Molecular Communication (MC) is a promising bio-inspired paradigm in which molecules are transmitted, propagated and received between nanoscale machines. One of the main challenges is the theoretical study of the maximum achievable information rate (capacity). The objective of this paper is to provide a mathematical expression for the capacity in MC nanonetworks when the propagation of the information relies on the free diffusion of molecules. Solutions from statistical mechanics and thermodynamics are used to derive a closed-form expression for the capacity as function of physical parameters, such as the size of the system, the temperature and the number of molecules as well as of the bandwidth of the system and the transmitted power. An extremely high order of magnitude of the capacity numerical values demonstrates the enormous potential of the diffusion-based MC systems.