In order to understand the physics behind the strange behaviors of materials at nano-scale, one of the most important factors is to investigate their extreme activity in different environments. This information comes directly from the cohesion (binding) energy of materials. In this report, we first review a simple thermodynamic-based theory for size dependence feature of total cohesion energy of metallic nano-particles. Then, regarding the size dependency of cohesion energy, simple theory for size dependency of enthalpy and Gibbs free energy formation of metallic nano-particles is developed. Moreover, to describe the relative activity of metallic nano-particles, hypothesis through the modified classical physico-chemical formalism of activity in a reactive medium will be presented. Series of computations for size dependency of relative activity (via relative reaction constant: nano/macro) for Zn, Al, Ag, Ga and W nano-particles in a reactive solution will be presented. Our computational results show that by decreasing the size of the particles less than 100 nm, the equilibrium reaction constant and consequently the relative activity of particles increases, which confirms the tendency observed in experiments so far. The suggested concept of size dependence reaction constant provides a quantitative scale for studying the reactions contain nano-particles.

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