## 3 Solved Example
### Design  
As experimenters, we were interested in investigating the factors affecting the leaching of Mo from waste CIGS solar cells. According to the leaching theory, many factors can affect the leaching efficiency, with the most common of them being (i) the leaching time, (ii) the type and concentration of leaching agent, (iii) the leaching temperature, (iv) the solid to liquid ratio (i.e., sample mass to leaching solution volume), (v) the particle size, and (vi) the type and speed of agitation [34]. Since there is currently no available literature on the leaching of Mo from solar cells, we considered it necessary to perform a factorial experiment, in order to investigate the significance of as many factors as possible, before continuing with other experiments. Therefore, five factors were chosen as our design factors: the leaching temperature (A), the presence of a tartrate salt in the leaching solution (B), the pH of the leaching solution (C), A/L (D), and the leaching time (E). Except for temperature (A) and time (E), the selection of which as design factors is expectable, the reasons behind the selection of factors B, C, and D as design factors were the following: The pH of the solution (C) is actually a measure of the concentration of the leaching agent (NaOH in this case). The surface to liquid ratio (D) was used instead of the solid to liquid ratio for our experiment, since the elements of interest were present in the solar cell in the form of very thin films (from nm to 3 \(\upmu\)m) deposited on a stainless-steel substrate and, thus, any mass measurement would mainly reflect the mass of the substrate of the cell and not of the leached films. Finally, regarding factor (B), it is known that tartrate ions can react with Mo (VI) [35; 36; 37], thus, their presence in the solution could potentially assist the Mo leaching. It is worth mentioning that the factor agitation was decided not to be taken into account, since it is usually of importance for free particles, which was not the case for our experiments (i.e., thin films deposited on a stainless-steel substrate). The levels of the factors were decided to be the ones indicated in Table 1. These levels were chosen by taking sustainability, chemistry, and technical aspects of potential future scale-up of the process into account. More specifically, factor A was kept between 30 and 50 \({}^{\circ}\)C, because, on one hand, higher temperatures usually accelerate the reaction rates [34], but, on the other hand, they are more energy-consuming, which was not desirable. Factor B was a qualitative factor and its minimum level L1 indicated the absence of the tartrate salt, while its maximum level L2 indicated the presence of the tartrate salt. The concentration of the salt was the same for all runs in which the salt was present, at about 0.25 M, sufficient for reactions with Mo (present at ppm levels in the leachate). The pH of the solution, i.e., factor C, ranged between 10 and 12, in order to create an alkaline environment, recommended for the leaching of Mo [38], without, at the same time, consuming very high amounts of chemicals. The A/L, i.e., factor D, was kept between 1/6 and 1/3 cm\({}^{2}\)/mL, since this range could guarantee that in case of future scale-up of the process, the solution volume would be high enough to allow the use of a conventional stirrer, while ensuring that the solution volume is not too high to render proper agitation difficult. Finally, preliminary leaching experiments performed in the past in our group using the specific type of solar cells at temperatures close to ambient had shown that the reactions needed a few hours to reach equilibrium (thus, the lower limit of 8 h was chosen); however, leaching times longer than 24 h would not make sense for industrial applications. The experiment was to be conducted in the following way: For each of the runs, the desired amount of leaching solution would be poured into a plastic container and the container would then be placed into a shaking water bath for the indicated leaching time.