During the process of respiration and photosynthesis implants i was what are the three primary elements that cycle between the mitochondria and the chloroplast

Those are glucose, oxygen and carbon dioxide (CO2).
Respiration and photosynthesis are opposite processes in the plant cell. Photosynthesis makes the glucose and releases oxygen and they are used in cellular respiration to make ATP. The glucose is broken down during the respiration into CO2, which is used in photosynthesis. While H2O is broken down to form oxygen during photosynthesis, in cellular respiration oxygen is combined with hydrogen to form H2O. 

Photo means light and synthesis means combination so combination of light