How does chemiosmotic coupling work?

Chemiosmotic coupling is the process that connects the movement of electrons through the electron transport chain to the production of ATP by utilizing the proton gradient established across a membrane. The stored energy in this proton gradient comes from two sources: chemical potential energy, due to the concentration difference of protons across the membrane, and electrical potential energy, resulting from the charge difference between the mitochondrial matrix (negative) and the intermembrane space (positive). ATP synthase utilizes the energy stored in the proton gradient to synthesize ATP from ADP and inorganic phosphate (Pi). As protons flow back into the mitochondrial matrix through ATP synthase, the enzyme undergoes conformational changes that harness this energy to drive the phosphorylation of ADP to ATP. Overall, ATP synthesis (which requires energy and is not naturally favorable) is made possible by coupling the energy released from the movement of protons across a membrane, which is a naturally favorable process.