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A new equation of state relating the macroscopic quadrupole moment density$Q$ to the gradient of the field $\nabla E$ in an isotropic fluid is derived:$Q = \alpha_Q(\nabla E - U \nabla.E/3)$, where the quadrupolarizability$\alpha_Q$ is proportional to the squared molecular quadrupole moment. Usingthis equation of state, a generalized expression for the Born energy of an iondissolved in quadrupolar solvent is obtained. It turns out that the potentialand the energy of a point charge in a quadrupolar medium are finite. From theobtained Born energy, the partial molar volume and the partial molar entropy ofa dissolved ion follow. Both are compared to experimental data for a largenumber of simple ions in aqueous solutions. From the comparison the value ofthe quadrupolar length $L_Q$ is determined, $L_Q = \sqrt{\alpha_Q/3\epsilon}=1-2 {\AA}$. Further, the extended Debye-H\"uckel model is generalized to ionsin a quadrupolar solvent. If quadrupole terms are allowed in the macroscopicCoulomb law, they result in suppression of the gradient of the electric field.In result, the electric double layer is slightly expanded. The activitycoefficients obtained within this model involve three characteristic lengths:Debye length, ion radius and quadrupolar length $L_Q$. Comparison toexperimental data shows that minimal distance between ions is equal to the sumof their bare ion radii; the concept for ion hydration as an obstacle for ionsto come into contact is not needed for the understanding of the experimentaldata.

Quadrupole terms in the Maxwell equations: Born energy, partial molar  volume and entropy of ions. Debye-H\"uckel theory in a quadrupolarizable  medium