In mitochondria, ATP synthesizing chemical reaction take place in the

Mitochondria are double-membrane organelles where the inner membrane serves as the primary site for ATP generation [2]. This membrane is folded into structures called cristae, which significantly increase the surface area available for chemical reactions [2]. The process of oxidative phosphorylation, the final stage of aerobic respiration, is catalyzed by the F1Fo-ATP synthase enzyme complex [4]. This complex is specifically localized within the inner mitochondrial membrane [3]. While the F1 domain of the ATP synthase protrudes into the mitochondrial matrix, the proton gradient that drives the synthesis is maintained across the inner membrane [5]. The outer membrane, by contrast, is highly permeable and does not host the ATP synthesis machinery [2]. Thus, the chemical reaction that synthesizes ATP from ADP and inorganic phosphate occurs at the inner membrane interface.

Sources

1. [2] https://pmc.ncbi.nlm.nih.gov/articles/PMC7877222/
2. [4] https://pmc.ncbi.nlm.nih.gov/articles/PMC3278611/
3. [3] https://www.sciencedirect.com/science/article/abs/pii/S1937644808006011
4. [5] https://www.khanacademy.org/science/ap-biology/cellular-energetics/cellular-respiration-ap/a/oxidative-phosphorylation-etc