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Why must the inner mitochondrial membrane be difficult for protons to cross?

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Fluorescent confocal image of HeLa cells with green microtubules outlining cell shapes, red mitochondria, and blue nuclei. — mitochondrion Mitochondria (red) are found throughout the cytoplasm of almost all eukaryotic cells (cell nucleus is shown in blue; cytoskeleton is shown in yellow).

The inner mitochondrial membrane must be difficult for protons to cross because it is essential for maintaining a closed space that supports the chemiosmotic theory.

During cellular respiration, the electron transport chain pumps protons from the mitochondrial matrix into the intermembrane space, creating an electrochemical gradient across the membrane. If the inner membrane were permeable to protons, they would simply flow back into the matrix, dissipating this gradient and preventing the storage of energy.12

By remaining impermeable to protons, the membrane forces them to return to the matrix through a specific enzyme complex, ATP synthase. As protons move through this enzyme's pore, the energy released from the gradient is harnessed to convert ADP and inorganic phosphate into ATP. Essentially, the membrane's impermeability allows the mitochondrion to convert chemical energy from food into an electrical potential that fuels the production of life-sustaining energy.12