in what named process and under what environment conditions would a mesophyll cell of a flowering plant give out oxygen

Gas exchange happens in the spongy mesophyll tissue of the leaf. Spongy mesophyll cells are covered by a thin layer of water and loosely packed. When the plant is photosynthesising during the day, these features allow carbon dioxide to diffuse into the spongy mesophyll cells, and oxygen to diffuse out of it.

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