  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. Using
this equation of state, a generalized expression for the Born energy of an ion
dissolved in quadrupolar solvent is obtained. It turns out that the potential
and the energy of a point charge in a quadrupolar medium are finite. From the
obtained Born energy, the partial molar volume and the partial molar entropy of
a dissolved ion follow. Both are compared to experimental data for a large
number of simple ions in aqueous solutions. From the comparison the value of
the 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 ions
in a quadrupolar solvent. If quadrupole terms are allowed in the macroscopic
Coulomb law, they result in suppression of the gradient of the electric field.
In result, the electric double layer is slightly expanded. The activity
coefficients obtained within this model involve three characteristic lengths:
Debye length, ion radius and quadrupolar length $L_Q$. Comparison to
experimental data shows that minimal distance between ions is equal to the sum
of their bare ion radii; the concept for ion hydration as an obstacle for ions
to come into contact is not needed for the understanding of the experimental
data.
