## 1 Introduction
In case of carbon, a reduction of zinc oxide can already be carried out at temperatures of at least 1150 \({}^{\circ}\)C. Since the selected process temperature is 1400 \({}^{\circ}\)C, theoretically the overall reduction rate can be increased, as both reactions occur side by side [21]. The conditions at the slag-gas interface provide the requirements for another reduction with an iron compound, as shown in (4). The low partial pressure of zinc at the boundary layer between the slag and the gas phase favors the reduction of ZnO with FeO [6; 19]. \[(\mathrm{ZnO})+2(\mathrm{FeO})=(\mathrm{Fe_{2}O_{3}})+\mathrm{Zn_{(g)}} \tag{4}\]  
The gaseous components rise through the slag layer, and can react with other compounds in the slag. In addition to Zn, which passes almost unhindered through the slag layer and passes into the gaseous phase, the CO serves as an accelerator for the reduction reactions in the process. The rising CO bubbles increase the reaction area in the system as they react with ZnO, as shown in (5). In addition, the CO bubbles cause a stirring effect that entrains iron particles into the slag, and further increase the reaction surface via an additional reduction path [6; 8; 10; 17; 18; 22]. \[(\mathrm{ZnO})+\mathrm{CO_{(g)}}=\mathrm{Zn_{(g)}}+\mathrm{CO_{2}}_{(g)} \tag{5}\]  
In case of reduction reactions with carbon, the Boudouard reaction, as shown in (6), can be added. At the process temperature of 1400 \({}^{\circ}\)C, the equilibrium of the Boudouard reaction is predominantly on the product side and, therefore, favors the production of CO. The crucial point is that the thermodynamically preferential reduction reaction of ZnO with the dissolved carbon in the melt (3) can be described as the sum reaction of (5) and (6). Consequently, the reaction progress and the reduction rate are also related to a fast and efficient expiration of the Boudouard reaction [22; 23; 24]. \[\mathrm{C}\ +\mathrm{CO_{2\ (g)}}=2\mathrm{CO_{(g)}} \tag{6}\]  
To achieve the maximum reduction rate of the Boudoud react, the pressure dependence of this reduction and thus of the entire described reduction system plays a desisive role. According to the principle of [PERSON], the equilibrium of a reaction tends to shift to reduce changes in reaction parameters. In the case of an increase in pressure, the equilibrium prefers the side of lower molar volume, equivalent to the side of less moles of gas. An increased pressure leads to an equilibrium that tends towards the reactants (CO\({}_{2}\) and C). Therefore, at high pressure, higher temperatures are required for the same amount of CO. The lower number of CO bubbles in the system reduces the reaction area in the slag and limits the mixing between slag and melt. Conversely, a decreased pressure favors the production of CO at lower temperatures and, therefore, leads to a system with a higher reduction potential, meaning the Boudouard reaction is the limiting step for the reduction of zinc oxide [7; 17; 18]. To sum up the reduction behavior of ZnO on a carbon-containing iron bath, Figure 1 compares the thermodynamic calculations of zinc oxide interacting with carbon and iron. For this purpose, the Gibbs energies are plotted as a function of temperature. The direct reduction with C shows the lowest reaction enthalpy and, therefore, the greatest driving force for the reduction of ZnO, followed by the reductions with Fe, CO, and FeO. With increasing temperature, all reactions show a decrease in delta G, of which the reaction with C again shows the greatest drop. The reaction products Fe\({}_{2}\)O\({}_{3}\) and FeO remain in the slag and, in the case of FeO, are available for a further reduction of ZnO at the slag-gas interface. At the slag-melt interface, a reduction of ZnO via liquid iron can occur. The reaction product--gaseous zinc--forms bubbles just as CO does, produced during carbothermic reduction. Carbon monoxide can be oxidized again in the slag, forming CO\({}_{2}\) via the reduction of ZnO. The reaction between FeO and ZnO can only arise in areas with very low Zn partial pressure.