We have presented a first-principle theory-based derivation of an exact expression for the solvent number dependent electron-detachment energy of a solvated species in the thermodynamic limit. We also propose a generalized equation bridging the electron detachment energies for small and infinitely large clusters, thus providing a newroute to calculate the ionization potential of a negatively charged ion from the electron-detachment energies of its stable hydrated clusters. Most importantly, it has the ability to predict the instability range of microhydrated anions. The calculated results for the ionization potential for a number of ions are found to be in good agreement with the available experimental results, and the predicted instability range for the doubly charged anions SO₂^{− 4} and C₂O₂⁻⁴ is also consistent with experimental and ab initio results.