In Table S1, twenty five well-known EOSs were presented for evaluating the compressibility factor of pure hard spheres. For more information about hard sphere EOSs, the reader is referred to Refs.  and . Dehghani and Modarress  modified a hard sphere EOS and compared the obtained results of their presented EOS with thirteen different hard sphere EOSs and simulation data for single electrolyte solution and hard sphere mixture. Mulero et al.  calculated the compressibility factor of single electrolyte solutions with twenty two hard sphere EOSs and compared their results with six different simulation works and they SB 216763 found no direct relation between accuracy and simplicity or complexity of analytical form of EOS.
2.1.2. Mixtures of hard spheres
To extend the pure hard sphere EOS to the hard sphere mixtures, different mixing rules namely Barrio and Solana , Santos et al. , generalized mixing rules  and etc. were commonly presented. Among the hard sphere EOSs, Carnahan–Starling EOS  and its extension MCSL (Mansoori–Carnahan–Sttarling–Leland)  are the most widely used. This EOS was derived by using an empirical generalization of the exact solution of the Percus–Yevick integral equation as presented by Lebowitz based on scaled particle theory (SPT)  and .