## 3 Results  
The temporal progression of ZnO in the slag, relative to the carbon content in the metal bath, is shown in Figure 3. An increased carbon concentration in the molten iron led to a faster decrease in ZnO in the first six minutes of the test. Additionally, the tests with higher C content in the metal bath showed an earlier formation of a plateau in the trend line. The level of the equilibrium concentration was in a similar range for the experiments with 2.16% C, 2.89% C, and 4.15% C (\(\sim\)2% ZnO). The trial with the lowest carbon concentration in the molten iron showed higher ZnO content after 15 min of process time. Therefore the 15-minute test with a C content of 0.85% could not be used for the analysis of the reaction kinetics, because of unrepresentative conditions during the trial. Furthermore, the tests with 0.85% carbon have limited significance. Considering the iron-carbon diagram, an iron alloy with 0.85% carbon content is not fully liquid at a temperature of 1400 \({}^{\circ}\)C. Although the iron alloy used for the experiment contains some alloying elements, which reduce the melting point (carbon equivalent = 1.15%), it is still present in the 2-phase liquid/solid area. Therefore, the transfer of carbon into the slag is limited. With decreasing carbon content during the reduction of ZnO, the liquidus temperature increases and the proportion of the solid phase rises further. Based on these facts, the test trials using the iron alloy with a carbon content of 0.85% can only be considered in a limited manner. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & & \\ \hline
**Compound** & **MgO** & **Al2O3** & **SiO2** & **CaO** \\ \hline wt-\% & 0.42 & 15.57 & 42.29 & 41.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of the synthetic slag. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & & \\ \hline
**Compound** & **FeO** & **Al2O3** & **SiO2** & **ZnO** & **PbO** & **CaO** \\ \hline wt-\% & 2.17 & 0.68 & 0.21 & 89.16 & 5.96 & 1.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chemical composition of the zinc oxide. For better illustration of the influence of the carbon concentration in the molten iron on the reaction of ZnO, the reduction rate was calculated from the experimental data. The trend lines correspond to a first-order reaction equation fitting the experimental data. The first-order reaction equation is shown in (7); the derivative, shown in (8), allows the calculation of the reaction rate [24,25]. \[\left[\text{ZnO}\right]_{\text{(t)}}=\left[\text{ZnO}\right]_{\text{(0)}}- \text{A}+\text{A}\times\text{e}^{-\text{kt}} \tag{7}\]  
\[\text{r}_{\text{(t)}}=-\frac{\text{d}\left[\text{ZnO}\right]_{\text{(t)}}}{ \text{dt}} \tag{8}\]  
\(\left[\text{ZnO}\right]_{\text{(0)}}\): ZnO content in the slag at time t (%);  
\(\left[\text{ZnO}\right]_{\text{(0)}}\): Initial ZnO content in the slag (%);  
A: Reaction constant (%);  
k: Reaction constant (min\({}^{-1}\));  
t: Time (min);  
r\({}_{\text{(t)}}\): Reaction rate at time t (%/min). The different concentration trends of ZnO in the slag resulted in various reaction rates, depending on the carbon concentration in the metal bath. The mathematical descriptions of the trend lines and the reaction rates calculated are shown in Table 4.  
Figure 3: Changes in the zinc oxide content of the slag. Plotting the reaction rate against the ZnO concentration in the slag results in the curves shown in Figure 4. The different graphs represent the various carbon concentrations in the molten iron. The reaction rates at the beginning of the tests are strongly dependent on the initial concentration of C in the metal bath. At 10% ZnO in the slag, the experiment using the iron bath with 4.15% carbon shows a reaction rate more than four times higher than that with 0.85% carbon. The low reactivity can be justified by the high melting point of an iron alloy with 0.85% carbon.