Static and dynamic laser light scattering techniques are used to monitor the slow self-assembly of 2.5-nm-diameter, hollow spherical, fully hydrophilic heteropolyoxometalate {Mo72Fe30} macro-ions into single-layer vesicle-like "blackberries" (averaging similar to 50-60 nm in diameter) in dilute salt-free and salt-containing aqueous solutions, to obtain the thermodynamic properties of the unique self-assembly. A very high activation energy is observed during the transition from the single ion (general solute state) to blackberries (so-called "second solute state"), which might be responsible for the interestingly slow self-assembly process in dilute solutions. The thermodynamic parameters of the blackberry formation can be affected by adding simple electrolytes into the solution, because the electrostatic interactions are responsible for the unique self-assembly, and the effects of various anions and cations (in the low salt concentration regimes) are discussed. Multivalent anions make the single {Mo72Fe30} macro-ions more stable and make the blackberry formation more difficult. Small cations carrying more charges tend to accelerate the self-assembly process. This is the first study on the thermodynamic properties of the novel self-assembly in dilute solutions and the equilibrium and transition between the two solute states of macro-ions in solution.