  The low-temperature picture of dipolar spin ice in terms of the Coulomb fluid
of its fractionalised magnetic monopole excitations has allowed analytic and
conceptual progress far beyond its original microscopic spin description. Here
we develop its thermodynamic treatment as a `magnetolyte', a fluid of singly
and doubly charged monopoles, an analogue of the electrochemical system ${\rm 2
H_2O = H_3O^+ +OH^- = H_4O^{2+} + O^{2-}}$, but with perfect symmetry between
oppositely charged ions. For this lattice magnetolyte, we present an analysis
based on Debye-H\"uckel theory, which is accurate at all temperatures and
incorporates `Dirac strings' imposed by the microscopic ice rule constraints at
the level of Pauling's approximation. Our results are in close agreement with
the specific heat from numerical simulations as well as new experimental
measurements with an improved lattice correction, which we present here, on the
spin ice materials $\mathrm{Ho_2Ti_2O_7}$ and $\mathrm{Dy_2Ti_2O_7}$. Our study
of the magnetolyte shows how electrochemistry can emerge in non-electrical
systems. We also provide new experimental tests of Debye-H\"uckel theory and
its extensions. The application of our results also yields insights into the
electrochemical behaviour of water ice and liquid water, which are closely
related to the spin ice magnetolyte.
