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The proton motive force arises from a combination of the concentration gradient of protons and a voltage gradient across the membrane (the protons are positively charged, so an imbalance of protons means that the side of the membrane with more protons has a positive charge relative to the side with fewer protons).
In biological processes the direction an ion will move by diffusion or active transport across membrane is determined by the electrochemical gradient. In mitochondria and chloroplasts, proton gradients are used to generate a chemiosmotic potential that is also known as a proton motive force.