Hydrogen ions are pumped through ATP synthase for the production of ATP in the matrix of the mitochondria.
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It isnt in the matrix. Hydrogen ions are pumped through ATP synthase for the production of ATP in the Electron Transport Chain... even though the Electron Transport Chain is in the matrix of the mitochondria... if you get that general. But its more specifically the Electron Transport Chain. Hope it helps... ik its a little confusing the way i put it.
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not enough detail: you should be talking about the whole process of the electron transport chain, and how H+ ions are accquired in the first place.