What is the chemiosmotic gradient and how does it affect ATP?

Basically, the membranes in a mitochondrion set up and maintain a chemiosmotic gradient - where there is a high concentration of an ion (hydrogen) on one side, and a low concentration on the other. Because things always want to diffuse from an area of high concentraion to an area of low concentration, the area of high concentration has potential energy. The mitochondrion membranes have structures that allow the hydrogen ions to move down their concentration gradient, but in doing so harvest their energy to make ATP.