# Generation and Inhibition of SO\({}_{3}\) in Lead Smelting Flue Gas
## 3 Results and Discussion
### Generation of SO\({}_{3}\) in Simulated Lead Smelting Flue Gas
#### 3.1.2 The Effect of Initial SO\({}_{2}\) Content on SO\({}_{3}\) Generation  
Assuming the fixed temperatures of 200 \({}^{\circ}\)C, 400 \({}^{\circ}\)C, 900 \({}^{\circ}\)C, and 1300 \({}^{\circ}\)C, the effects of the initial SO\({}_{2}\) content (0-20% range) on the content of various substances during the final equilibrium of the reaction were studied, as shown in Figure 2.  
As depicted in Figure 2a, the equilibrium SO\({}_{3}\) concentration exhibits a three-stage response to increasing initial SO\({}_{2}\) levels: initial stability, followed by a marked increase and eventual stabilization. When the SO\({}_{2}\) concentration exceeds 7%, SO\({}_{3}\) begins accumulating in the gas phase. This phenomenon arises because the limited moisture content at low temperatures becomes insufficient to sustain sulfuric acid (H\({}_{2}\)SO\({}_{4}\)) formation via SO\({}_{3}\) hydration. At SO\({}_{2}\) concentrations of >15%, SO\({}_{3}\) plateaus at 9.62% due to oxygen depletion, i.e., insufficient O\({}_{2}\) availability, preventing further SO\({}_{2}\)-to-SO\({}_{3}\) oxidation and leading to additional inconsequential SO\({}_{2}\) increases. Figure 2b reveals similar SO\({}_{3}\) trends under 400 \({}^{\circ}\)C conditions. Notably, thermodynamic calculations confirm the absence of liquid H\({}_{2}\)SO\({}_{4}\) across all SO\({}_{2}\) concentrations, with sulfur species existing exclusively as gaseous SO\({}_{3}\), SO\({}_{2}\), and H\({}_{2}\)SO\({}_{4}\) vapor. The initial linear SO\({}_{3}\) increase demonstrates near-complete SO\({}_{2}\) conversion efficiency (up to 15% SO\({}_{2}\)), constrained ultimately by O\({}_{2}\) limitations. Figure 2c,d show analogous SO\({}_{3}\) trends at elevated temperatures. While 1300 \({}^{\circ}\)C conditions suppress SO\({}_{3}\) formation due to thermal instability, a weak positive correlation persists between SO\({}_{2}\) and SO\({}_{3}\) concentrations. This subdued response highlights temperature-dependent reaction kinetics overriding stoichiometric drivers. Key conclusions from the analysis of Figure 2 are as follows: when the temperature is <500 \({}^{\circ}\)C, SO\({}_{2}\) enrichment promotes SO\({}_{3}\) generation until O\({}_{2}\) depletion imposes thermodynamic constraints; the maximum achievable SO\({}_{3}\) concentration is 9.62% (15% SO\({}_{2}\) threshold); and at a temperature >1200 \({}^{\circ}\)C, thermal decomposition dominates, minimizing SO\({}_{3}\) yields despite SO\({}_{2}\) availability, and residual SO\({}_{3}\) shows a weak dependence on initial SO\({}_{2}\) concentrations. 3.1.3. The Effect of Initial O\({}_{2}\) Content on SO\({}_{3}\) Generation  
Assuming the fixed temperatures of 200 \({}^{\circ}\)C, 400 \({}^{\circ}\)C, 900 \({}^{\circ}\)C, and 1300 \({}^{\circ}\)C, the effects of initial O\({}_{2}\) content (0-10% range) on the content of various substances during the final equilibrium of the reaction were studied, as shown in Figure 3.  
According to the thermodynamic analysis results of Figure 2a,b, in the low-temperature region below the thermodynamic decomposition temperature of SO\({}_{3}\) (at approximately 783 \({}^{\circ}\)C), reducing the oxygen concentration in the reaction atmosphere can significantly inhibit SO\({}_{3}\) formation. When the temperature is 400 \({}^{\circ}\)C, and as the volume fraction of O\({}_{2}\) decreases from 5% to 1%, the concentration of SO\({}_{3}\) in the system drops sharply from 8.5% to 1.0%. This phenomenon confirms the crucial regulatory role of oxygen concentration in the oxidation reaction of SO\({}_{2}\)\(\rightarrow\)SO\({}_{3}\): this reaction is essentially an oxygen-dependent process, and the absence of O\({}_{2}\) in the system directly leads to the interruption of the formation pathway of SO\({}_{3}\). The thermodynamic calculation results indicate that, in the ultra-low oxygen range of 0-0.5%, sulfur-containing components mainly stably exist in the form of S\({}_{2}\)(g), which essentially explains the complete inhibition of SO\({}_{2}\) formation at the molecular level.