Explain how an electrochemical gradient is formed in the mitochondria, and how this gradient is used to synthesise ATP.

At the first proton pump and associated electron carrier of the inner mitochondrial membrane reduced NAD releases two H⁺ ions and two electrons. An electron travels down a series of electron carriers, each with a higher affinity for the electron. At each transfer, energy is released. This energy is used by the proton pumps to actively transport H⁺ ions from the mitochondrial matrix, across the inner mitochondrial membrane, and into the intermembrane space against their concentration gradient. H⁺ ions accumulate in the intermembrane space of the mitochondria, forming an electrochemical gradient.
The only route for the H⁺ ions to return to the mitochondrial matrix is via the proton channel of the ATP-synthetase complex. H⁺ ions diffuse passively from the intermembrane space, across the inner mitochondrial membrane, and into the mitochondrial matrix. This flow of protons provides the energy required for the ATP synthetase enzyme to convert ADP and Pi (inorganic phosphate) into ATP.