Explain how a concentration gradient, a membrane protein, and hydrogen ions work together to provide a mitochondrion with the energy needed to join small molecules together?

During the electron transport, chan energy stored in electrons is used to pump hydrogen protons from the mitochondrial matrix to the intermembrane space. The numbers of protons increase this creates a chemical gradient(because there is a higher concentration of ions) and an electrical gradient(because the intermembrane space becomes more positive than the matrix because of the protons-H⁺). Those protons need to flow towards the matrix for equilibrium to occur. As we know the inside membrane of the mitochondria has a reduced permeability. The main place where protons can diffuse is the ATP-synthase(a protein that turns ADP and inorganic phosphate into ATP). When protons pass through they release the energy necessary for this reaction to occur(ADP+H₃PO₄-->ATP+H₂O)