First, it is important to note that a concentration gradient of H+ ions is generated between the matrix of the mitochrondria and the inter-membrane space. This is because H+ ion pumps pump H+ ions from the matrix to the intermembrane space. This is using the energy released by the electrons as they travel through the electron transport chain. In aerobic respiration, chemiosmosis is the process where H+ ions diffuse from the intermembrane space of the mitochondrion to the matrix, through the ATP synthase in the inner mitochondrial membrane. This diffusion is possible because the earlier mentioned concentration gradient of H+ ions between the matrix of the mitochrondria and the inter-membrane space. The kinetic energy released by the movement of H+ ions by diffusion is used to phosphorylate ADP, to produce ATP.