In this work, the a priori computational tool for screening ILs, developed in previous part 1, is extended to the simultaneous prediction of a set of IL properties for 45 imidazolium-based ILs. In addition, current part 2 reports the development of a more useful design strategy, which introduces the target IL properties as input, resulting in the selections of counterions as output, that is directly designing ILs on the computer. For this purpose, inverse neural networks are used to estimate the S sigma-profile molecular descriptor of a potential IL solvent by the specification of its required properties, following a reverse quantitative structure-property relationship scheme. Subsequently, a statistical tool based on Euclidean distances is developed to select an adequate set of anion+cation combinations that fulfill the estimated S sigma-profile values, to obtain, in this case, the tailor-made ILs. Finally, the proposed computational tool for designing ILs is applied in liquid-liquid extraction of a system model (toluene/n-heptane). In view of the inherent modular nature of ILs, the proposed methodology is here used in the formulation of IL mixtures to enhance the performance of extractive solvents in the aromatic/aliphatic separation.