ Calcite & 25 \({}^{\circ}\)C & 1.01025 & [9] \\ Calcite & 25 \({}^{\circ}\)C & 1.01030 & [10] \\ Calcite & 50 \({}^{\circ}\)C & 1.00924 & [9] \\ Calcite & 50 \({}^{\circ}\)C & 1.00937 & [10] \\ Calcite & 75 \({}^{\circ}\)C & 1.00853 & [9] \\ Calcite & 75 \({}^{\circ}\)C & 1.00856 & [10] \\ Dolomite & 100 \({}^{\circ}\)C & 1.00913 & [11] \\ Ankerite & 100 \({}^{\circ}\)C & 1.00901 & [11] \\ Siderite & 100 \({}^{\circ}\)C & 1.00881 & [11] \\ Siderite & 150 \({}^{\circ}\)C & 1.00771 & [11] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimentally determined oxygen isotope acid fractionation factors (AFFs) between CO\({}_{2}\) and carbonate minerals. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run No.** & **T (\({}^{\circ}\)C)** & **Reaction Time** & **\(\mathbf{\delta^{13}C_{PDB}}\) (\%)** & **\(\mathbf{\delta^{18}O_{SMOW}}\) (\%)** \\ \hline
31089 & 100 & 1 h & 2.51 & 23.71 \\
31072 & 120 & 1 h & 2.57 & 23.44 \\
31091 & 120 & 1 h & 2.52 & 23.50 \\
31074 & 150 & 1 h & 2.56 & 23.03 \\
31075 & 150 & 1 h & 2.55 & 23.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: Temperature dependence of the \(\delta^{18}\)O values of the CO\({}_{2}\) evolved from the CaCO\({}_{3}\)-1.  
be ordered depending on the type of carbonate minerals over a wide temperature range. A maximum value was commonly found in each CO\({}_{2}\)-carbonate dataset at low temperatures. Comparing several carbonate minerals in Figure 3, the fractionation factors appear to depend on the size of the carbonate crystal lattice. The isotope fractionations were primarily attributed to the effect of differences in the cation radius of the parent carbonate during bond fission [12]. The carbonates of intermediate chemical composition, particularly dolomite (CaCO\({}_{3}\)-MgCO\({}_{3}\) group minerals), can be considered to behave, to a first approximation, as ideal mixtures of calcite and magnetite [12]. [PERSON] and [PERSON] [13] concluded that the oxygen isotope-reduced partition function ratios correlate well with the ionic radius of the cation in the carbonate and the reduced mass of the carbonate molecule. However, neither parameter by itself can be used as a precise predictor of the fractionation factors [13]. Oxygen Isotope Acid Fractionation between CO\({}_{2}\) and Calcite at Low-to-Intermediate Temperatures  
The oxygen isotope acid fractionation factors (AFFs) between CO\({}_{2}\) and calcite between 1 \({}^{\circ}\)C and 150 \({}^{\circ}\)C obtained in this study are listed in Table 3. No intense experimental isotope fractionation factors have been obtained between 1 \({}^{\circ}\)C and 150 \({}^{\circ}\)C to date. Notably, the fractionation factor at each temperature was calculated using the \(\delta\)18O value of CO\({}_{2}\) (Table 3) and the \(\delta\)18O value of CaCO\({}_{3}\)-1 calcite (15.45%).